How to Calculate and Solve for Road Bank Angle, Velocity and Radius of a Body in Motion of Circular Path | The Calculator Encyclopedia

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( / 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( / 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.

Continue reading How to Calculate and Solve for Road Bank Angle, Velocity and Radius of a Body in Motion of Circular Path | The Calculator Encyclopedia

How to Calculate and Solve for Centripetal Acceleration, Angular Velocity and Radius of Circular Path of a Body | The Calculator Encyclopedia

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.

Continue reading How to Calculate and Solve for Centripetal Acceleration, Angular Velocity and Radius of Circular Path of a Body | The Calculator Encyclopedia

How to Calculate and Solve for Maximum Velocity, Coefficient of Friction and Radius of a Body in Motion of Circular Path | Nickzom Calculator

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:

Vmax = √(μgr)

Where;
Vmax = 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

Vmax = √(μgr)
Vmax = √(14 x 7 x 9.8)
Vmax = √(960.40)
Vmax = 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
Vmax = 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;
Vmax = 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.

Continue reading How to Calculate and Solve for Maximum Velocity, Coefficient of Friction and Radius of a Body in Motion of Circular Path | Nickzom Calculator

How to Calculate and Solve for Superelevation, Guage of Track, Velocity and Radius of a Body in Circular Path Motion | The Calculator Encyclopedia

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.

Continue reading How to Calculate and Solve for Superelevation, Guage of Track, Velocity and Radius of a Body in Circular Path Motion | The Calculator Encyclopedia

How to Calculate and Solve for Mass, Angular Velocity, Radius and Centrifugal Force of a Body | The Calculator Encyclopedia

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 Radius (r).

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.

Continue reading How to Calculate and Solve for Mass, Angular Velocity, Radius and Centrifugal Force of a Body | The Calculator Encyclopedia

How to Calculate and Solve for the Height and Volume of a Conical Frustum | The Calculator Encyclopedia

The image above is a conical frustum.

To compute the volume of a conical frustum, three essential parameters are needed and this parameters are radius of the lower base (R), radius of the upper base (r) and height (h).

The formula for calculating the volume of a conical frustum:

V = πh(R² + Rr + r²)3

Where;
V = Volume of the conical frustum
R = Radius of the lower base
r = Radius of the upper base
h = Height of the conical frustum

Let’s solve an example;
Find the volume of the conical frustum when the lower base is 5 cm with an upper base of 9 cm and a height of 11 cm.

This implies that;
R = Radius of the lower base = 5 cm
r = Radius of the upper base = 9 cm
h = Height of the conical frustum = 11 cm

V = π(11)((5)² + (5)(9) + (9)²)3
V = (34.557)((25) + (45) + (81))3
V = (34.557)(151)3
V = 5218.1853
V = 1739.39

Therefore, the volume of the conical frustum is 1739.39 cm3.

Continue reading How to Calculate and Solve for the Height and Volume of a Conical Frustum | The Calculator Encyclopedia

How to Calculate and Solve for Escape Velocity | The Calculator Encyclopedia

The image above represents the escape velocity.

To compute the escape velocity of a field, two essential parameters are needed and the parameters are acceleration due to gravity (g) and radius (r).

The formula for calculating the escape velocity:

V = √(2gR)

Where;
V = Escape velocity
g = Acceleration due to gravity
R = Radius

Let’s solve an example;
Find the escape velocity of a field when the acceleration due to gravity is 12 and the radius is 24 cm.

This implies that;
g = Acceleration due to gravity = 12
r = Radius = 24 cm

V = √(2gR)
V = √(2 x 12 x 24)
V = √(576)
V = 24

Therefore, the escape velocity is 24 m/s.

Continue reading How to Calculate and Solve for Escape Velocity | The Calculator Encyclopedia

How to Calculate and Solve for Gravitational Potential | The Calculator Encyclopedia

The image above represents the Gravitational potential.

To compute the gravitational potential of a field, two essential parameters are needed which are mass (m) and radius (r).

The formula for calculating the gravitational potential;

V = (Gm) / r

Where;
V = Gravitational potential
m = Mass
r = Radius

Let’s solve an example;
Find the gravitational potential of a field when the mass is 14 cm with a radius of 9 cm.

This implies that;
m = Mass = 14 cm
r = Radius = 9 cm

V = (Gm) / r
V = (6.67 x 10-11 x 14) / 9
V = 1.0375e-10 / 9
V = 1.0375e-10

Therefore, the gravitational potential is 1.0375e-10 Volts (V).

Continue reading How to Calculate and Solve for Gravitational Potential | The Calculator Encyclopedia

How to Calculate and Solve for Gravitational Force | The Calculator Encyclopedia

The image above represents the gravitational force.

To compute the gravitational force of a field, three parameters are needed and this parameters are mass (m1), mass (m2) and radius between the masses (R).

The formula for calculating the gravitational force:

F = Gm1m2 /

Where;
F = Gravitational force
m1 = Mass 1
m2 = Mass 2
r = Radius between the masses

Let’s solve an example;
Find the gravitational force of a field when the mass 1 is 8 cm, mass 2 is 10 cm and the radius between masses is 14 cm.

This implies that;
m1 = Mass 1 = 8 cm
m2 = Mass 2 = 10 cm
r = Radius between the masses = 14 cm

F = Gm1m2 /
F = (6.67 x 10-11 x 8 x 10) / 196
F = 5.336e-9 / 196
F = 2.722e-11

Therefore, the gravitational force is 2.722e-11 Newton (N).

Continue reading How to Calculate and Solve for Gravitational Force | The Calculator Encyclopedia

How to Calculate and Solve for the Radius, Height and Surface Area of a Spherical Segment | The Calculator Encyclopedia

The image above is a spherical segment.

To compute the surface area of a spherical segment requires two essential parameters which are the radius of the sphere (R) and the height (h).

The formula for calculating the surface area of the spherical segment:

A = 2πRh

Where;
A = Surface area of the spherical segment
R = Radius of the sphere
h = Height of the spherical segment

Let’s solve an example;
Find the surface area of a spherical segment when the radius of the sphere is 12 cm and the height is 16 cm.

This implies that;
R = Radius of the sphere = 12 cm
h = Height of the spherical segment = 16 cm

A = 2πRh
A = 2π (12 x 16)
A = 2π (192)
A = 6.28 (192)
A = 1206.37

Therefore, the surface area of the spherical segment is 1206.37 cm2.

Calculating the Radius of the Sphere using the Surface Area of the Spherical Segment and the Height.

R = A / 2πh

Where;
R = Radius of the sphere
A = Surface area of the spherical segment
h = Height of the spherical segment

Let’s solve an example;
Find the radius of a sphere with a surface area of 300 cm2 and a height of 12 cm.

This implies that;
A = Surface area of the spherical segment = 300 cm2
h = Height of the spherical segment = 12 cm

R = A / 2πh
R = 300 / 2 x π x 12
R = 300 / 75.41
R = 3.978

Therefore, the radius of the sphere is 3.978 cm.

Continue reading How to Calculate and Solve for the Radius, Height and Surface Area of a Spherical Segment | The Calculator Encyclopedia