The image above represents the true stress.

To compute for the true stress, two essential parameters are needed and these parameters are **force (F)** and **instantaneous area (A _{i})**.

The formula for calculating true stress:

σ_{T} = ^{F} / _{Ai}

Where;

_{T} = True Stress

F = Force

A_{i} = Instantaneous Area

Let’s solve an example;

Find the true stress when the instantaneous area is 60 with a force of 25.

This implies that;

F = Force = 25

A_{i} = Instantaneous Area = 60

σ_{T} = ^{F} / _{Ai}

σ_{T} = ^{25} / _{60}

σ_{T} = 0.416

Therefore, the **true stress** is **0.416 Pa**.

**Calculating the Force when True Stress and Instantaneous Area is Given.**

F = A_{i} x σ_{T}

Where;

F = Force

σ_{T} = True Stress

A_{i} = Instantaneous Area

Let’s solve an example;

Find the force when the instantaneous area is 30 with a true stress of 15.

This implies that;

σ_{T} = True Stress = 15

A_{i} = Instantaneous Area = 30

F = A_{i} x σ_{T}

F = 30 x 15

F = 450

Therefore, the **force** is **450.**

**Calculating the Instantaneous Area when True Stress and Force is Given.**

A_{i} = ^{F} / _{σT}

Where;

A_{i} = Instantaneous Area

F = Force

σ_{T} = True Stress

Let’s solve an example;

Find the instantaneous area when the force is 440 with a true stress of 22.

This implies that;

σ_{T} = True Stress = 22

F = Force = 440

A_{i} = ^{F} / _{σT}

A_{i} = ^{440} / _{22}

A_{i} = 20

Therefore, the **instantaneous area** is **20**.

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the true stress.

To get the answer and workings of the true stress using the **Nickzom Calculator – The Calculator Encyclopedia. **First, you need to obtain the app.

You can get this app via any of these means:

**Web** – https://www.nickzom.org/calculator-plus

To get access to the **professional **version via web, you need to **register** and **subscribe **for** NGN 1,500 **per** annum** to have utter access to all functionalities.

You can also try the **demo **version via https://www.nickzom.org/calculator

**Android (Paid)** – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator

**Android (Free)** – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator

**Apple (Paid)** – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8

Once, you have obtained the calculator encyclopedia app, proceed to the **Calculator Map, **then click on **Material & Metallurgical **under **Engineering**

Now, Click on **Mechanical Properties **under **Material & Metallurgical**

Click on **True Stress**** **under **Material & Metallurgical**

The screenshot below displays the page or activity to enter your value, to get the answer for the true stress according to the respective parameter which are the **force (F)** and **instantaneous area (A _{i})**.

Now, enter the value appropriately and accordingly for the parameter as required by the **force (F) **is **25**** **and **instantaneous area (A _{i}) **is

Finally, Click on Calculate

As you can see from the screenshot above, **Nickzom Calculator** – The Calculator Encyclopedia solves for the true stress and presents the formula, workings and steps too.

The image above represents the maximum velocity to avoid overturning of a vehicle moving along a level circular path.

To compute for the maximum velocity, four essential parameters are needed and these parameters are **Acceleration due to Gravity (g), Height of Centre of Gravity of the Vehicle from Ground Level (h), Radius of Circular Path (r) and Half of the Distance between the Centre Lines of the Wheel (a).**

The formula for calculating the maximum velocity:

v_{max} = √(^{gra} / _{h})

Where:

v_{max} = Maximum Velocity to avoid Overturning of a Vehicle moving along a Level Circular Path

g = Acceleration due to Gravity

h = Height of Centre of Gravity of the Vehicle from Ground Level

r = Radius of Circular Path

a = Half of the Distance between the Centre Lines of the Wheel

Let’s solve an example;

Find the maximum velocity when the Acceleration due to Gravity (g) is 10.2, Height of Centre of Gravity of the Vehicle from Ground Level (h) is 14, Radius of Circular Path (r) is 22 and Half of the Distance between the Centre Lines of the Wheel (a) is 32.

This implies that;

g = Acceleration due to Gravity = 10.2

h = Height of Centre of Gravity of the Vehicle from Ground Level = 14

r = Radius of Circular Path = 22

a = Half of the Distance between the Centre Lines of the Wheel = 32

v_{max} = √(^{gra} / _{h})

v_{max} = √(^{(10.2)(22)(32)}/_{14})

v_{max} = √(^{(7180.79)}/_{14})

v_{max} = √(512.91)

v_{max} = 22.647

Therefore, the **maximum velocity to avoid Overturning of a Vehicle moving along a Level Circular Path** is **22.647 m/s.**

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the maximum velocity to avoid overturning of a vehicle moving along a level circular path.

