Answer to Question #289375 in Physics for Mikey

Question

2) After using your DVD player to watch a movie, you pressed the “stop” button, and the disc started to slow down. Initially, the disc is rotating at 30.0 rad/s, and then slos down at a constant rate of 10.0 rad/s². At the same time, line AB on the disc is at the x-axis as shown in the figure. (a) What is the angular velocity of the disc at t = 0.400 s? (b) Find the angle that line AB makes with the x-axis at the given time.

Answer 1

(a) The angular velocity of the disc is

$$\omega_f=\omega_i-\alpha t=26\text{ rad/s}.$$

(b) The angular displacement is

$$\Delta\theta=\omega_it-\dfrac{\alpha t^2}{2}=11.2\text{ rad}.$$