Exam 11: Rotational Dynamics and Static Equilibrium

A 82.0 kg painter stands on a long horizontal board 1.55 m from one end. The 15.5 kg board is 5.50 m long. The board is supported at each end. (a) What is the total force provided by both supports? (b) With what force does the support, closest to the painter, push upward?

The drive chain in a bicycle is applying a torque of 0.850 Nm to the wheel of the bicycle. Treat the wheel as a hoop with a mass of 0.750 kg and a radius of 33.0 cm. What is the angular acceleration of the wheel?

A child runs and jumps tangentially onto an initially stationary playground merry-go-round. As a result, the merry-go-round begins to turn. Explain in terms of the child-merry-go-round system.

FIGURE 11-5 -An 82.0 kg-diver stands at the edge of a light 5.00-m diving board, which is supported by two pillars 1.60 m apart, as shown in Figure 11-5. Find the force exerted by pillar B.

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 x-axis?

As you are leaving a building, the door opens outward. If the hinges on the door are on your right, what is the direction of the angular velocity of the door as you open it?

When a car is weighed, it is allowed to move over a scale which records a reading as the front wheels go over the scale, and a second reading when the rear wheels go over the scale. The weight of the car is equal to

FIGURE 11-8 -A stepladder consists of two halves, hinged at the top, and connected by a tie rod which keeps the two halves from spreading apart. In this particular instance, the two halves are 2.50 m long, the tie rod is connected to the center of each half and is 70.0 cm long. An 800-N person stands 3/5 of the way up the stepladder, as shown in Figure 11-8. Neglecting the weight of the ladder, and assuming that the ladder is resting on a smooth floor, what is the tension in the tie rod? Note: To solve this problem you must "cut" the ladder in half and consider the equilibrium of forces and torques acting on each half of the ladder.

A person sits on a freely spinning lab stool (no friction). When this person extends her arms,

A mass of 355 g hangs from one end of a string that goes over a pulley with a moment of inertia of 0.0125 kg∙m² and a radius of 15.0 cm. A mass of 680 g hangs from the other end. When the masses are released, the larger mass accelerates downward, the lighter mass accelerates upward, and the pulley turns without the string slipping on the pulley. What is the acceleration of the masses?

In a lab experiment, a student brings up the rotational speed of a rotational motion apparatus to 30.0 rpm. She then allows the apparatus to slow down on its own, and counts 240 revolutions before the apparatus comes to a stop. The moment of inertia of the flywheel is 0.0850 kg∙m². What is the retarding torque on the flywheel?

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 an axis perpendicular to the x-y plane and passing through the origin?

FIGURE 11-7 -A child is trying to stack two uniform wooden blocks, 12 cm in length, so they will protrude as much as possible over the edge of a table, without tipping over, as shown in Figure 11-7. What is the maximum possible overhang distance?

The attraction of the Moon causes tides on Earth. Because of friction, tidal action slows the rotation of Earth. What happens to the angular momentum of the Earth-Moon system, and does this affect the motion of the moon?

A 40.0-kg child running at a speed 3.00 m/s jumps on a stationary playground merry-go-round at a distance 1.50 m from the axis of rotation of the merry-go-round. The child is traveling tangential to the edge of the merry-go-round which has a 600 kg∙m² moment of inertia about its axis of rotation as she is running. What is the angular speed of the merry-go-round after the child jumps on it?

A 15.0-kg child is sitting on a playground teeter-totter, 1.50 m from the pivot. What is the minimum distance, on the other side of the pivot, such that a 220-N force will make the child lift off the ground?

A 15.0-kg child is sitting on a playground teeter-totter, 1.50 m from the pivot. What force, applied 0.300 m on the other side of the pivot, is needed to make the child lift off the ground?