To download the complete and accurate content document, go to: https://testbankbell.com/download/test-bank-for-college-physics-7th-edition-jerry-d-wil son/
1) State the difference between pure translational and pure rotational motion.
Answer: If an object has only (pure) translational motion every particle in it has the same instantaneous velocity, which means that the object is not rotating. An object may have only (pure) rotational motion - motion about a fixed axis if all of the particles of the object have the same instantaneous angular velocity and travel in circles about the axis of rotation.
Diff: 1 Var: 1 Page Ref: Sec. 8.1
2) A car is traveling along a highway at 65 mph. Which point in the tires is moving forward at 65 mph?
Answer: the center of the tire
Diff: 1 Var: 1 Page Ref: Sec. 8.1
3) A car is traveling along a highway at 65 mph. What is the linear speed of the top of the tires?
Answer: 130 mph
Diff: 1 Var: 1 Page Ref: Sec. 8.1
4) A car is traveling along a highway at 65 mph. What is the linear speed of the bottom of the tires?
Answer: 0 mph
Diff: 1 Var: 1 Page Ref: Sec. 8.1
5) Consider a car with its wheels rolling (not sliding) on the road. How fast must the auto move for some point on a wheel to reach the speed of sound? Explain.
Answer: Half the speed of sound. The bottom of the wheel has zero linear speed, the middle has the car's speed, and the top of the wheel is moving at twice the axis speed.
Diff: 3 Var: 1 Page Ref: Sec. 8.1
6) Jane says that the magnitude of the torque exerted by a force of magnitude F is equal to the perpendicular distance from the axis of rotation r ⊥ multiplied by F, while Jason insists that it is equal to the distance from the axis of rotation r multiplied by the magnitude of the perpendicular component of the force, F ⊥ Who is right?
Answer: They are both right. Both answers are equivalent to τ = F r sinθ, where θ is the angle between the force and the radial line.
Diff: 1 Var: 1 Page Ref: Sec. 8.2
7) If the net force on an object is zero N, does the net torque on the object have to be zero Nm?
Answer: No. For example, the object might be subjected to two equal and opposite forces that are not along the same straight line. This would produce a torque, but the net force would be zero N.
Diff: 1 Var: 1 Page Ref: Sec. 8.2
8) State the condition of stable equilibrium.
Answer: An object is in stable equilibrium as long as its center of gravity after a small displacement still lies above and inside the object's original base of support. That is, the line of action of the weight force through the center of gravity intersects the original base of support.
Diff: 1 Var: 1 Page Ref: Sec. 8.2
9) A hollow cylinder and a solid cylinder are constructed so they have the same mass and radius. Which cylinder has the larger moment of inertia?
Answer: the hollow cylinder
Diff: 1 Var: 1 Page Ref: Sec. 8.3
10) Is it easier to swing a bat holding the handle at the end, or "choked up"? Why?
Answer: "Choked up", because the moment of inertia is less about the axis of rotation (bat center of mass moved toward axis)
Diff: 2 Var: 1 Page Ref: Sec. 8.3
11) The moment of inertia of a solid sphere about any diameter is 2/5 MR2. What is the moment of inertia about an axis that is tangent to the surface?
Answer: 2/5 MR2 + MR2 = 7/5 MR2
Diff: 2 Var: 1 Page Ref: Sec. 8.3
12) A sphere of radius R and mass M is released from rest, and rolls without slipping down a plane inclined at angle G above horizontal. What is the speed of the sphere after it has moved a distance L?
Answer: (5/6) g L sin G
Diff: 3 Var: 1 Page Ref: Sec. 8.4
13) The moon has an elliptical orbit around the Earth. The lunar rotational kinetic energy increases as it comes closer to the Earth and decreases as it moves away. What mechanism changes the rotational kinetic energy?
Answer: As the moon approaches Earth it has a component of motion along the gravitational force, so work is done on the moon and as it moves away energy is removed.
Diff: 3 Var: 1 Page Ref: Sec. 8.4
14) State the conservation of angular momentum.
Answer: In the absence of an external, unbalanced torque, the total (vector) angular momentum of a system is conserved (remains constant).
