Chapter 12: Rotation of a Rigid Body

How fast, in rpm, would a $5.0kg22cm$diameter bowling ball have to spin to have an angular momentum of $0.23{\mathrm{kgm}}^2/\mathrm{s}$?

A V $2.0\mathrm{kg},20-\mathrm{cm}$-diameter turntable rotates at $100rpm$on frictionless bearings. Two $500g$blocks fall from above, hit the turntable simultaneously at opposite ends of a diameter, and stick. What is the turntable's angular velocity, in rpm, just after this event?

A 75 g, 6.0-cm-diameter solid spherical top is spun at 1200 rpm on an axle that extends 1.0 cm past the edge of the sphere. The tip of the axle is placed on a support. What is the top’s precession frequency in rpm?

A toy gyroscope has a ring of mass M and radius R attached to the axle by lightweight spokes. The end of the axle is distance R from the center of the ring. The gyroscope is spun at angular velocity v, then the end of the axle is placed on a support that allows the gyroscope to precess. a. Find an expression for the precession frequency Ω in terms of M, R, v, and g. b. A 120 g, 8.0-cm-diameter gyroscope is spun at 1000 rpm and allowed to precess. What is the precession period?

A $300g$ball and a $600g$ball are connected by a $40cm$-long massless, rigid rod. The structure rotates about its center of mass at $100rpm$. What is its rotational kinetic energy?

How far from the center of the earth is the center of mass of the earth +moon system? Data for the earth and moon can be found inside the back cover of the book.

The center of mass of the Earth-Moon system from the center of the Earth is $4.67\times {10}^6\text{m}$.

An 800 g steel plate has the shape of the isosceles triangle shown in FIGURE P12.50. What are the x- and y-coordinates of the center of mass?
Hint: Divide the triangle into vertical strips of width dx, then relate the mass dm of a strip at position x to the values of x and dx.

Determine the moment of inertia about the axis of the object shown in FIGURE P12.51.

What is the moment of inertia of a 2.0 kg, 20-cm-diameter disk for rotation about an axis

(a) through the center, and
(b) through the edge of the disk?

Calculate by direct integration the moment of inertia for a thin rod of mass M and length L about an axis located distance d from one end. Confirm that your answer agrees with Table 12.2 when d = 0 and when d = L /2.