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Translational and Rotational Equilibrium

A rigid body ...

Question

A rigid body is rotating about an axis. Different particles are at different distances from the axis. Which of the following is true?A rigid body is rotating about an axis. Different particles are at different distances from the axis. Which of the following is true?

A

Different particles possess the same linear velocity

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B

Different particles possess the same angular acceleration

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C

Different particles possess the same linear acceleration

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D

Different particles possess the same angular velocity

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Solution

The correct option is D
Different particles possess the same angular velocity

Different particles possess the same angular velocity and equal to the angular velocity of rigid body.

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Q. Consider the following two statements A and B and identify the correct option:
A) When a rigid body is rotating about its own axis at a given instant, all particles of body possess same angular velocity.
B) When a rigid body is rotating about its own axis, the linear velocity of a particle is directly proportional to its perpendicular distance from axis.

Q. A rigid body is in pure rotation, about a fixed axis. Then which of the following statement(s) is/are true ?

Q. A rigid body of mass m rotates with angular velocity

ω

about an axis at a distance a from the centre of mass C. The radius of gyration about C is K. Then, kinetic energy of rotation of the body about new parallel axis is :

Q. Assertion (A) : Moment of inertia of a rotating rigid body remains constant irrespective of its angular velocity.
Reason (R) : Neither mass of rigid body nor distances of particles of rigid body from axis of rotation change during the rotation.

Q. Assertion :STATEMENT-1 : If two different axes are at same distance from centre of mass of a rigid body, then moment of inertia of the given rigid body about both axis will always be same. Reason: STATEMENT-2 : From parallel axis theorem

I = I_{c m} + m d^{2},

where all terms have usual meaning.

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