Diff: 1 Var: 1 Page Ref: Sec. 8.5
15) The moon causes a tidal bulge on the Earth, and the lunar pull on the bulge slows the rotation velocity of the Earth. Where does the lost angular momentum go?
Answer: The Earth also exerts a torque on the moon increasing its angular momentum, so total angular momentum is conserved.
Diff: 2 Var: 1 Page Ref: Sec. 8.5
16) When a rigid body rotates about a fixed axis all the points in the body have the same linear displacement.
Answer: FALSE
Diff: 1 Var: 1 Page Ref: Sec. 8.1
17) When a rigid body rotates about a fixed axis all the points in the body have the same angular speed.
Answer: TRUE
Diff: 1 Var: 1 Page Ref: Sec. 8.1
18) Unbalanced torques produce rotational accelerations, and balanced torques produce rotational equilibrium.
Answer: TRUE
Diff: 1 Var: 1 Page Ref: Sec. 8.2
19) If an object is in unstable equilibrium, any small displacement results in a restoring force or torque, which tends to return the object to its original equilibrium position.
Answer: FALSE
Diff: 1 Var: 1 Page Ref: Sec. 8.2
20) The perpendicular-axis theorem can be applied to any object.
Answer: FALSE
Diff: 1 Var: 1 Page Ref: Sec. 8.3
21) An object in motion with constant speed along a straight line can never have nonzero angular momentum.
Answer: FALSE
Diff: 1 Var: 1 Page Ref: Sec. 8.5
22) The condition for rolling without slipping is that the center of mass speed is
A) Vcm= r ω2
B) Vcm = 2 r ω
C) Vcm = r ω / 2
D) Vcm = r ω
E) Vcm = r2 ω
Answer: D
Diff: 1 Var: 1 Page Ref: Sec. 8.1
23) Consider a rigid body that is rotating. Which of the following is an accurate statement?
A) Its center of rotation must be at rest, i.e., not moving.
B) Its center of rotation must be moving with a constant velocity.
C) All points on the body are moving with the same angular velocity.
D) Its center of rotation is its center of gravity.
E) All points on the body are moving with the same linear velocity.
Answer: C
Diff: 2 Var: 1 Page Ref: Sec. 8.1
24) What condition or conditions is/are necessary for rotational equilibrium?
A) ΣFy = 0
B) ΣFx = 0, ΣFy = 0
C) Στ = 0
D) ΣFx = 0
E) ΣFx = 0, ΣFy = 0, Στ = 0
Answer: C
Diff: 1 Var: 1 Page Ref: Sec. 8.2
25) A pencil balanced on its tip such that it does not move
A) is in unstable equilibrium.
B) is in stable equilibrium.
C) has a net torque acting on it.
D) has a net vertical force.
E) has a zero moment of inertia.
Answer: A
Diff: 1 Var: 1 Page Ref: Sec. 8.2
26) If a constant net torque is applied to an object, that object will
A) rotate with constant linear velocity.
B) rotate with constant angular velocity.
C) rotate with constant angular acceleration.
D) having an increasing moment of inertia.
E) having a decreasing moment of inertia.
Answer: C
Diff: 1 Var: 1 Page Ref: Sec. 8.2
27) 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) the first at the midpoint
B) the second at the doorknob
C) both exert equal non-zero torques
D) both exert zero torques
E) additional information is needed
Answer: B
Diff: 1 Var: 1 Page Ref: Sec. 8.2
28) Two equal forces are applied to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30° to the plane of the door. Which force exerts the greater torque?
A) the first applied perpendicular to the door
B) the second applied at an angle
C) both exert equal non-zero torques
D) both exert zero torques
E) additional information is needed
Answer: A
Diff: 2 Var: 1 Page Ref: Sec. 8.2
29) Five forces act on a massless rod free to pivot at point P, as shown in Fig. 8-1. Which force is producing a counter-clockwise torque about point P?
A) A
B) B
C) C
D) D
E) E
Answer: C
Diff: 2 Var: 1 Page Ref: Sec. 8.2
30) What condition or conditions is/are necessary for static equilibrium?
