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Rotational Motion
1. Rigid Body
Rigid body is defined as a system of particles in which distance between each pair of particles remains constant (with respect to time) that means the shape and size do not change, during the motion. Eg. Fan, Pen, Table, stone and so on.
Our body is not a rigid body, two blocks with a spring attached between them is also not a rigid body. For every pair of particles in a rigid body, there is no velocity of seperation or approach between the particles. In the figure shown velocities of A and B with respect to ground are 
and 
respectively
If the above body Is rigid
VA cos θ1 = VB cos θ2
Note : With respect to any particle of rigid body the motion of any other particle of that rigid body is circular.
VBA = relative velocity of B with respect to A.
1.1. Pure Translational Motion :
A body is said to be in pure translational motion if the displacement of each particle is same during any time interval however small or large. In this motion all the particles have same 
at an instant.
example.
A box is being pushed on a horizontal surface.
of any particle, 
of any particle
of any particle
For pure translational motion :-
Where m1, m2, m3, ......... are the masses of different particles of the body having accelerations 
respectively.
But acceleration of all the particles are same So, 
Where M = Total mass of the body
= acceleration of any particle or of centre of mass of body
Where m1, m2, m3 ...... are the masses of different particles of the body having velocities 
respectively
But velocities of all the particles are same so 
Where 
= velocity of any particle or of centre of mass of the body.
Total Kinetic Energy of body = 
1.2. Pure Rotational Motion :
A body is said to be in pure rotational motion if the perpendicular distance of each particle remains constant from a fixed line or point and do not move parallel to the line, and that line is known as axis of rotation. In this motion all the particles have same 
and at an instant. Eg. : - a rotating ceiling fan, arms of a clock.
For pure rotation motion :-
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FAQs on Rotational Motion & Moment of Inertia - Physics for JEE Main & Advanced
| 1. What is rotational motion and how does it differ from linear motion? |  |
| 2. What is moment of inertia and how is it calculated? | |
Ans. Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It depends on the mass distribution of the object and the axis of rotation. The moment of inertia of an object can be calculated by summing the products of each particle's mass and its squared distance from the axis of rotation.
| 3. How does the distribution of mass affect the moment of inertia? | |
Ans. The distribution of mass affects the moment of inertia by determining how the mass is spread out around the axis of rotation. Objects with more mass concentrated farther from the axis of rotation have a larger moment of inertia, while objects with more mass concentrated closer to the axis have a smaller moment of inertia.
| 4. What is the relationship between moment of inertia and rotational motion? | |
Ans. The moment of inertia plays a crucial role in determining an object's rotational motion. According to Newton's second law of rotational motion, the torque acting on an object is equal to the moment of inertia multiplied by the angular acceleration. Therefore, the moment of inertia affects how quickly or slowly an object rotates when a torque is applied.
| 5. How does the moment of inertia affect an object's stability? | |
Ans. The moment of inertia affects an object's stability by determining its resistance to changes in its rotational motion. Objects with larger moments of inertia are generally more stable since they require a larger external torque to change their rotational state. On the other hand, objects with smaller moments of inertia are less stable and can be easily rotated with less applied torque.
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