To get the answer and workings of the maximum velocity to avoid overturning of a vehicle moving along a level circular path using the **Nickzom Calculator – The Calculator Encyclopedia. **First, you need to obtain the app.

You can get this app via any of these means:

**Web** – https://www.nickzom.org/calculator-plus

To get access to the **professional **version via web, you need to **register** and **subscribe **for** NGN 1,500 **per** annum** to have utter access to all functionalities.

You can also try the **demo **version via https://www.nickzom.org/calculator

**Android (Paid)** – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator

**Android (Free)** – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator

**Apple (Paid)** – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8

Once, you have obtained the calculator encyclopedia app, proceed to the **Calculator Map, **then click on **Mechanics **under **Engineering**

Now, Click on **Motion of Circular Path **under **Mechanics**

Click on **M****aximum Velocity to avoid overturning of a vehicle moving along a level circular path**** **under **Motion of Circular Path**

The screenshot below displays the page or activity to enter your value, to get the answer for the maximum velocity to avoid overturning of a vehicle moving along a level circular path according to the respective parameter which are the **Acceleration due to Gravity (g), Height of Centre of Gravity of the Vehicle from Ground Level (h), Radius of Circular Path (r) and Half of the Distance between the Centre Lines of the Wheel (a).**

Now, enter the value appropriately and accordingly for the parameter as required by the** Acceleration due to Gravity (g)** is **10.2**,** Height of Centre of Gravity of the Vehicle from Ground Level (h)** is **14**,** Radius of Circular Path (r)** is **22**** and Half of the Distance between the Centre Lines of the Wheel (a)** is **32**.

Finally, Click on Calculate

As you can see from the screenshot above, **Nickzom Calculator** – The Calculator Encyclopedia solves for the maximum velocity to avoid overturning of a vehicle moving along a level circular path and presents the formula, workings and steps too.

The image represents reaction at the inner wheel of a vehicle moving along a level circular path.

To compute for the reaction, six essential parameters are needed and these parameters are **Mass of the Vechicle (m), Acceleration due to Gravity (g), Velocity of the Vehicle (v), Height of Centre of Gravity of the Vehicle from Ground Level (h), Radius of Circular Path (r) and Half of the Distance between the Centre Lines of the Wheel (a).**

The formula for calculating the reaction at the inner wheel of a vehicle moving along a level circular path:

R_{A} = ^{mg} / _{2}[1 – ^{v²h} / _{gra}]

Where:

R_{A} = Reaction at the Inner Wheel of a Vehicle moving along a Level Circular Path

m = Mass of the Vechicle

g = Acceleration due to Gravity

v = Velocity of the Vehicle

h = Height of Centre of Gravity of the Vehicle from Ground Level

r = Radius of Circular Path

a = Half of the Distance between the Centre Lines of the Wheel

Let’s solve an example;

Find the reaction when Mass of the Vechicle (m) is 13, Acceleration due to Gravity (g) is 9.8, Velocity of the Vehicle (v) is 11, Height of Centre of Gravity of the Vehicle from Ground Level (h) is 5, Radius of Circular Path (r) is 7 and Half of the Distance between the Centre Lines of the Wheel (a) is 3.

This implies that;

m = Mass of the Vechicle = 13

g = Acceleration due to Gravity = 9.8

v = Velocity of the Vehicle = 11

h = Height of Centre of Gravity of the Vehicle from Ground Level = 5

r = Radius of Circular Path = 7

a = Half of the Distance between the Centre Lines of the Wheel = 3

R_{A} = ^{mg} / _{2}[1 – ^{v²h} / _{gra}]

RA = ^{13(9.8)} / _{2}[1 – ^{(11)²(5)} / _{(9.8)(7)(3)}]

RA = ^{127.4} / _{2}[1 – ^{(121)(5)} / _{205.8}]

RA = 63.7[1 – ^{605} / _{205.8}]

RA = 63.7[1 – 2.939]

RA = 63.7[-1.939]

RA = -123.56

Therefore, the **reaction at the inner wheel of a vehicle moving along a level of circular path** is **-123.56 N.**

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the reaction of the inner wheel of a vehicle moving along a level circular path.

To get the answer and workings of the reaction of the inner wheel of a vehicle moving along a level circular path using the **Nickzom Calculator – The Calculator Encyclopedia. **First, you need to obtain the app.

