Chapter 9 physics

Two uniform solid balls are placed side by side at the top of an incline plane and, starting from rest, are allowed to roll down the incline. Which ball, if either, has the greater translational speed at the bottom if (a) they have the same radii, but one is more massive than the other; and (b) they have the same mass, but one has a larger radius? (a) the ball with the smaller mass (b) the ball with the larger radius (a) neither (b) neither (a) the ball with the greater mass (b) the ball with the larger radius (a) the ball with the smaller mass (b) the ball with the smaller radius (a) the ball with the greater mass (b) the ball with the smaller radius

(a) neither (b) neither

Three forces (magnitudes either F or 2F) act on each of the thin, square sheets shown in the drawing. In parts A and B of the drawing, the force labeled acts at the center of the sheet. When considering angular acceleration, use an axis of rotation that is perpendicular to the plane of a sheet at its center. Determine in which drawing (a) the translational acceleration is equal to zero, but the angular acceleration is not equal to zero; (b) the translational acceleration is not equal to zero, but the angular acceleration is equal to zero; and (c) both the translational and angular accelerations are zero. (a) part A (b) part C (c) part B (a) part B (b) part C (c) part A (a) part A (b) part B (c) part C (a) part C (b) part A (c) part B

(a) part C (b) part A (c) part B

At a given instant an object has an angular velocity. It also has an angular acceleration due to torques that are present. Therefore, the angular velocity is changing. Does the angular velocity at this instant increase, decrease, or remain the same (a) if additional torques are applied so as to make the net torque suddenly equal to zero and (b) if all the torques are suddenly removed? (a) remain the same (b) remain the same (a) remain the same (b) increase (a) remain the same (b) decrease (a) increase (b) remain the same (a) decrease (b) remain the same

(a) remain the same (b) remain the same

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, does the translational velocity increase, decrease, or remain the same? (b) Does the angular velocity increase, decrease, or remain the same? (a) remain the same (b) remain the same (a) remain the same (b) increase (a) remain the same (b) decrease (a) increase (b) remain the same (a) decrease (b) remain the same

(a) remain the same (b) remain the same

Is it possible (a) for a large force to produce a small, or even zero, torque and (b) for a small force to produce a large torque? (a) yes (b) yes (a) yes (b) no (a) no (b) yes (a) no (b) no

(a) yes (b) yes

A wrench is used to tighten a nut as shown in the figure. A 12-N force is applied 7.0 cm from the axis of rotation. What is the magnitude of the torque due to the applied force? 14 N m 58 N m 0.58 N m 0.84 N m 1.71 N m

0.84 N m

A hoop is rolling (without slipping) on a horizontal surface so it has two types of kinetic energy: translational kinetic energy and rotational kinetic energy. The entire mass M of the hoop is concentrated at its rim, so its moment of inertia is I = MR2, where R is the radius. What is the ratio of the translational kinetic energy to the rotational kinetic energy? 4 2 1

1

The drawing shows a top view of a door that is free to rotate about an axis of rotation that is perpendicular to the screen. Find the net torque (magnitude and direction) produced by the forces F1 and F2 about the axis. 28.5 N·m, counterclockwise 23.3 N·m, counterclockwise 9.3 N·m, counterclockwise 23.3 N·m, clockwise 9.3 N·m, clockwise

23.3 N·m, counterclockwise

A string is tied to a doorknob 0.72 m from the hinge as illustrated in the figure. At the instant shown, the force applied to the string is 5.0 N. What is the magnitude of the torque on the door? 0.60 N m 2.1 N m 1.0 N m 0.78 N m 3.0 N m

3.0 N m

Five hockey pucks are sliding across frictionless ice. The drawing shows a top view of the pucks and the three forces that act on each one. The forces can have different magnitudes (F, 2F, or 3F), and can be applied at different points on the puck. Only one of the five pucks could be in equilibrium. Which one? 5 1 3 2 4

4

A solid sphere of radius R rotates about a diameter with an angular speed . The sphere then collapses under the action of internal forces to a final radius R/2. What is the final angular speed of the sphere? 4w w/4 2w w/2 w

4w

Three massless rods (A, B, and C) are free to rotate about an axis at their left end (see the drawing). The same force is applied to the right end of each rod. Objects with different masses are attached to the rods, but the total mass (3m) of the objects is the same for each rod. Rank the angular acceleration of the rods, largest to smallest. C, B, A A, B, C B, C, A B, A, C

