Question

a bicycle wheel turns with constant angular accceleration of 0.64 rad/s²:

a) how much time does it take to reach an angular velocity of 8 rad/sec starting from rest?

b) how many revolutions does the wheel turn in this time interval?

Answer 1

(a)

$$\omega=\omega_0+\beta t$$

$$t=\frac{\omega-\omega_0}{\beta}=\frac{8-0}{0.64}=12.5\;\rm s$$

(b)

$$N=\frac{\theta}{2\pi}=\frac{\omega+\omega_0}{2*2\pi}t$$

$$N=\frac{8+0}{2*2\pi}*12.5=8$$