# How to Calculate and Solve for the Reaction at the Inner Wheel of a Vehicle moving along a Level Circular Path | The Calculator Encyclopedia

**Last Updated on February 18, 2024**

The image represents a reaction at the inner wheel of a vehicle moving along a level circular path. To calculate 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)}]

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

RA = 63.7[1 – ^{605} / _{205.8}]

RA = 63.7[1 – 2.939]

Then, 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.**

**How to Calculate the Reaction at the Inner Wheel of a Vehicle Moving along a Level Circular Path With The Calculator Encyclopedia**

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.

**Get the Nickzom Calculator**

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.