Centrifugal Force and Acceleration- Introduction & Explanation

Key Concepts

• Centrifugal force

• Acceleration

• Angular acceleration

Introduction: 

In this session we are going to study centrifugal force. We are going to differentiate between acceleration in rectilinear motion and uniform circular motion, and derive a relation to calculate the same. 

Centrifugal force: 

An outward force on a rotating or revolving body is called a centrifugal force. Centrifugal means “center-fleeing.” Centrifugal force does not pull an object outward. This is a misconception. 

Newton’s First Law says that if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force. It is not due to any real force rather due to inertia. The centrifugal force is not a true force as it is an effect of rotation. It is equal and opposite to the centripetal force 

Acceleration: 

It is defined as the rate of change of velocity.  

Acceleration =

change in velocityTimechange in velocityTime

Acceleration exists when there is a change in velocity. Velocity is a vector quantity. It has both magnitude as well as direction associated with it.  

If u is the initial velocity and v is the final velocity and t is the time taken then the formula is : 

a =

v−utv−ut

This formula is used for linear motion, for the uniform circular motion we calculate the angular acceleration. 

Centrifugal Acceleration:

It depends on the radius of the circle and the speed of the object. 

It is denoted by “a_c” Its unit is “m/s .” 

Questions and answers 

Question 1: Draw the direction of the centrifugal force if the object is released from its orbit at point 1 and 2. 

Answer: 

For object 1 it will go in horizontal direction towards the right.  

For object 2 it will go vertically down.

Question 2: The speed of a boy of weight 40 Kg in a merry-go-round of radius 20 m is 40 m/s. What is the centrifugal force experienced by the system? 

Answer: 

Given that:  

Speed of boy = 40 m/s 

Radius of merry go round = 20 m 

Mass of boy = 40 kg 

Using formula,

FC=mv2r𝑭𝑪=𝒎𝒗𝟐𝒓

==

40

(40220)40220 =

40×40×402040×40×4020 = 3200 N  

Question 3: What is the centripetal acceleration of an object if it going round in circles with velocity of 20 km/h and comes to rest in 20 s. The radius of the circle is 20 m.  

Answer: 

Given that:  

Initial velocity, 

u = 20 km/h  = 20

 ×10003600  ×10003600 

=

200 m/s36200 m/s36

Final velocity, v = 0 m/s 

Radius, r = 20 m 

Time period t = 20 s 

aC=v2raC=v2r

=

(20036)2

××

120  =

200 ×20020 ×36 × 36 = 1.54 m/s²

Summary

• An outward force on a rotation or revolving body is called a Centrifugal force.
• It is pointed outwards.
• Centrifugal force is an inertial force.

Fc = Mv²/R

• Centrifugal acceleration depends upon velocity and radius.

ac=v²/r