A, B, C

The drawing shows three objects rotating about a vertical axis. The mass of each object is given in terms of m0, and its perpendicular distance from the axis is specified in terms of r0. Rank the three objects according to their moments of inertia, largest to smallest. B, C, A C, A, B A, B, C A, C, B B, A, C

A, C, B

Two hoops, starting from rest, roll down identical inclined planes. The work done by nonconservative forces, such as air resistance, is zero (Wnc = 0 J). Both have the same mass M, but, as the drawing shows, one hoop has twice the radius as the other. The moment of inertia for each hoop is I = Mr2, where r is its radius. Which, if either, has the greater total kinetic energy (translational plus rotational) at the bottom of the incline? The smaller hoop. Both have the same total kinetic energy. The larger hoop.

Both have the same total kinetic energy.

Therefore, since τ = Fl, lengthening the wrench (increasing l) decreases the force needed to generate a fixed torque. For instance, suppose the person must produce a 4 N.m torque. If the wrench is .1 m long, then he must apply a 40 N force. But if the wrench is .2 m long, he needs only a 20 N force. Student 1 is: Correct, even though the torque that the wrench must exert to lift the block doesn't depend on the wrench's length. Correct, because using a longer wrench decreases the torque it must exert on the winch. Incorrect, because the torque that the wrench must exert to lift the block doesn't depend on the wrench's length. Incorrect, because using a longer wrench decreases the torque it must exert on the winch.

Correct, even though the torque that the wrench must exert to lift the block doesn't depend on the wrench's length.

The drawing shows a wine rack for a single bottle of wine that seems to defy common sense as it balances on a tabletop. Where is the center of gravity of the combined wine rack and bottle of wine located? At the neck of the bottle where it passes through the wine rack Directly above the point where the wine rack touches the tabletop At a location to the right of where the wine rack touches the tabletop

Directly above the point where the wine rack touches the tabletop

Under what condition(s) is the angular momentum of a rotating body, such as a spinning ice skater, conserved? Each external force acting on the body must be zero. Each external force and each external torque acting on the body must be zero. Each external force may be non-zero, but the sum of the forces must be zero. Each external torque may be non-zero, but the sum of the torques must be zero.

Each external torque may be non-zero, but the sum of the torques must be zero.

An object, which is considered a rigid body, is not in equilibrium. Which one of the following statements must be true concerning the magnitude of the angular acceleration α and translational acceleration a of the object? a > 0 m/s2, but α = 0 rad/s2 α > 0 rad/s2, but a > 0 m/s2 Either α > 0 rad/s2 or a > 0 m/s2 α = 0 rad/s2 and a = 0 m/s2 α > 0 rad/s2, but a = 0 m/s2

Either α > 0 rad/s2 or a > 0 m/s2

The meter stick in the drawing can rotate about an axis located at the 20.0-cm mark. The axis is perpendicular to the screen. A force F acts at the left end; the force is perpendicular to the meter stick and has a magnitude of 175 N. A second force, either F1 or F2, acts at the 80.0-cm mark, as the drawing shows. The meter stick is in equilibrium. Which force, F1 or F2, acts on the meter stick, and what is its magnitude? F2, magnitude = 58.3 N F2, magnitude = 102 N F2, magnitude = 71.2 N F1, magnitude = 102 N F1, magnitude = 71.2 N

F2, magnitude = 71.2 N

What happens when a spinning ice skater draws in her outstretched arms? Her moment of inertia decreases causing her to spin faster. Her moment of inertia decreases causing her to slow down. Her angular momentum decreases. The torque that she exerts increases her moment of inertia. Her angular momentum increases.

Her moment of inertia decreases causing her to spin faster.

Which one of the following statements concerning the moment of inertia I is false? I depends on the angular acceleration of the object as it rotates. Of the particles that make up an object, the particle with the smallest mass may contribute the greatest amount to I. I may be expressed in units of kg m2. I depends on the orientation of the rotation axis relative to the particles that make up the object. I depends on the location of the rotation axis relative to the particles that make up the object.

I depends on the angular acceleration of the object as it rotates.

