Conceptual Questions

ssm Solution is in the Student Solutions Manual

| 1 | In the drawing, the flat triangular sheet ABC is lying in the plane of the paper. This sheet is going to rotate about an axis that also lies in the plane of the paper and passes through point A. Draw two such axes that are oriented so that points B and C will move on circular paths having the same radii.

| 2 | A pair of scissors is being used to cut a string. Does each blade of the scissors have the same angular velocity (both magnitude and direction) at a given instant? Give your reasoning.

| 3 | An electric clock is hanging on the wall in the living room. The battery is removed, and the second hand comes to a halt over a brief period of time. During this period, what is the direction of the angular acceleration of the second hand? Why?

| 4 | The earth rotates once per day about its axis. Where on the earth’s surface should you stand in order to have the smallest possible tangential speed? Justify your answer.

| 5 | ssm A thin rod rotates at a constant angular speed. Consider the tangential speed of each point on the rod for the case when the axis of rotation is perpendicular to the rod (a) at its center and (b) at one end. Explain for each case whether there are any points on the rod that have the same tangential speeds.

| 6 | A car is up on a hydraulic lift at a garage. The wheels are free to rotate, and the drive wheels are rotating with a constant angular velocity. Does a point on the rim of a wheel have (a) a tangential acceleration and (b) a centripetal acceleration? In each case, give your reasoning.

| 7 | Two points are located on a rigid wheel that is rotating with an increasing angular velocity about a fixed axis. The axis is perpendicular to the wheel at its center. Point 1 is located on the rim, and point 2 is halfway between the rim and the axis. At any given instant, which point (if either) has the greater (a) angular velocity, (b) angular acceleration, (c) tangential speed, (d) tangential acceleration, and (e) centripetal acceleration? Provide a reason for each of your answers.

| 8 | A building is located on the earth’s equator. Which has the greatest tangential speed due to the earth’s rotation, the top floor, the bottom floor, or neither? Justify your answer.

| 9 | ssm Section 5.6 discusses how the uniform circular motion of a space station can be used to create artificial gravity for the astronauts. This can be done by adjusting the angular speed of the space station, so the centripetal acceleration at the astronaut’s feet equals g, the magnitude of the acceleration due to gravity (see Figure 5-19). If such an adjustment is made, will the acceleration due to the artificial gravity be greater than, equal to, or less than g at the astronaut’s head? Account for your answer.

| 10 | It is possible, but not very practical, to build a clock in which the tips of the second hand, the minute hand, and the hour hand move with the same tangential speed. Explain why not.

| 11 | Explain why a point on the rim of a tire has an acceleration when the tire is on a car that is moving at a constant linear velocity.

| 12 | A bicycle is turned upside down, the front wheel is spinning (see the drawing), and there is an angular acceleration. At the instant shown, there are six points on the wheel that have arrows associated with them. Which of the following quantities could the arrows represent: (a) tangential velocity, (b) tangential acceleration, (c) centripetal acceleration? In each case, answer why the arrows do or do not represent the quantity.

| 13 | ssm Suppose that the speedometer of a truck is set to read the linear speed of the truck, but uses a device that actually measures the angular speed of the tires. If larger-diameter tires are mounted on the truck, will the reading on the speedometer be correct? If not, will the reading be greater than or less than the true linear speed of the truck? Why?

| 14 | The blades of a fan rotate more and more slowly after the fan is shut off. Eventually they stop rotating altogether. In such a situation, we sometimes assume that the angular acceleration of the blades is constant and apply the equations of rotational kinematics as an approximation. Explain why the angular acceleration can never really be constant in this kind of situation.

| 15 | Rolling motion is one example that involves rotation about an axis that is not fixed. Give three other examples. In each case, identify the axis of rotation and explain why it is not fixed.

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