A) ΣFy = 0
B) ΣFx = 0, ΣFy = 0
C) Στ = 0
D) ΣFx = 0
E) ΣFx = 0, ΣFy = 0, Στ = 0
Answer: E
Diff: 2 Var: 1 Page Ref: Sec. 8.2
31) A heavy boy and a lightweight girl are balanced on a massless seesaw. If they both move forward so that they are one-half their original distance from the pivot point, what will happen to the seesaw?
A) The side the boy is sitting on will tilt downward.
B) Nothing, the seesaw will still be balanced.
C) The side the girl is sitting on will tilt downward.
D) It is impossible to say without knowing the masses of the children.
E) It is impossible to say without knowing the values of the original distances.
Answer: B
Diff: 2 Var: 1 Page Ref: Sec. 8.2
32) A heavy seesaw is out of balance. A lightweight girl sits on the end that is tilted downward, and a heavy boy sits on the other side so that the seesaw now balances. If the boy and girl both move forward so that they are one-half their original distance from the pivot point, what will happen to the seesaw?
A) The side the girl is sitting on will once again tilt downward.
B) The side the boy is sitting on will now tilt downward.
C) Nothing, the seesaw will still be balanced.
D) It is impossible to say without knowing the masses of the children.
E) It is impossible to say without knowing the values of the original distances.
Answer: A
Diff: 2 Var: 1 Page Ref: Sec. 8.2
33) Consider a solid object which is subjected to a net torque. That object will experience which of the following?
A) a linear acceleration and an angular acceleration
B) an angular acceleration
C) a constant angular velocity
D) a changing moment of inertia
Answer: B
Diff: 1 Var: 1 Page Ref: Sec. 8.3
34) Consider two uniform solid spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is
A) 2.
B) 10.
C) 4.
D) 8.
E) 6.
Answer: A
Diff: 2 Var: 1 Page Ref: Sec. 8.3
35) A solid cylinder and a hollow cylinder have the same mass and the same radius. Which statement is true concerning their moment of inertia about an axis through the exact center of the flat surfaces?
A) The hollow cylinder has the greater moment of inertia.
B) The solid cylinder has the greater moment of inertia.
C) Both cylinders have the same moment of inertia.
D) The moment of inertia cannot be determined since it depends on the amount of material removed from the inside of the hollow cylinder.
Answer: A
Diff: 2 Var: 1 Page Ref: Sec. 8.3
36) A boy and a girl are riding on a merry-go-round that is turning. The boy is twice as far as the girl from the merry-go-round's center. If the boy and girl are of equal mass, which statement is true about the boy's moment of inertia with respect to the axis of rotation?
A) His moment of inertia is 4 times the girl's.
B) The boy has a greater moment of inertia, but it is impossible to say exactly how much more.
C) His moment of inertia is twice the girl's.
D) His moment of inertia is half the girl's.
E) The moment of inertia is the same for both.
Answer: A
Diff: 2 Var: 1 Page Ref: Sec. 8.3
37) A ball, solid cylinder, and a hollow pipe all have equal masses and radii. If the three are released simultaneously at the top of an inclined plane, which will reach the bottom first?
A) ball
B) pipe
C) cylinder
D) they all reach bottom in the same time
Answer: A
Diff: 2 Var: 1 Page Ref: Sec. 8.4
38) Angular momentum cannot be conserved if
A) the angular displacement changes.
B) the angular velocity changes.
C) there is a net force on the system.
D) the moment of inertia changes.
E) there is net torque on the system.
Answer: E
Diff: 1 Var: 1 Page Ref: Sec. 8.5
39) A ball is attached to a string and revolves in a horizontal circle with angular momentum. When the string breaks at point B on the circumference, the ball moves off tangentially along path B-Q. As it moves along B-Q, increasing its distance from the center of the circle, its angular momentum
A) decreases.
B) is now zero.
C) remains constant.
D) increases.
Answer: C
Diff: 2 Var: 1 Page Ref: Sec. 8.5
40) An ice skater performs a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rotation?
A) It does not change.
B) It increases.
C) It changes, but it is impossible to tell which way.
D) It decreases.
