Answer to Question #172854 in Physics for allen

Question

A disk speeds up from rest at a constant rate of 4 rad/s2 (a) What is the final angular speed of the disk after 15sec? (b) How many revolutions will the disk go through during this time period?

Answer 1

(a) We can find the final angular speed of the disk after 15 sec as follows:

$$\omega=\omega_0+\alpha t,$$ $$\omega=0+4.0\ \dfrac{rad}{s^2}\cdot15\ s=60\ \dfrac{rad}{s}.$$

(b) Let's find the angle in radians that the disk rotates in 15 s from the kinematic equation:

$$\theta=\omega_0t+\dfrac{1}{2}\alpha t^2,$$ $$\theta=\dfrac{1}{2}\cdot4.0\ \dfrac{rad}{s^2}\cdot(15.0\ s)^2=450\ rad.$$

Then, we can find the number of revolutions the disk go through during this time period:

$$n=450\ rad\cdot\dfrac{1\ rev}{2\pi\ rad}=72\ rev.$$