Conceptual Questions

ssm Solution is in the Student Solutions Manual

| 1 | Sometimes, even with a wrench, one cannot loosen a nut that is frozen tightly to a bolt. It is often possible to loosen the nut by slipping a long pipe over the wrench handle. The purpose of the pipe is to extend the length of the handle, so that the applied force can be located farther away from the nut. Explain why this trick works.

| 2 | Explain (a) how it is possible for a large force to produce only a small, or even zero, torque, and (b) how it is possible for a small force to produce a large torque.

| 3 | A magnetic tape is being played on a cassette deck. The tension in the tape applies a torque to the supply reel. Assuming the tension remains constant during playback, discuss how this torque varies as the reel becomes empty.

| 4 | A flat rectangular sheet of plywood can rotate about an axis perpendicular to the sheet through one corner. How should a force (acting in the plane of the sheet) be applied to the plywood so as to create the largest possible torque? Give your reasoning.

| 5 | The drawing shows two tubes of toothpaste. The tubes themselves are the same, and the cap on each tube is threaded and must be removed by unscrewing it. However, one cap is advertised as being an “easy-off’ cap, the other being a normal cap. Using the concept of torque, explain why the “easy-off” cap is easier to unscrew than the normal cap.

| 6 | Suppose you are standing on a train, both feet together, facing a window. The front of the train is to your left. The train starts moving forward. To keep from falling, you slide your right foot out toward the rear of the train. Explain in terms of torque how this action keeps you from falling over.

| 7 | Starting in the spring, fruit begins to grow on the outer end of a branch on a pear tree. Explain how the center of gravity of the peargrowing branch shifts during the course of the summer.

| 8 | ssm The free-body diagram in the drawing shows the forces that act on a thin rod. The three forces are drawn to scale and lie in the plane of the paper. Are these forces sufficient to keep the rod in equilibrium, or are additional forces necessary? Explain.

| 9 | An A-shaped stepladder is standing on frictionless ground. The ladder consists of two sections joined at the top and kept from spreading apart by a horizontal crossbar. Draw a free-body diagram showing the forces that keep one section of the ladder in equilibrium.

| 10 | The drawing shows a wine rack for a single bottle of wine that seems to defy common sense as it balances on a table top. Treat the rack and wine bottle as a rigid body and draw the external forces that keep it in equilibrium. In particular, where must the center of gravity of the rigid body be located? Give your reasoning. (Hint: The physics here is the same as in Figure 9-10c.)

| 11 | A flat triangular sheet of uniform material is shown in the drawing. There are three possible axes of rotation, each perpendicular to the sheet and passing through one corner, A, B, or C. For which axis is the greatest net external torque required to bring the triangle up to an angular speed of 10.0 rad/s in 10.0 s, starting from rest? Explain, assuming that the net torque is kept constant while it is being applied.

| 12 | An object has an angular velocity. It also has an angular acceleration due to torques that are present. Therefore, the angular velocity is changing. What happens to the angular velocity if (a) additional torques are applied so as to make the net torque suddenly equal to zero and (b) all the torques are suddenly removed?

| 13 | The space probe in the drawing is initially moving with a constant translational velocity and zero angular velocity. (a) When the two engines are fired, each generating a thrust of magnitude T, will the translational velocity increase, decrease, or remain the same? Why? (b) Explain what will happen to the angular velocity.

| 14 | ssm Sit-ups are more difficult to do with your hands placed behind your head instead of on your stomach. Why?

| 15 | For purposes of computing the translational kinetic energy of a rigid body, its mass can be considered as concentrated at the center of mass. If one wishes to compute the body’s moment of inertia, can the mass be considered as concentrated at the center of mass? If not, why not?

| 16 | A thin sheet of plastic is uniform and has the shape of an equilateral triangle. Consider two axes for rotation. Both are perpendicular to the plane of the triangle, axis A passing through the center of the triangle and axis B passing through one corner. If the angular speed about each axis is the same, for which axis does the triangle have the greater rotational kinetic energy? Explain.

| 17 | Bob and Bill have the same weight and wear identical shoes. Keeping both feet flat on the floor and the body straight, Bob can lean over farther than Bill can before falling. Whose center of gravity is closer to the ground? Account for your answer.

| 18 | A hoop, a solid cylinder, a spherical shell, and a solid sphere are placed at rest at the top of an incline. All the objects have the same radius. They are then released at the same time. What is the order in which they reach the bottom? Justify your answer.

| 19 | A woman is sitting on the spinning seat of a piano stool with her arms folded. What happens to her (a) angular velocity and (b) angular momentum when she extends her arms outward? Justify your answers.

| 20 | Review Example 14 as an aid in answering this question. Suppose the ice cap at the South Pole melted and the water was distributed uniformly over the earth’s oceans. Would the earth’s angular velocity increase, decrease, or remain the same? Explain.

| 21 | The concept behind this question is discussed in Example 14. Many rivers, like the Mississippi River, flow from north to south toward the equator. These rivers often carry a large amount of sediment that they deposit when entering the ocean. What effect does this redistribution of the earth’s soil have on the angular velocity of the earth? Why?

| 22 | Example 14 provides background for this question. A cloud of interstellar gas is rotating. Because the gravitational force pulls the gas particles together, the cloud shrinks, and, under the right conditions, a star may ultimately be formed. Would the angular velocity of the star be less than, equal to, or greater than, the angular velocity of the rotating gas? Justify your answer.

| 23 | ssm A person is hanging motionless from a vertical rope over a swimming pool. She lets go of the rope and drops straight down. After letting go, is it possible for her to curl into a ball and start spinning? Justify your answer.

| 24 | The photograph shows a workman struggling to keep a stack of boxes balanced on a dolly. The man’s right foot is on the axle of the dolly. Assuming that the boxes are identical, which one creates the greatest torque with respect to the axle? Why?

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