You can get this app via any of these means:

**Web** – https://www.nickzom.org/calculator-plus

To get access to the **professional **version via web, you need to **register** and **subscribe **for** NGN 1,500 **per** annum** to have utter access to all functionalities.

You can also try the **demo **version via https://www.nickzom.org/calculator

**Android (Paid)** – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator

**Android (Free)** – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator

**Apple (Paid)** – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8

Once, you have obtained the calculator encyclopedia app, proceed to the **Calculator Map, **then click on **Mechanics **under **Engineering**

Now, Click on **Motion of Circular Path **under **Mechanics**

Click on **Reaction of the inner wheel of a vehicle moving along a level circular path**** **under **Motion of Circular Path**

The screenshot below displays the page or activity to enter your value, to get the answer for the reaction of the inner wheel of a vehicle moving along a level circular path according to the respective parameter which are the **Mass of the Vechicle (m), Acceleration due to Gravity (g), Velocity of the Vehicle (v), Height of Centre of Gravity of the Vehicle from Ground Level (h), Radius of Circular Path (r) and Half of the Distance between the Centre Lines of the Wheel (a).**

Now, enter the value appropriately and accordingly for the parameter as required by the **Mass of the Vechicle (m)** is **13**, **Acceleration due to Gravity (g)** is **9.8**, **Velocity of the Vehicle (v)** is **11**, **Height of Centre of Gravity of the Vehicle from Ground Level (h)** is **5**, **Radius of Circular Path (r)** is **7** and **Half of the Di****stance between the Centre Lines of the Wheel (a)** is **3**.

Finally, Click on Calculate

As you can see from the screenshot above, **Nickzom Calculator** – The Calculator Encyclopedia solves for the reaction of the inner wheel of a vehicle moving along a level circular path and presents the formula, workings and steps too.

The image represents road bank angle in circular motion.

To compute for the road bank angle, three essential parameters are needed and these parameters are **velocity (v), acceleration due to gravity (g) and radius (r).**

The formula for calculating the road bank angle;

θ = tan^{-1}(^{v²} / _{gr})

Where;

θ = Road Bank Angle

v = Velocity

g = Acceleration due to Gravity

r = Radius

Let’s solve an example;

Find the road bank angle where the acceleration due to gravity is 9.8, velocity is 35 and radius is 18.

This implies that;

v = Velocity = 35

g = Acceleration due to Gravity = 9.8

r = Radius = 18

θ = tan^{-1}(^{v²} / _{gr})

θ = tan^{-1}(^{35²} / _{(9.8)(18)})

θ = tan^{-1}(^{1225} / _{176.4})

θ = tan^{-1}(6.94)

θ = 81.81°

Therefore, the **road bank angle** is **81.81°.**

**Calculating the Velocity when Road Bank Angle, Acceleration due to Gravity and Radius is Given.**

v = √gr.tan θ

Where;

v = Velocity

θ = Road Bank Angle

g = Acceleration due to Gravity

r = Radius

Let’s solve an example;

Given that the road bank angle is 50, radius is 15 and acceleration due to gravity is 9.8. Find the velocity?

This implies that;

θ = Road Bank Angle = 50

g = Acceleration due to Gravity = 9.8

r = Radius = 15

v = √gr.tan θ

v = √(9.8 x 15)(tan 50)

v = √(147)(1.1917)

v = √175.1799

v = 13.235

Therefore, the **velocity** is **13.235.**

**Calculating the Radius when Road Bank Angle, Acceleration due to Gravity and Velocity is Given.**

r = ^{v2} / _{g.tanθ}

Where;

r = Radius

θ = Road Bank Angle

v = Velocity

g = Acceleration due to Gravity

Let’s solve an example;

Given that the road bank angle is 70, velocity is 30 and acceleration due to gravity is 9.8. Find the radius?

This implies that;

θ = Road Bank Angle = 70

g = Acceleration due to Gravity = 9.8

v = Velocity = 30

r = ^{v2} / _{g.tanθ}

r = ^{302} / _{9.8 x tan70}

r = ^{900} / _{9.8 x 2.74}

r = ^{900} / _{26.852}

r = 35.517

Therefore, the **radius** is **35.517.**

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the road bank angle.

To get the answer and workings of the road bank angle using the **Nickzom Calculator – The Calculator Encyclopedia. **First, you need to obtain the app.

You can get this app via any of these means:

**Web** – https://www.nickzom.org/calculator-plus

**professional **version via web, you need to **register** and **subscribe **for** NGN 1,500 **per** annum** to have utter access to all functionalities.

