What is Centripetal Force and how to calculate it?

The centripetal force is a physics topic. It is a kind of force. The label centripetal refers to any force that keeps something turning in a circle.

Tension, gravity, friction, electrical attraction, the normal force, or any other force could be involved.

What is Centripetal Force?

Centripetal force is a force that makes a body follow a curved path. Its direction is always orthogonal to the motion of the body.

A centripetal force is a net force that acts on an object to keep it moving along a circular path.

In Newtonian mechanics, gravity causes astronomical orbits. One common example involving centripetal force is the cause in which a body moves with uniform speed along a circular path. Its unit is Newton (N).

The tension force in the string of a swinging tethered ball is an example of centripetal force.

Centripetal Force

The gravitational force keeping a satellite in orbit is another example of centripetal forcee.

What is Centripetal Force

The formula of centripetal force is,

Centripetal force = mass x velocity square / radius

Fc = mv2/r

Is derived from the Newton 2nd law.

a = F/m

and then put the centripetal acceleration a = v2/r.

v2/r = F/m

After rearranging,

Fc = mv2/r

how to calculate Centripetal Force

Let us take some examples in order to understand how to apply the formula of centripetal force.

 

Example 1

Calculate the centripetal force of an object if it is moving in a circle having a radius of 50 m, the mass of the body is 100 kg, and the velocity is 5 m/s.

Solution

Step 1: Identify the values.

Radius = r = 50 m

Mass = m = 100 kg

Velocity = v = 5 m/s

Step 2: Place the given values in the formula of centripetal force.

Fc = mv2/r

Fc =100 × (5)2/50

Fc =100 × 25/50

Fc =100 × ½

Fc = 50 N

 

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Example 2

Calculate the centripetal force of an object if it is moving in a circle having a radius of 10 m, the mass of the body is 1000 kg, and the velocity is 25 m/s.

Solution

Step 1: Identify the values.

Radius = r = 10 m

Mass = m = 1000 kg

Velocity = v = 25 m/s

Step 2: Place the given values in the formula of centripetal force.

Fc = mv2/r

Fc =1000 × (25)2/10

Fc =1000 × 625/10

Fc =1000 × 125/2

Fc =500 × 125

Fc =62500 N

Centripetal force can also be calculated online by using an online Centripetal Force Calculator.

 

Other forms of formula

The centripetal force formula is also applicable to find the radius or mass or velocity.

Radius

The formula of the radius is,

Radius = mass x velocity square / centripetal force

r = mv2/ Fc

Example 1

Calculate the radius of an object if it is moving in a circle having centripetal force 62500N, the mass of the body is 1000 kg, and the velocity is 25 m/s.

Solution

Step 1: Identify the values.

Centripetal force = Fc = 62500N

Mass = m = 1000 kg

Velocity = v = 25 m/s

Step 2: Place the given values in the formula of radius.

r = mv2/ Fc

r =1000 × (25)2/62500

r =1000 × 625/62500

r =625000/62500

r =6350/625

r =10 m

Example 2

Calculate the radius of an object if it is moving in a circle having centripetal force 356N, the mass of the body is 23 kg, and the velocity is 9 m/s.

Solution

Step 1: Identify the values.

Centripetal force = Fc = 356 N

Mass = m = 23 kg

Velocity = v = 9 m/s

Step 2: Place the given values in the formula of radius.

r = mv2/ Fc

r =23 × (9)2/356

r =23 × 9×9/356

r =23 ×81/356

r =1863/356

r =5.23 m

Mass

The formula of mass is,

Mass = centripetal force x radius / velocity square

m = Fc r/ v2

Example

Calculate the mass of an object if it is moving in a circle having a radius of 50 m, the centripetal force of the object is 50 Nand the velocity is 5 m/s.

Solution

Step 1: Identify the values.

Radius = r = 50 m

Centripetal force = Fc = 50 N

Velocity = v = 5 m/s

Step 2: Place the given values in the formula of mass.

m = Fc r/ v2

m =50 × 50/ (5)2

m =2500/25

m =100 kg

Velocity

The formula of velocity is,

Velocity square = centripetal force x radius / mass

v2 = Fc r/m

 v = sqrt (Fc r/m)

Example

Calculate the velocity of an object if it is moving in a circle having centripetal force 62500N, the mass of the body is 1000 kg, and radius is 10 m.

Solution

Step 1: Identify the values.

Centripetal force = Fc = 62500N

Mass = m = 1000 kg

Radius = r = 10 m

Step 2: Place the given values in the formula of radius.

v = sqrt (Fc r/m)

v =sqrt (62500 × 10/1000)

v =sqrt (625000/1000)

v =sqrt (625)

v = sqrt (252)

v = 25

 

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Examples of Centripetal Force in daily life

Some examples of centripetal force in daily life are given below.

  • Loop of Roller Coaster.
  • Orbiting of Planets.
  • Electrons Orbiting around Nucleus.
  • Twirling a Lasso.
  • Banked Roads.
  • Cream Separator.
  • Washing machine dryer.
  • Driving on curves.

 

Applications of Centripetal Force

The centripetal force has a wide range of applications used in daily life.

  • Motion in a vertical circle.
  • Banking of curved roads and tracks.
  • In satellites.
  • Bending of a cyclist around a curve.
  • Condition for skidding.

Centripetal force is used widely in these terms. It is also used in many other rotating items of electronic and non-electronic appliances.

Relationship between centripetal force and centrifugal force

Both are the same but opposite in direction. The centripetal force acts inwardly (pulls the objects toward the center) while centrifugal forces push it away from the center.

Both have the same formulas. The only difference is accompanied by a negative sign.

The formula of centripetal force is,

Centripetal force = mass x velocity square / radius

Fc = mv2/r

The formula of centrifugal force is,

Centrifugal force = – mass x velocity square / radius

Fc = – mv2/r

Summary

Centripetal force is a kind of force used to find a net force that acts on an object to keep it moving along a circular path.By using the formula, we can calculate the centripetal force.

That formula is derived by using Newton’s second law and angular acceleration. By using this formula, we can also calculate the radius, mass, and velocity of a moving object.

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