### 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/s^{2}

### 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 = Mv^{2}/R

- Centrifugal acceleration depends upon velocity and radius.

ac=v^{2}/r

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