You can also try the **demo **version via https://www.nickzom.org/calculator

**Android (Paid)** – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator

**Android (Free)** – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator

**Apple (Paid)** – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8

Once, you have obtained the calculator encyclopedia app, proceed to the **Calculator Map, **then click on **Mechanics **under **Engineering**

Now, Click on **Motion of Circular Path **under **Mechanics**

Click on **Road Bank Angle **under **Motion of Circular Path**

The screenshot below displays the page or activity to enter your value, to get the answer for the road bank angle according to the respective parameter which are the **velocity (v), acceleration due to gravity (g) and radius (r).**

Now, enter the value appropriately and accordingly for the parameter as required by the **velocity (v)** is **35**,** acceleration due to gravity (g)** is **9.8 **and** radius (r) **is **18.**

Finally, Click on Calculate

As you can see from the screenshot above, **Nickzom Calculator** – The Calculator Encyclopedia solves for the road bank angle and presents the formula, workings and steps too.

The image represents reaction at the outer wheel of a vehicle moving along a level circular path.

To compute for the reaction, six essential parameters are needed and these parameters are **Mass of the Vechicle (m), Acceleration due to Gravity (g), Velocity of the Vehicle (v), Height of Centre of Gravity of the Vehicle from Ground Level (h), Radius of Circular Path (r) and Half of the Distance between the Centre Lines of the Wheel (a).**

The formula for calculating the reaction at the outer wheel of a vehicle moving along a level circular path:

R_{B} = ^{mg} / _{2}[1 + ^{v²h}/_{gra}]

Where;

R_{B} = Reaction at the Outer Wheel of a Vehicle moving along a Level Circular Path

m = Mass of the Vechicle

g = Acceleration due to Gravity

v = Velocity of the Vehicle

h = Height of Centre of Gravity of the Vehicle from Ground Level

r = Radius of Circular Path

a = Half of the Distance between the Centre Lines of the Wheel

Let’s solve an example;

Find the reaction when Mass of the Vechicle (m) is 12, Acceleration due to Gravity (g) is 9.8, Velocity of the Vehicle (v) is 28, Height of Centre of Gravity of the Vehicle from Ground Level (h) is 16, Radius of Circular Path (r) is 8 and Half of the Distance between the Centre Lines of the Wheel (a) is 4.

This implies that;

m = Mass of the Vechicle = 12

g = Acceleration due to Gravity = 9.8

v = Velocity of the Vehicle = 28

h = Height of Centre of Gravity of the Vehicle from Ground Level = 16

r = Radius of Circular Path = 8

a = Half of the Distance between the Centre Lines of the Wheel = 4

R_{B} = ^{mg} / _{2}[1 + ^{v²h}/_{gra}]

R_{B} = ^{12 x 9.8} / _{2}[1 + ^{28² x 16}/_{9.8 x 8 x 4}]

R_{B} = ^{117.60} / _{2}[1 + ^{784 x 16}/_{313.6}]

R_{B} = 58.80[1 + 40]

R_{B} = 58.80[41]

R_{B} = 58.80[41]

R_{B} = 2410.8

Therefore, the **reaction of the outer wheel of a vehicle moving along a level circular path** is **2410.8 N.**

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the reaction of the outer wheel of a vehicle moving along a level circular path.

To get the answer and workings of the reaction of the outer wheel of a vehicle moving along a level circular path using the **Nickzom Calculator – The Calculator Encyclopedia. **First, you need to obtain the app.

You can get this app via any of these means:

**Web** – https://www.nickzom.org/calculator-plus

**professional **version via web, you need to **register** and **subscribe **for** NGN 1,500 **per** annum** to have utter access to all functionalities.

You can also try the **demo **version via https://www.nickzom.org/calculator

**Android (Paid)** – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator

**Android (Free)** – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator

**Apple (Paid)** – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8

**Calculator Map, **then click on **Mechanics **under **Engineering**

Now, Click on **Motion of Circular Path **under **Mechanics**

Click on **Reaction of the outer wheel of a vehicle moving along a level circular path**** **under **Motion of Circular Path**

The screenshot below displays the page or activity to enter your value, to get the answer for the reaction of the outer wheel of a vehicle moving along a level circular path according to the respective parameter which are the

Now, enter the value appropriately and accordingly for the parameter as required by the **Mass of the Vechicle (m)** is **12**, **Acceleration due to Gravity (g)** is **9.8**, **Velocity of the Vehicle (v)** is **28**, **Height of Centre of Gravity of the Vehicle from Ground Level (h)** is **16**, **Radius of Circular Path (r)** is **8** and **Half of the Di****stance between the Centre Lines of the Wheel (a)** is **4**.

