Exam 11: Rotational Dynamics and Static Equilibrium

A man is holding an 8.00-kg vacuum cleaner at arm's length, a distance of 0.550 m from his shoulder. What is the torque on the shoulder joint if the arm is horizontal?

FIGURE 11-2 -A croquet mallet balances when suspended from its center of mass, as shown in Figure 11-2. If you cut the mallet in two at its center of mass, as shown, how do the masses of the two pieces compare?

A puck moves on a horizontal air table. It is attached to a string that passes through a hole in the center of the table. As the puck rotates about the hole, the string is pulled downward very slowly and shortens the radius of rotation, so the puck gradually spirals in towards the center. What happens to the puck's linear speed?

Tightrope walkers often employ a long pole to help them retain their balance. What advantage is there to using a very flexible pole so that the ends droop?

A merry-go-round spins freely when Janice moves quickly to the center along a radius of the merry-go-round. It is true to say that

When you ride a bicycle, in what direction is the angular velocity of the wheels?

FIGURE 11-6 -A store's sign, with a mass of 20.0 kg and 3.00 m long, has its center of gravity at the center of the sign. It is supported by a loose bolt attached to the wall at one end and by a wire at the other end, as shown in Figure 11-6. The wire makes an angle of 25.0° with the horizontal. What is the tension in the wire?

If you stand with your back towards a wall and your heels touching the wall, you cannot lean over to touch your toes. Why?

A 1.8 kg solid disk pulley of radius 0.11 m rotates about an axis through its center. (a) What is its moment of inertia? (b) Starting from rest, a torque of 0.22 m-N will produce what angular acceleration?

A ballerina spins initially at 1.5 revolutions/second when her arms are extended. She then draws in her arms to her body and her moment of inertia becomes 0.88 kg- and her angular speed increases to 4.0 rev/s. Determine her initial moment of inertia.

A chain, 10.0 m in length and with a mass of 3.00 kg/m but negligible thickness, is wrapped around a spool with a radius of 25.0 cm and a moment of inertia (not including the chain) of 0.360 kg∙m². With 1.00 m of chain hanging over the side, the spool is released so that it can turn freely about its axle. What is the angular speed of the spool at the moment that 5.00 m of chain are hanging over the side?

FIGURE 11-9 -The L-shaped object shown in Figure 11-9 consists of the masses connected by light rods. How much work must be done to accelerate the object from rest to an angular speed of 3.25 rad/s about the y-axis?

The drive chain in a bicycle is applying a torque of 0.850 Nm to the wheel of the bicycle. The wheel has a moment of inertia of 0.100 kg∙m². What is the angular acceleration of the wheel?

In recent years, many planetary systems have been discovered around distant stars. This has been accomplished, not by direct observation of the planets themselves, but indirectly, by observing a wobbling motion in the star. Why is this wobbling motion evidence of a planet?

When a car decelerates, its front end goes down. Explain.

A heavy boy and a lightweight girl are balanced on a massless seesaw. If they both move forward so that they are one-half their original distance from the pivot point, what will happen to the seesaw?

Jane says that the magnitude of the torque exerted by a force of magnitude F is equal to the perpendicular distance from the axis of rotation r_⊥ multiplied by F, while Jason insists that it is equal to the distance from the axis of rotation r multiplied by the magnitude of the perpendicular component of the force, F_⊥. Who is right?

A horizontal 2.00-m long, 5.00-kg uniform beam that lies along the east-west direction is acted on by two forces. At the east end of the beam, a 200-N forces pushes downward. At the west end of the beam, a 200-N force pushed upward. What is the angular acceleration of the beam?

FIGURE 11-6 -A 5.00-m-long ladder, weighing 200 N, rests against a smooth vertical wall with its base on a horizontal rough floor, a distance of 1.20 m away from the wall. The center of mass of the ladder is 2.50 m from its base, and the coefficient of static friction between the ladder and the floor is 0.200. How far up the ladder, measured along the ladder, can a 600-N person climb before the ladder begins to slip?

FIGURE 11-3 -A mill grinds corn by means of a grinding wheel attached to a long horizontal axle that is hinged to a vertical rotating axle as shown in Figure 11-3. The rotation of the vertical axle forces the horizontal axle to follow it. Thus, the wheel moves in a circular path, and its motion makes it rotate. The wheel then crushes the corn in its path. The force exerted by the wheel on the corn is