“Moment of Inertia and its Significance” MHT-CET Class 12 Physics Crash Course| Chapter Rotational Dynamics
In this session G.S. Khairnar discussed the theory and MCQ’s of “Moment of Inertia and its Significance”. The session will be useful for all the aspirants of MHT-CET 2022. The session will be in Marathi and English.
Moment of Inertia and its Significance:-
Hello everyone, when body rotates or spins about axis of rotation, the different particles of the body revolves in different circles, then the body said to perform rotational motion.
Rigid body: The body, in which the distance between any particles does not change under the action of force, is called rigid body.
In translational motion body has tendency to oppose any change in its state of motion called as inertia. Mass in linear motion provides the property of inertia.
Similarly in rotational motion the body has tendency to oppose any change in its state of motion. This property is called M.I. It is represented by mass & distribution of mass from axis of rotation.
Let’s discuss the concept of moment of inertia or rotational inertia……!
Consider a rigid body is rotating about axis of rotation which consists of ‘n’ number of particles of masses m1, m2…….. mn situated at distance r1 , r2, …… rn respectively from the axis of rotation The M.I. is given by,
Definition:
The M.I. of rigid body about a given axis of rotation is defined as the sum of products of mass of each particle of the body & square of its distance from the axis of rotation.
In general,
I= MR2
SI unit is kg.m2
Dimensions of moment of inertia is [M1L2T0]
Let’s discuss the physical significance of Moment of inertia…..!
In translational motion, if ‘m’ is mass of object and ‘a’ is an acceleration in motion,
Force = mass acceleration
In rotational motion,
Torque = M.I. angular acceleration
From these relations,
- Force is responsible for translational Motion while Torque is responsible for rotational motion. Thus torque is analogues to force.
- Acceleration is rate of change of velocity with time. Angular acceleration is rate of charge of angular velocity with time. Thus angular acceleration is analogous to acceleration.
- By comparing the two expressions it is clear that moment of inertia motion is analogous to inertia.
- In translational motion mass represent inertia of body to oppose any change in its state of translational motion. While in rotational motion M.I. represents inertia of body to oppose any change in its state of rotational motion.
- Thus M.I. plays the same role in rotational motion as mass plays in translational motion M.I. is analogues to mass. Therefore M.I. is also called rotational inertia.
Some Important Terms:
Moment of Inertia and its Significance
Let’s solve the following MCQ’s….….!
Q.1) The body, in which the distance between any particles does not change under the action of force, is known as….
a) plastic body
b) elastic body
c) rigid body
d) none of these
Answer
c) rigid body
Q.2) Which of the following is the correct representation of moment of inertia of a body?
Q.3) SI unit and dimensions of moment of inertia are…
a) m2 and [M1L2T0]
b) kg2.m2 and [M2L2T0]
a) m and [M1L2T0]
b) kg2.m2 and [M2L2T0]
Answer
a) m2 and [M1L2T0]
Q.4) Moment of inertia of spherical bob of mass 100 g tied to string of length 50 cm and rotated in clockwise sense is…
Q.5) A body rotating at the rate of 60 rpm has moment of inertia 1.2 kg.m2, kinetic energy of rotating body is…
A) 23.66 J
B) 23.66 erg
c) 2366 J
D) 23.66 erg
Q.6) Four balls of masses 0.3 kg each are tied to string of length 50 cm and other ends joined at the a fixed point, the moment of inertia of system is…
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