Finally, Click on Calculate

As you can see from the screenshot above, **Nickzom Calculator** – The Calculator Encyclopedia solves for the reaction of the outer wheel of a vehicle moving along a level circular path and presents the formula, workings and steps too.

The image above represents centripetal acceleration in a motion of circular path.

To compute for the centripetal acceleration, two essential parameters are needed and these parameters are **angular velocity (ω) **and **radius of circular path (r).**

The formula for the calculating centripetal acceleration:

a = ω²r

Where:

a = Centripetal Acceleration

ω = Angular Velocity

r = Radius of Circular Path

Let’s solve an example;

Find the centripetal acceleration with an angular velocity of 33 and a radius of 21.

This implies that;

ω = Angular Velocity = 33

r = Radius of Circular Path = 21

a = ω²r

a = 33² x 21

a = 1089 x 21

a = 22869

Therefore, the **centripetal acceleration** is **22869 m/s².**

**Calculating the Angular Velocity when Centripetal Acceleration and Radius of Circular path is Given.**

ω = √^{a} / _{r}

Where:

ω = Angular Velocity

a = Centripetal Acceleration

r = Radius of Circular Path

Let’s solve an example;

Find the angular velocity with a centripetal acceleration of 320 and a radius of 8.

This implies that;

a = Centripetal Acceleration = 320

r = Radius of Circular Path = 8

ω = √^{a} / _{r}

ω = √^{320} / _{8}

ω = √40

ω = 6.32

Therefore, the **angular velocity** is **6.32.**

**Calculating the Radius of Circular path when Centripetal Acceleration and Angular Velocity is Given.**

r = ^{a} / _{ω2}

Where:

r = Radius of Circular Path

a = Centripetal Acceleration

ω = Angular Velocity

Let’s solve an example;

Find the radius with a centripetal acceleration of 450 and an angular velocity of 15.

This implies that;

a = Centripetal Acceleration = 450

ω = Angular Velocity = 15

r = ^{a} / _{ω2}

r = ^{450} / _{152}

r = ^{450} / _{225}

r = 2

Therefore, the **radius** is **2.**

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the centripetal acceleration.

To get the answer and workings of the centripetal acceleration using the **Nickzom Calculator – The Calculator Encyclopedia. **First, you need to obtain the app.

You can get this app via any of these means:

**Web** – https://www.nickzom.org/calculator-plus

**professional **version via web, you need to **register** and **subscribe **for** NGN 1,500 **per** annum** to have utter access to all functionalities.

You can also try the **demo **version via https://www.nickzom.org/calculator

**Android (Paid)** – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator

**Android (Free)** – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator

**Apple (Paid)** – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8

**Calculator Map, **then click on **Mechanics **under **Engineering**

Now, Click on **Motion of Circular Path **under **Mechanics**

Click on **Centripetal Acceleration**** **under **Motion of Circular Path**

The screenshot below displays the page or activity to enter your value, to get the answer for the centripetal acceleration according to the respective parameter which are the **angular velocity (ω) **and **radius of circular path (r).**

Now, enter the value appropriately and accordingly for the parameter as required by the **angular velocity (ω) **is **33 **and **radius of circular path (r)** is **21**.

Finally, Click on Calculate

As you can see from the screenshot above, **Nickzom Calculator** – The Calculator Encyclopedia solves for the centripetal acceleration and presents the formula, workings and steps too.

The image above represents maximum velocity in circular motion.

To compute for the maximum velocity, three essential parameters are needed and these parameters are** coefficient of friction (μ), radius (r) and acceleration due to gravity (g).**

The formula for calculating maximum velocity:

V_{max} = √(μgr)

Where;

V_{max} = maximum velocity

μ = coefficient of friction

r = radius

g = acceleration due to gravity

Let’s solve an example;

Find the maximum velocity when the coefficient of friction is 14 with a radius of 7 and acceleration due to gravity of 9.8.

This implies that;

μ = coefficient of friction = 14

r = radius = 7

g = acceleration due to gravity = 9.8

V_{max} = √(μgr)

V_{max} = √(14 x 7 x 9.8)

V_{max} = √(960.40)

V_{max} = 30.99

Therefore, the **maximum velocity** is **30.99 m/s.**

**Calculating the Coefficient of Friction when the Maximum Velocity, Radius and Acceleration due to Gravity is Given.**

μ = ^{Vmax2} / _{gr}

Where;

μ = coefficient of friction

V_{max} = maximum velocity

r = radius

g = acceleration due to gravity

Let’s solve an example;

Find the coefficient of friction with a maximum velocity of 120, radius of 15 and acceleration due to gravity is 9.8?