Which one of the following statements most accurately describes the center of gravity of an object? It is the point where all the mass is concentrated. It is the point on the object where all the weight is concentrated. It is the only point where gravity acts on the object. It is the point from which the torque produced by the weight of the object can be calculated. It must be experimentally determined for all objects.

It is the point from which the torque produced by the weight of the object can be calculated.

Starting in the spring, fruit begins to grow on the outer end of a branch on a pear tree. As the fruit grows, which of the following is true for the center of gravity of the pear-growing branch? It moves toward the pears at the end of the branch. It moves away from the pears. It does not move at all.

It moves toward the pears at the end of the branch.

Which one of the following expressions allows one to calculate the angular momentum for a rigid body about a fixed axis? 2Iω (1/2)MRv2 (1/2)MR2 (1/2)Iω2 Iω

Iω

Consider the drawing. A small disk with a radius r shares an axis with a wheel of radius 4r. An object of mass M1 hangs from a rope that is attached and wrapped around the wheel as shown. Another object of mass M2 hangs from a rope that is attached and wrapped around the disk as shown. Which one of the following conditions must be true if this system is in equilibrium? M1>M2 M1=M2 M1<M2

M1<M2

Which of the following is true about students 2 and 3? Students 2 and 3 are both correct. Student 2 is correct, but student 3 is incorrect. Student 3 is correct, but student 2 is incorrect. Students 2 and 3 are both incorrect.

Students 2 and 3 are both incorrect.

A ball moves in a circular path on a horizontal, frictionless surface as shown. It is attached to a light string that passes through a hole in the center of the table. If the string is pulled down, thereby reducing the radius of the path of the ball, the speed of the ball is observed to increase. Which one of the following statements provides an explanation for this increase? When the string is pulled downward, the angular momentum must increase. The linear momentum of the ball is conserved in this process. The angular momentum of the ball is conserved in this process. This follows directly from applying Newton's third law of motion. The total mechanical energy of the ball must remain constant because energy is conserved.

The angular momentum of the ball is conserved in this process.

A child standing on the edge of a freely spinning merry-go-round moves quickly to the center. Which one of the following statements is necessarily true concerning this event and why? The angular speed of the system increases because the moment of inertia of the system has increased. The angular speed of the system increases because the moment of inertia of the system has decreased. The angular speed of the system remains the same because the net torque on the merry-go-round is zero N · m. The angular speed of the system decreases because the moment of inertia of the system has increased. The angular speed of the system decreases because the moment of inertia of the system has decreased.

The angular speed of the system increases because the moment of inertia of the system has decreased.

The wheels on a moving bicycle wheel have both translational (or linear) and rotational motions. What is meant by the phrase "a rigid body, such as a bicycle wheel, is in equilibrium?" The body cannot have translational motion, but it can have rotational motion. The body can have translational and rotational motions, as long as its translational acceleration and angular acceleration are zero. The body cannot have translational or rotational motion of any kind. The body can have translational motion, but it cannot have rotational motion.

The body can have translational and rotational motions, as long as its translational acceleration and angular acceleration are zero.

The drawing shows a top view of a square box lying on a frictionless floor. Three forces, which are drawn to scale, act on the box. Consider an angular acceleration with respect to an axis through the center of the box (perpendicular to the screen). Which one of the following statements is correct? The box will have both a translational and an angular acceleration. The box will have an angular acceleration, but not a translational acceleration. The box will have neither a translational nor an angular acceleration. It is not possible to determine whether the box will have a translational or an angular acceleration. The box will have a translational acceleration, but not an angular acceleration.

The box will have an angular acceleration, but not a translational acceleration.

A force is applied to a doorknob. This force will be most effective in causing the door to rotate when which of the following is true? The lever arm is parallel to the direction of the force. The direction of the force is at an angle of 90° with respect to the door. The lever arm length is zero meters. The lever arm is perpendicular to the door. The direction of the force is at an angle of 45° with respect to the door.

The direction of the force is at an angle of 90° with respect to the door.

A flat disk, a solid sphere, and a hollow sphere each have the same mass m and radius r. The three objects are arranged so that an axis of rotation passes through the center of each object. The rotation axis is perpendicular to the plane of the flat disk. Which of the three objects has the largest moment of inertia? The solid sphere and hollow sphere have the same moment of inertia; and it is the largest. The hollow sphere has the largest moment of inertia. The solid sphere has the largest moment of inertia. The flat disk has the largest moment of inertia. The flat disk and hollow sphere have the same moment of inertia; and it is larger than that of the solid sphere.

