Exam 11: Rotational Dynamics and Static Equilibrium

A meter stick balances at the 50.0-cm mark. If a mass of 50.0 g is placed at the 90.0-cm mark, the stick balances at the 61.3-cm mark. What is the mass of the meter stick?

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 magnitude of the force exerted by the bolt on the sign?

FIGURE 11-2 -Angular momentum cannot be conserved if

FIGURE 11-6 -A 3.00-m-long ladder, weighing 200 N, rests against a smooth vertical wall with its base on a horizontal rough floor, a distance of 1.00 m away from the wall. If the center of mass of the ladder is 1.20 m from its base, what frictional force must the floor exert on the base of the ladder in order for the ladder to be in static equilibrium?

Why is it recommended that if you are lifting a heavy object you should lift it as close to your body as possible?

Two equal forces are applied to a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

A mass of 375 g hangs from a string that is wrapped around the circumference of a pulley with a moment of inertia of 0.0125 kg∙m² and a radius of 26.0 cm. When the mass is released, the mass accelerates downward and the pulley rotates about its axis as the string unwinds. What is the tension in the string?

FIGURE 11-2 -A figure skater is spinning slowly with arms outstretched. She brings her arms in close to her body and her moment of inertia decreases by 1/2. By what factor does her rotational kinetic energy change?

A truck is carrying a 120-kg refrigerator, which is 2.20 m tall and 85.0 cm wide has its center of mass at its geometrical center. The refrigerator is facing sideways and a short strip on the bed of the truck keeps the refrigerator from sliding. What is the maximum acceleration that the truck can have before the refrigerator begins to tip over?

A diver can change her rate of rotation in the air by "tucking" her head in and bending her knees. Let's assume that when she is stretched out straight she is rotating at 1 revolution per second. Now she goes into the "tuck and bend," effectively shortening the length of her body by half. What will her rate of rotation be now?

A uniform meter stick with a mass of 135 g rotates about an axis perpendicular to the stick passing through the center of the stick with an angular speed of 3.50 rad/s². What is the magnitude of the angular momentum of the stick?

Two forces are applied to a doorknob, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of the second is

The wheelbase on a truck is 2.4 m wide and the truck's center of mass is located along the vertical centerline of the truck and 2.0 m above the bottom of the tires. The truck is going around a banked turn, when it is forced to stop. What is the maximum slope that the bank can have such that the truck will not tip over?

FIGURE 11-1 -The rotating systems shown in Figure 11-1 differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left), or a distance r/2 from the axis of rotation (right). If you release the hanging blocks simultaneously from rest, and call t_L the time taken by the block on the left and t_R the time taken by the block on the right to reach the bottom, respectively, then

You are walking holding on to the axle of a spinning bicycle wheel with one hand on either side of the wheel. The top part of the wheel is moving away from you and the bottom is moving toward you and the axle is horizontal. As you start to turn left, you feel the right side of the axle

If the net force on an object is zero N, does the net torque on the object have to be zero Nm?

A 3.50-g bullet, traveling at 250 m/s, hits a hinged, light board at right angles, at a distance of 55.0 cm from its hinges, and emerges on the other side of the board with a speed of 150 m/s. The board is initially stationary but is free to rotate about its hinges and has a moment of inertia of 0.275 kg∙m². What is the angular speed of the board after the bullet emerges?

A 320-g mass and a 400-g mass are attached to the two ends of a string that goes over a pulley with a radius of 8.70 cm. Because of friction, the pulley does not begin to rotate. What is the magnitude of the frictional torque on the bearing of the pulley if the system is in static equilibrium?

The wheelbase on a 50,000-kg truck is 2.40 m wide and the truck's center of mass is located along the vertical centerline of the truck and 2.00 m above the bottom of the tires. The truck is going around a horizontal turn with a radius of 180 m. What is the maximum speed at which the truck can go around the curve without some of its tires lifting off the road?

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 held at 30.0° below the horizontal?