This implies that;

V_{max} = maximum velocity = 120

r = radius = 15

g = acceleration due to gravity = 9.8

μ = ^{Vmax2} / _{gr}

μ = ^{1202} / _{15 x 9.8}

μ = ^{14400} / _{147}

μ = 97.96

Therefore, the **coefficient of friction** is **97.96.**

**Calculating the Radius when the Maximum Velocity, Coefficient of Friction and Acceleration due to Gravity is Given.**

r = ^{Vmax2} / _{gμ}

Where;

r = radius

V_{max} = maximum velocity

μ = coefficient of friction

g = acceleration due to gravity

Let’s solve an example;

Find the radius with a maximum velocity of 90, coefficient of friction of 24 and acceleration due to gravity is 9.8?

This implies that;

V_{max} = maximum velocity = 90

μ = coefficient of friction = 24

g = acceleration due to gravity = 9.8

r = ^{Vmax2} / _{gμ}

r = ^{902} / _{9.8 x 24}

r = ^{8100} / _{235.2}

r = 34.44

Therefore, the **radius** is **34.44.**

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the maximum velocity.

To get the answer and workings of the maximum velocity using the **Nickzom Calculator – The Calculator Encyclopedia. **First, you need to obtain the app.

You can get this app via any of these means:

**Web** – https://www.nickzom.org/calculator-plus

**professional **version via web, you need to **register** and **subscribe **for** NGN 1,500 **per** annum** to have utter access to all functionalities.

You can also try the **demo **version via https://www.nickzom.org/calculator

**Android (Paid)** – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator

**Android (Free)** – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator

**Apple (Paid)** – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8

**Calculator Map, **then click on **Mechanics **under **Engineering**

Now, Click on **Motion of Circular Path **under **Mechanics**

Click on **Maximum Velocity**** **under **Motion of Circular Path**

The screenshot below displays the page or activity to enter your value, to get the answer for the maximum velocity according to the respective parameter which are the **coefficient of friction (μ)**,** radius (r)** and** acceleration due to gravity (g)****.**

Now, enter the value appropriately and accordingly for the parameter as required by the **coefficient of friction (μ)** is **14**,** radius (r)** is **7 **and** acceleration due to gravity (g) **is **9.8.**

Finally, Click on Calculate

As you can see from the screenshot above, **Nickzom Calculator** – The Calculator Encyclopedia solves for the maximum velocity and presents the formula, workings and steps too.

The image above represents a body in superelevation.

To compute for the Superelevation, four essential parameters are needed and these parameters are **Gauge of the track (G), velocity of the body (v), radius of the curve (r) **and **acceleration due to gravity (g).**

The formula for calculating the circular path motion:

S = ^{Gv²} / _{gr}

Where:

S = Superelevation

G = Gauge of the track

v = velocity of the body

r = radius of the curve

g = acceleration due to gravity

Let’s solve an example;

Find the circular path motion when Gauge of the track is 14, velocity of the track is 47, radius of the curve is 21 and acceleration due to gravity is 9.8.

This implies that;

G = Gauge of the track = 14

v = velocity of the body = 47

r = radius of the curve = 21

g = acceleration due to gravity = 9.8

S = ^{Gv²} / _{gr}

S = ^{14 x 47²} / _{9.8 x 21}

S = ^{14 x 2209} / _{205.8}

S = ^{30926} / _{205.8}

S = 150.27

Therefore, the **superelevation** is **150.27** **m**.

**Calculating the Gauge of the track when Superelevation, Velocity of the body, Radius of the curve and Acceleration due to gravity.**

G = ^{Sgr} / _{v2}

Where;

G = Gauge of the track

S = Superelevation

v = velocity of the body

r = radius of the curve

g = acceleration due to gravity

Let’s solve an example;

With a superelevation of 180, velocity of the body is 32, radius of the curve is 12 and acceleration due to gravity as 9.8. Find the gauge of the track?

This implies that;

S = Superelevation = 180

v = velocity of the body = 32

r = radius of the curve = 12

g = acceleration due to gravity = 9.8

G = ^{Sgr} / _{v2}

G = ^{180 x 12 x 9.8} / _{322}

G = ^{21168} / _{1024}

G = 20.67

Therefore, the **gauge of the track** is **20.67.**

**Calculating the Velocity of the body when Superelevation, Gauge of the track, Radius of the curve and Acceleration due to gravity.**

v = √^{Sgr} / _{G}

Where;

v = velocity of the body

S = Superelevation

G = Gauge of the track

r = radius of the curve

g = acceleration due to gravity

Let’s solve an example;

With a superelevation of 120, gauge of the track is 28, radius of the curve is 7 and acceleration due to gravity as 9.8. Find the velocity of the body?

