Question

1. Calculate the rotational inertia of a 27.0 kg solid cylinder whose diameter is 0.24m about an axis of the cylinder.

2. A disk spins at a rate of 6000 radians every 10 minutes.

(a) What is the angular velocity of the disk in rad/s. (b) What is the angular velocity of the wheel in rpm (rotations per minute)?

3. A car wheel of radius 20 inches rotates at 8 revolutions per second on the highway. What is the angular speed of the tire?

Answer 1

1. Inertia of the solid cylinder:

$$I = \dfrac{MR^2}{2} = \dfrac{27kg\cdot (0.24m/2)^2}{2} \approx 0.19kg\cdot m^2$$

2a. There are 60 s in one minute. Angular velocity:

$$\omega = \dfrac{6000rad}{10min\cdot 60s/min} = 10rad/s$$

2b. One rotation is $2\pi$ radians. Thus, have:

$$\omega = \dfrac{6000rad\cdot \dfrac{1}{2\pi}r/rad}{10min} \approx 95rpm$$

3. The angular speed is $\omega =2\pi f$, where $f = 8rps$. Thus, have:

$$\omega = 2\pi \cdot 8 \approx 50 rad/s$$

Answer. 1) 0.19kg*m^2, 2a) 10 rad/s, 2b) 95 rpm, 3) 50 rad/s.