Answer to Question #118118 in Classical Mechanics for Lizwi

Question

A horizontal disk rotates about a vertical axis through its center. Point P is midway between the center and the rim of the disk, and point Q is on the rim. If the disk turns with constant angular velocity, which of the following statements about it are true? (There may be more than one correct choice.)
1 : P and Q have the same linear acceleration.
2 : Q is moving twice as fast as P.
3 : The linear acceleration of Q is twice as great as the linear acceleration of P.
4 : The linear acceleration of P is twice as great as the linear acceleration of Q.
5 : The angular velocity of Q is twice as great as the angular velocity of P.

Answer 1

Linear acceleration is given by $\alpha r$ and linear velocity is given by $\omega r$

Hence the disk is rotating with constant angular velocity hence $\alpha=0$ which means linear acceleration of all particles on the disc will be equal to zero

linear velocity is dependent on r so greater the r greater the linear velocity

Here Q is at distance twice than that of distance of P from the center hence linear velocity of Q will be twice of P

Hence 1 and 2 are correct