This implies that;

S = Superelevation = 120

G = gauge of the track = 28

r = radius of the curve = 7

g = acceleration due to gravity = 9.8

v = √^{Sgr} / _{G}

v = √^{120 x 9.8 x 7} / _{28}

v = √^{8232} / _{28}

v = √294

v = 17.146

Therefore, the **velocity of the body** is **17.146.**

**Calculating the Radius of the curve when Superelevation, Gauge of the track, Velocity of the body and Acceleration due to gravity.**

r = ^{Gv2} / _{Sg}

Where;

r = radius of the curve

v = velocity of the body

S = Superelevation

G = Gauge of the track

g = acceleration due to gravity

Let’s solve an example;

With a superelevation of 170, gauge of the track is 18, velocity of the body is 9 and acceleration due to gravity as 9.8. Find the radius of the curve?

This implies that;

S = Superelevation = 170

G = gauge of the track = 18

v = velocity of the body = 9

g = acceleration due to gravity = 9.8

r = ^{Gv2} / _{Sg}

r = ^{18 x 92} / _{170 x 9.8}

r = ^{1458} / _{1666}

r = 0.875

Therefore, the **radius of the curve** is **0.875.**

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the superelevation.

To get the answer and workings of the superelevation using the **Nickzom Calculator – The Calculator Encyclopedia. **First, you need to obtain the app.

You can get this app via any of these means:

**Web** – https://www.nickzom.org/calculator-plus

**professional **version via web, you need to **register** and **subscribe **for** NGN 1,500 **per** annum** to have utter access to all functionalities.

You can also try the **demo **version via https://www.nickzom.org/calculator

**Android (Paid)** – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator

**Android (Free)** – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator

**Apple (Paid)** – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8

**Calculator Map, **then click on **Mechanics **under **Engineering**

Now, Click on **Motion of Circular Path **under **Mechanics**

Click on **Superelevation**** **under **Motion of Circular Path**

The screenshot below displays the page or activity to enter your value, to get the answer for the superelevation according to the respective parameter which are the **Gauge of the track (G), velocity of the body (v), radius of the curve (r) **and **acceleration due to gravity (g).**

Now, enter the value appropriately and accordingly for the parameter as required by the **Gauge of the track (G)** is **14**,** velocity of the body (v)** is **47**,** radius of the curve (r)** is **21** and **acceleration due to gravity (g)** is **9.8**.

Finally, Click on Calculate

As you can see from the screenshot above, **Nickzom Calculator** – The Calculator Encyclopedia solves for the superelevation and presents the formula, workings and steps too.

The image above represent angular velocity.

To compute the angular velocity, one essential parameter is needed and its parameter is **Number of Revolutions per Minute (N).**

The formula for calculating angular velocity:

ω = ^{2πN} / _{60}

Where;

ω = Angular velocity

N = Number of revolutions per minute

Let’s solve an example;

Find the Angular Velocity with a number of revolutions per minute as 60.

This implies that;

N = Number of revolutions per minute = 60

ω = ^{2πN} / _{60}

ω = ^{2 x π x 24} / _{60}

ω = ^{150.816}/ _{60}

ω = 2.5136

Therefore, the **angular velocity** is **2.5136 rad/s.**

**Calculating the Number of Revolutions per Minute when Angular Velocity is Given.**

N = ^{ω60} / _{2π}

Where;

N = Number of revolutions per minute

ω = Angular velocity

Let’s solve an example;

With an angular velocity of 40. Find the number of revolutions per minute?

This implies that;

ω = Angular velocity = 40

N = ^{ω60} / _{2π}

N = ^{40 x 60} / _{6.284}

N = ^{2400} / _{6.284}

N = 381.9

Therefore, the **number of revolutions per minute** is **381.9 min.**

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the angular velocity.

To get the answer and workings of the angular force using the **Nickzom Calculator – The Calculator Encyclopedia. **First, you need to obtain the app.

You can get this app via any of these means:

**Web** – https://www.nickzom.org/calculator-plus

**professional **version via web, you need to **register** and **subscribe **for** NGN 1,500 **per** annum** to have utter access to all functionalities.

