Question

A disk with a diameter of 30 cm speeds up from 20 rad/s to 40 rad/s in 20s. (a) How many revolutions will the disk go through during that time period? (b.) What is the average linear acceleration of the disk?

Answer 1

(a)

$$N=\frac{\theta}{2\pi}=\frac{1}{2\pi}\frac{\omega_f+\omega_i}{2}t$$

$$N=\frac{1}{2\pi}\frac{40+20}{2}*20=96\:\rm rev$$

(b)

$$\alpha=\frac{\omega_f-\omega_i}{t}=\frac{40-20}{20}=1\:\rm rad/s^2$$

$$a=\alpha R=1\:\rm rad/s^2*0.15\: m=0.15\: m/s^2$$