The hollow sphere has the largest moment of inertia.

An object, which is considered a rigid body, is in equilibrium. Which one of the following statements is false when determining the forces and torques acting on the object? The linear acceleration and/or the angular acceleration of the object may not be equal to zero. The sum of the torques due to external forces must equal zero N · m. The location of the rotational axis is arbitrary. Therefore, it can be placed at any point on the object that is convenient. A free body diagram of the external forces acting on the object is useful in analyzing this situation. In placing an x-y coordinate system on the object, the +x direction is arbitrary and it can be directed toward any direction that is convenient.

The linear acceleration and/or the angular acceleration of the object may not be equal to zero.

Which one of the following statements concerning the moment of inertia is false? The moment of inertia depends on the angular acceleration of the object as it rotates. The moment of inertia depends on the orientation of the rotation axis relative to the particles that make up the object. Of the particles that make up an object, the particle with the smallest mass may contribute the greatest amount to the moment of inertia. The moment of inertia depends on the location of the rotation axis relative to the particles that make up the object. The moment of inertia may be expressed in units of kg · m2.

The moment of inertia depends on the angular acceleration of the object as it rotates.

Two uniform solid spheres, A and B have the same mass. The radius of sphere B is twice that of sphere A. The axis of rotation passes through the center of each sphere. Which one of the following statements concerning the moments of inertia of these spheres is true? The moment of inertia of A is 5/4 that of B. The moment of inertia of A is 5/2 that of B. The moment of inertia of A is one-half that of B. The two spheres have equal moments of inertia. The moment of inertia of A is one-fourth that of B.

The moment of inertia of A is one-fourth that of B.

Two solid spheres have the same mass, but one is made from lead and the other from wood. How do the moments of inertia of the two spheres compare? The moment of inertia of the lead sphere is greater than that of the one made of wood. The moment of inertia of the wood sphere is the same as that of the one made of lead. The moment of inertia of the wood sphere is greater than that of the one made of lead. There is no way to compare the spheres without knowing their radii.

The moment of inertia of the wood sphere is greater than that of the one made of lead.

The same force F is applied to the edge of two hoops. The hoops have the same mass, although the radius of the larger hoop is twice that of the smaller one. The entire mass of each hoop is concentrated at its rim, so the moment of inertia is I = Mr2, where M is the mass and r is the radius. Which hoop has the greater angular acceleration, and how many times as great is it compared to that of the other hoop? The smaller hoop; two times as great. Both have the same angular acceleration. The smaller hoop; four times as great. The larger hoop; two times as great. The larger hoop; four times as great.

The smaller hoop; two times as great.

A spinning star begins to collapse under its own gravitational pull. Which one of the following occurs as the star becomes smaller? The star's angular velocity remains constant. Both the star's angular momentum and its angular velocity remain constant. The star's angular velocity decreases. The star's angular momentum increases. The star's angular momentum remains constant.

The star's angular momentum remains constant.

An object is rolling, so its motion involves both rotation and translation. Which one of the following statements must be true concerning this situation? The rotational kinetic energy must be constant as the object rolls. The gravitational potential energy must be changing as the object rolls. The total mechanical energy is equal to the sum of the translational kinetic energy and the gravitational potential energy of the object. The total mechanical energy is equal to the sum of the translational and rotational kinetic energies plus the gravitational potential energy of the object. The translational kinetic energy may be equal to zero joules.

The total mechanical energy is equal to the sum of the translational and rotational kinetic energies plus the gravitational potential energy of the object.

A solid cylinder is rolling along a flat, horizontal plane. The center of mass of the cylinder is moving toward the south at constant velocity. Which one of the following statements concerning the translational and rotational kinetic energies of the cylinder is true? The sum of the translational and rotational kinetic energies equals zero joules. The translational kinetic energy is greater than the rotational kinetic energy. The translational kinetic energy is less than the rotational kinetic energy. The translational kinetic energy is equal to the rotational kinetic energy. The sum of the translational and rotational kinetic energies equals the gravitational potential energy of the cylinder

The translational kinetic energy is greater than the rotational kinetic energy.