You can also try the **demo **version via https://www.nickzom.org/calculator

**Android (Paid)** – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator

**Android (Free)** – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator

**Apple (Paid)** – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8

**Calculator Map, **then click on **Mechanics **under **Engineering**

Now, Click on **Motion of Circular Path **under **Mechanics**

Click on **Angular Velocity**** **under **Motion of Circular Path**

The screenshot below displays the page or activity to enter your value, to get the answer for the angular velocity according to the respective parameter which are the **Number of revolutions per minute (N).**

Now, enter the value appropriately and accordingly for the parameter as required by the **Number of revolutions per minute (N) **is **24.**

Finally, Click on Calculate

As you can see from the screenshot above, **Nickzom Calculator** – The Calculator Encyclopedia solves for the angular velocity and presents the formula, workings and steps too.

The image above represents the centrifugal force.

To compute for the centrifugal force, three essential parameters are needed and these parameters are **Mass of the body (m)**, **Angular Velocity of the body ( w)** and

The formula for calculating the centrifugal force:

F = mω²r

Where:

F = Centrifugal Force

m = mass of the body

ω = angular velocity

r = radius

Let’s solve an example;

Find the centrifugal force with mass of the body as 12, angular velocity as 32 and a radius of 8.

This implies that;

m = mass of the body = 12

ω = angular velocity = 32

r = radius = 8

F = mω²r

F = 12 x 32² x 8

F = 12 x 1024 x 8

F = 98304

Therefore, the **centrifugal** **force** is **98304** **N**.

**Calculating the Mass of the body (m) when the Centrifugal Force, Angular Velocity and Radius is Given.**

m = ^{F} / _{w2r}

Where;

m = mass of the body

F = Centrifugal Force

ω = angular velocity

r = radius

Let’s solve an example;

Find the mass of a body when centrifugal force is 140 with an angular velocity of 24 and a radius of 10.

This implies that;

F = Centrifugal Force = 140

ω = angular velocity = 24

r = radius = 10

m = ^{F} / _{w2r}

m = ^{140} / _{24210}

m = ^{140} / _{576 x 10}

m = ^{140} / _{5760}

m = 0.024

Therefore, the **mass of the body** is **0.024 kg.**

**Calculating the Angular Velocity ( w) when the Centrifugal Force, Mass of the body (m) and Radius is Given.**

*w* = √^{F} / _{mr}

Where;

ω = angular velocity

m = mass of the body

F = Centrifugal Force

r = radius

Let’s solve an example;

Find the angular velocity when centrifugal force is 220 with a mass of the body of 14 and a radius of 6.

This implies that;

F = Centrifugal Force = 220

m = mass of the body = 14

r = radius = 6

*w* = √^{F} / _{mr}

*w* = √^{220} / _{14 x 6}

*w* = √^{220} / _{84}

*w* = √2.619

*w* = 1.618

Therefore, the **angular velocity** is **1.618.**

**Calculating the Radius (r) when the Centrifugal Force, Mass of the body (m) and Angular Velocity is Given.**

r = ^{F} / _{mw2}

Where;

r = radius

F = Centrifugal Force

ω = angular velocity

m = mass of the body

Let’s solve an example;

Find the radius with a centrifugal force of 280, mass of the body is 16 and an angular velocity of 22.

This implies that;

F = Centrifugal Force = 280

ω = angular velocity = 22

m = mass of the body = 16

r = ^{F} / _{mw2}

r = ^{280} / _{16 x 222}

r = ^{280} / _{16 x 44}

r = ^{280} / _{704}

r = 0.397

Therefore, the **radius** is **0.397.**

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the centrifugal force.

To get the answer and workings of the centrifugal force using the **Nickzom Calculator – The Calculator Encyclopedia. **First, you need to obtain the app.

You can get this app via any of these means:

**Web** – https://www.nickzom.org/calculator-plus

**professional **version via web, you need to **register** and **subscribe **for** NGN 1,500 **per** annum** to have utter access to all functionalities.

You can also try the **demo **version via https://www.nickzom.org/calculator

**Android (Paid)** – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator

**Android (Free)** – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator

**Apple (Paid)** – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8

**Calculator Map, **then click on **Mechanics **under **Engineering**

Now, Click on **Motion of Circular Path **under **Mechanics**

Click on **Centrifugal Force **under **Motion of Circular Path**

The screenshot below displays the page or activity to enter your values, to get the answer for the centrifugal force according to the respective parameters which are the **mass of the body (m), ****angular ****velocity (v) **and **radius (r).**

Now, enter the values appropriately and accordingly for the parameters as required by the **mass of the body (m)** is **12**, **angular ****velocity (v) **is **32 **and **radius (r)** is **8**.

Finally, Click on Calculate

As you can see from the screenshot above, **Nickzom Calculator** – The Calculator Encyclopedia solves for the centrifugal force and presents the formula, workings and steps too.