Chapter 12: Rotation of a Rigid Body

Calculate the moment of inertia of the rectangular plate in FIGURE P12.54 for rotation
about a perpendicular axis through the center.

a. A disk of mass M and radius R has a hole of radius r centered on the axis. Calculate the moment of inertia of the disk.
b. Confirm that your answer agrees with Table 12.2 when r = 0 and when r = R.
c. A 4.0-cm-diameter disk with a 3.0-cm-diameter hole rolls down a 50-cm-long, 20^o ramp. What is its speed at the bottom? What percent is this of the speed of a particle
sliding down a frictionless ramp?

Consider a solid cone of radius R, height H, and mass M. The volume of a cone is 1/3 πHR²

a. What is the distance from the apex (the point) to the center of mass?
b. What is the moment of inertia for rotation about the axis of the cone?
Hint: The moment of inertia can be calculated as the sum of the moments of inertia of lots of small pieces.

A person’s center of mass is easily found by having the person lie on a reaction board. A horizontal, 2.5-m-long, 6.1 kg reaction board is supported only at the ends, with one end resting on a scale and the other on a pivot. A 60 kg woman lies on the reaction board with her feet over the pivot. The scale reads 25 kg. What is the distance from the woman’s feet to her center of mass?

3.0-m-long ladder, as shown in Figure 12.35, leans against a frictionless wall. The coefficient of static friction between the ladder and the floor is 0.40. What is the minimum angle the
ladder can make with the floor without slipping?

In Figure P12.59, an 80 kg construction worker sits down 2.0 m from the end of a 1450 kg
steel beam to eat his lunch. What is the tension in the cable?

The three masses shown in FIGURE EX12.6 are connected by massless, rigid rods. What are the coordinates of the center of mass?

A 40 kg, 5.0-m-long beam is supported by, but not attached to, the two posts in Figure P12.60. A 20 kg boy starts walking along the beam. How close can he get to the right end of the beam without it falling over?

Your task in a science contest is to stack four identical uniform bricks, each of length L, so that the top brick is as far to the right as possible without the stack falling over. Is it possible, as Figure P12.61 shows, to stack the bricks such that no part of the top brick is over the table? Answer this question by determining the maximum possible value of d.

A 120-cm-wide sign hangs from a 5.0 kg, 200-cm-long pole. A cable of negligible mass supports the end of the rod as shown in Figure P12.62. What is the maximum mass of the sign if the maximum tension in the cable without breaking is 300 N?