Which one of the following descriptions indicates that the object is in translational equilibrium? Translational equilibrium occurs only if the object is at rest. Translational equilibrium occurs only if the object is at moving with constant (but not zero) velocity. Translational equilibrium occurs if the object is at rest or moving with constant velocity. Translational equilibrium occurs only if the object is moving with constant acceleration. Translational equilibrium occurs if the object is moving with constant velocity or with constant acceleration.

Translational equilibrium occurs if the object is at rest or moving with constant velocity.

A compact disc rotates about its center at constant angular speed. Which one of the following quantities is constant and non-zero for a dust particle near the edge of the disc? torque about the center of the disc centripetal acceleration angular acceleration angular momentum linear velocity

angular momentum

A woman is sitting on a spinning seat of a piano stool with her arms folded. Ignore any friction in the spinning stool. What happens to her angular velocity and angular momentum when she extends her arms outward? angular velocity changes and angular momentum changes angular velocity changes and angular momentum remains the same both remain the same

angular velocity changes and angular momentum remains the same

Complete the following statement: When a net torque is applied to a rigid object, it always produces a rotational equilibrium. change in angular velocity. constant angular velocity. constant acceleration. constant angular momentum.

change in angular velocity.

Review Conceptual Exercise 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? increase decrease remain the same

decrease

Complete the following statement: When determining the net torque on a rigid body, only the torques due to internal forces are considered. forces that form action-reaction pairs as in applying Newton's third law of motion are considered. only forces that are either parallel or perpendicular to the lever arm are considered. both internal and external forces are considered. external forces are considered.

external forces are considered.

If several wrenches all apply the same torque to a nut, which graph best expresses the relationship between the force the person must apply to the wrench, and the length of the wrench? graph A graph B graph C graph D

graph D

Conceptual 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? less than greater than equal t

greater than

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 one end of a long pipe over the wrench handle and pushing at the other end of the pipe. With the aide of the pipe, does the applied force produce a smaller torque, a greater torque, or the same torque on the nut? smaller torque greater torque same torque

greater torque

Which one of the following choices represents the SI units for angular momentum? kg · m2/s kg · m · rad/s2 kg · m2/s2 kg · rad/s2 kg · m/s2

kg · m2/s

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 (fastest first)? shell, hoop, cylinder, solid sphere hoop, cylinder, shell, solid sphere solid sphere, cylinder, shell, hoop cylinder, shell, solid sphere, hoop

solid sphere, cylinder, shell, hoop

The moment of inertia of a wheel about its axle does not depend on which one of the following properties? the diameter of the wheel the angular velocity of the wheel as it rotates the location of the particles that compose the wheel the mass of the wheel

the angular velocity of the wheel as it rotates

A hollow cylinder of mass M and radius R rolls down an inclined plane. A block of mass M easily slides down an identical inclined plane. Complete the following statement: If both objects are released at the same time from the top of their inclined planes, the block will reach the bottom first. the block will reach the bottom with the greater kinetic energy. the cylinder will reach the bottom first. the cylinder will reach the bottom with the greater kinetic energy. both the block and the cylinder will reach the bottom at the same time.

the block will reach the bottom first.

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? the box farthest to the right at the bottom the box in the middle at the top the box at the bottom closest to his right foot the box farthest to the left at the top

the box farthest to the right at the bottom

Consider the following four objects: a hoop, a flat disk, a solid sphere, and a hollow sphere. Each of the objects has mass M and radius R. The axis of rotation passes through the center of each object, and is perpendicular to the plane of the hoop and the plane of the flat disk. Which of these objects requires the largest torque to give it the same angular acceleration? the solid sphere the hoop the hollow sphere the flat disk both the solid and the hollow spheres

the hoop

The drawing illustrates an overhead view of a door and its axis of rotation. The axis is perpendicular to the screen. There are four forces acting on the door, and they have the same magnitude. Rank the torque τ that each force produces, largest to smallest. τ2, τ3 and τ4 (a two-way tie), τ1 τ2, τ4, τ3, τ1 τ1, τ4, τ3, τ2 τ4, τ3, τ2, τ1 τ3, τ2, τ1 and τ4 (a two-way tie)

τ3, τ2, τ1 and τ4 (a two-way tie)