Question

A uniform rod rotates in a horizontal plane about a vertical axis through a point

which is 2 m away from its center. The rod is 8 m long, weighs 8 N, and rotates at 100

rev/minute. Calculate

(a) Its rotational inertia about the axis of rotation.

(b) The magnitude of its angular momentum about the axis.

Answer 1

(a) Its rotational inertia about the axis of rotation:

$$I=\frac1{12}mL^2+md^2,\\\space\\ I=\frac1{12}·\frac8{9.8}·8^2+\frac8{9.8}·2^2=7.6\text{ kg}·\text{m}^2.$$

(b) The magnitude of its angular momentum about the axis:

$$L=I\omega=I·2\pi n=4775\text{ kg}·\text{rad/s}.$$