How to Calculate Centripetal Force

What is Centripetal Force?

In this post, you will learn how to calculate centripetal force of an object. I will explain important points before I start solving problems on the topic.

Definition of Centripetal force: Centripetal force is the force of an object around a circular path that keeps the object moving at a constant speed in a circular path. When a body is under the effect of centripetal force, the direction of the motion of the object will continue to change. The symbol for centripetal is F_T. Newton is the S.I unit of centripetal force

The formula for calculating centripetal force is

F_T = mv²/r

where

F_T = centripetal force

m = mass of the object and is measured in kilogram

v = velocity of the object and is measured in meters per second

r = radius of the circle and is measured in meter

Centripetal force is perpendicular to the direction of the velocity of the object and it’s an inward force towards the center of the circle. This force keeps the body moving around the circle at a constant speed.

Examples of centripetal force are as follows:

• The way the moon moves around the earth
• How the earth moves around the sun
• The way an attached stone to a wheel keeps going around the wheel while in motion.

Examples of How to Calculate Centripetal Force

Here are examples of how to calculate centripetal force:

Example 1

A mass of 20 kilograms is moving in a circular path of radius 4 meters with a uniform velocity of 100 meters per second. Find the centripetal force of the object.

Solution

Data:

mass, m = 20 kg

radius, r = 4 m

centripetal force, F_T = ?

unoform velocity, v = 100 m/s

Centripetal force is calculated by using the formula which says

Force = mass x acceleration

and the formula for centripetal acceleration is a=v²/r

Which implies that a = 100²/4 = 2,500ms^-2

Since F_T = ma

we can now say that

F_T = 20 x 2,500 = 50,000 N

Therefore, the centripetal force F_T is 50,000 Newtons

Example 2

An object with a mass of 8 kg is moving in a circular path with a radius of 3 meters at a tangential velocity of 15 m/s. What is the centripetal force acting on the object?

Solution

Data:

Mass, m = 8 kg

Radius, r = 3 m,

Velocity, v = 15 m/s

Centripetal force, F_T =?

and the formula for calculating centripetal force is F_T = mv²/r

We can now substitute our data into the above formula to get

F_T = (8 x 15²)/3 = (8 x 225)/3 = 1,800/3 = 600 N

Therefore, the centripetal force is 600 Newtons.

Example 3

An object of mass 500 grams attached to a string is whirled around in a horizontal circle of radius 2.0 meters with a constant speed of 8 m/s. Calculate the centripetal force of the object.

Solution

Data:

Mass, m = 500 g = 500/1000 kg = 0.5 kg

radius, r = 2.0 m

Speed, v = 8 ms^-1

F_T =?

While F_T = mv²/r

We can now plugin our data into the above formula

F_T = (0.5 x 8²)/2 = 32/2 = 16 N

Therefore, the centripetal force is 16 Newtons

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