Question

A disk is free to rotate about an axis perpendicular to the disk through its center. If the disk starts from rest and accelerates uniformly at the rate of 2 radians/S2 for 4 s, its angular displacement during this time is
(A) 6 radians
(B) 12 radians
(C) 16 radians
(D) 24 radians
(E) 48 radians

Answer 1

Answer:

(C) 16 radians

Explanation:

The angular displacement is given by the following equation:

$\Delta \theta=\omega_i t+\frac{1}{2}\alpha t^2$

Here

$\Delta \theta$ Is the angular displacement of the body at the indicated time (t).

$\omega_i$ Is the angular velocity of the body at the initial moment.

$\alpha$ Is the angular acceleration of the body.

The disk starts from rest, so $\omega_i=0$

Replacing the given values:

$\Delta \theta=\frac{1}{2}(2\frac{radians}{s^2})(4s)^2\\\Delta \theta=16 radians$