Chapter 10
Conceptual Questions
1. When tightening a bolt, mechanics sometimes extend the length of a wrench handle by
slipping a section of pipe over the handle. Why could this procedure easily damage the bolt?
5. (a) Can you change the location of your body's center of mass? How? (b) Can you change
your body's moment of inertia? How?
8. (a) If the forces on an object balance, do the torques necessarily balance? (b) If the torques on
an object balance, do the forces necessarily balance? Illustrate your answers with clear examples.
10. True or false? In picking an axis about which to compute torques in rotational equilibrium, it
is nearly always best to choose an axis through the center of mass of the object. Explain your
reasoning.
15. If two spinning objects have the same angular momentum, will they necessarily have the
same rotational kinetic energy? If they have the same rotational kinetic energy, will they necessarily have the same angular momentum?
Problems
4. • In Figure 10.44, forces A, B, C, and D, each have magnitude 50 N and act at the same point
on the object, (a) What torque (magnitude and direction) does each of these forces exert on the
object about point PI (b) What is the total torque about point PI
8.•• A 750 gram grinding wheel 25.0 cm in diameter is in the shape of a uniform solid disk. (We
can ignore the small hole at the center.) When it is in use, it turns at a constant 220 rpm about an
axle perpendicular to its face through its center. When the power switch is turned off, you
observe that the wheel stops in 45.0 s with constant angular acceleration due to friction at the
axle. What torque does friction exert while this wheel is slowing down?
14. •• A thin, light string is wrapped around the rim of a 4.00 kg solid uniform disk that is 30.0
cm in diameter. A person pulls on the string with a constant force of 100.0 N tangent to the disk,
as shown in Figure 10.49. The disk is nor at-lacked to anything and is free to move and turn,
(a) Find the Pr°blem 14. angular acceleration of the disk about its center of mass and the linear
acceleration of its center of mass, (b) If the disk ii replaced by a hollow thin-walled cylinder of
the same mass, and diameter, what will be the accelerations in part (a)?
26• A woman with mass 50.0 kg is standing on the rim of a large disk that is rotating at 0.50
rev/s about an axis perpendicular to it through its center. The disk has a mass of 110 kg and a
radius of 4.0 m. Calculate the magnitude of the total angular momentum of the woman-plus-disk
system, assuming that you can treat the woman as a point.
27. •• A certain drawbridge can be modeled as a uniform 15,000 N bar, 12.0 m long, pivoted
about its lower end. When this bridge is raised to an angle of 60.0° above the horizontal, the
cable holding it suddenly breaks, allowing the bridge to fall. At the instant after the cable breaks,
(a) what is the torque on this bridge about the pivot and (b) at what rate is its angular momentum
changing?
29. • The spinning figure skater. The outstretched hands and arms of a figure skater preparing
for a spin can be considered a slender rod pivoting about an axis through its center. (See Figure
10.53.) When the skater's hands and arms are brought in and wrapped around his body to execute
the spin, the hands and arms can be considered a thin-walled hollow cylinder. His hands and
arms have a combined mass of 8.0 kg. When outstretched, they span 1.8 m; when wrapped, they
form a cylinder of radius 25 cm. The moment of inertia about the axis of rotation of the
remainder of his body is constant and equal to 0.40 kg • m2. If the skater's original angular speed
is 0.40 rev/s, what is his final angular speed?
40. •• Two people carry a heavy electric motor by placing it on a light board 2.00 m long. One
person lifts at one end with a force of 400.0 N, and the other lifts at the opposite end with a force
of 600.0 N. (a) Start by making a free-body diagram of the motor. (b) What is the weight of the
motor? (c) Where along the board is its center of gravity located?
46. • A uniform ladder 7.0 m long weighing 450 N rests with one end on the ground and the
other end against a perfectly smooth vertical wall. The ladder rises at 60.0° above the horizontal
floor. A 750 N painter finds that she can climb 2.75 m up the ladder, measured along its length,
before it begins to slip, (a) Make a free-body diagram of the ladder, (b) What force does the wall
exert on the ladder? (c) Find the friction force and normal force that the floor exerts on the
ladder.