Question

(iii) In rotational motion of a rigid body, all particles move
with
(a) same linear velocity and same angular velocity
(b) same linear velocity and different angular velocity
(c) different linear velocities and same angular velocities
(d) different linear velocities and different angular velocities

Answer 1

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option (b) is correct .

as in rotational motion; the particles move with uniform motion/speed but the direction keeps changing (due to rotation).

if direction changes; velocity of particles will also change because velocity is a vector quantity.

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Answer 2

(c) different linear velocities and same angular velocities

Explanation:

During the rotation of a rigid body the particles of the body executing the motion are in the variable linear motion and also posses the angular velocity.

As we know that the linear velocity of a rotating body is given as :

$v=r\times \omega$

where:

v= linear velocity of the partilcle

r= radial distance of the particle form the center of rotation

So, more precisely the particles at same radial distance will have same linear velocity but the angle trace by all the particles in a certain time is equal, hence their angular velocity is equal.

Angular velocity is given as:

$\omega=\frac{\theta}{t}$

where:

$\theta=$ angle traced by the particle

t= time taken

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TOPIC: angular motion

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