Answer: A
Diff: 2 Var: 1 Page Ref: Sec. 8.5
41) An ice skater performs a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the axis of rotation?
A) It does not change.
B) It decreases.
C) It increases.
D) It changes, but it is impossible to tell which way.
Answer: B
Diff: 2 Var: 1 Page Ref: Sec. 8.5
42) An ice skater performs a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis of rotation?
A) It changes, but it is impossible to tell which way.
B) It increases.
C) It does not change.
D) It decreases.
Answer: B
Diff: 2 Var: 1 Page Ref: Sec. 8.5
43) We can best understand how a diver is able to control his rate of rotation while in the air (and thus enter the water in a vertical position) by observing that while in the air
A) his linear momentum is constant.
B) his potential energy is constant.
C) his kinetic energy is constant.
D) his angular momentum is constant.
E) his total energy is constant.
Answer: D
Diff: 2 Var: 1 Page Ref: Sec. 8.5
44) A planet speeds up in its orbit as it gets closer to the sun because of
A) the torque exerted on the planet by the sun.
B) conservation of energy.
C) conservation of momentum.
D) conservation of angular momentum.
E) inertia.
Answer: D
Diff: 2 Var: 1 Page Ref: Sec. 8.5
45) A planet of constant mass orbits the sun in an elliptical orbit. Neglecting any friction effects, what happens to the planet's rotational kinetic energy about the sun's center?
A) It decreases continually.
B) It increases continually.
C) It remains constant.
D) It increases when the planet approaches the sun, and decreases when it moves farther away.
E) It decreases when the planet approaches the sun, and increases when it moves farther away.
Answer: D
Diff: 2 Var: 1 Page Ref: Sec. 8.5
46) Consider two equal mass cylinders rolling with the same translational velocity. The first cylinder (radius = R) is hollow and has a moment of inertia about its rotational axis of M R2, while the second cylinder (radius = r) is solid and has a moment of inertia about its axis of 0.5 M r2. What is the ratio of the hollow cylinder's angular momentum to that of the solid cylinder?
A) r2 to 2R2
B) 2R2 to r2
C) r to 2R
D) 2R to r
E) R to 2r
Answer: D
Diff: 3 Var: 1 Page Ref: Sec. 8.5
1) A cylinder, of radius 8.0 cm, rolls 20. cm in 5.0 s. Through what angular displacement does the cylinder move in this time?
Answer: 143°
Diff: 2 Var: 1 Page Ref: Sec. 8.1
2) A 50. cm diameter wheel is rotating initially at 2.0 revolutions per second. It slows down uniformly and comes to rest in 15 seconds.
(a) What was its angular acceleration?
(b) Through how many revolutions did it turn in those 15 s?
Answer:
(a) -0.13 rev/s2 = -0.84 rad/s2
(b) 15. rev
Diff: 3 Var: 1 Page Ref: Sec. 8.1
3) A wheel slows down uniformly and comes to rest in 15 seconds. It is rotating initially at 2.0 revolutions per second and has a diameter of 50.cm.
(a) What was the centripetal acceleration at the instant when it was rotating initially?
(b) What was the tangential acceleration?
Answer:
(a) 39. m/s2
(b) -0.21 m/s2
Diff: 3 Var: 1 Page Ref: Sec. 8.1
4) A wheel of diameter 0.70 m rolls without slipping. A point at the top of the wheel moves with a tangential speed 2.0 m/s.
(a) At what speed is the axis of the wheel moving?
(b) What is the angular speed of the wheel?
Answer:
(a) 1.0 m/s
(b) 2.9 rad/s
Diff: 3 Var: 1 Page Ref: Sec. 8.1
5) A girl weighing 450. N sits on one end of a seesaw that is 3.0 m long and is pivoted 1.3 m from the girl. If the seesaw is just balanced when a boy sits at the opposite end, what is his weight? Neglect the weight of the seesaw.
Answer: 344. Newtons
Diff: 2 Var: 1 Page Ref: Sec. 8.2
6) 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 Fig. 8-2.
(a) Find the force exerted by pillar A.
(b) Find the force exerted by pillar B.
Answer:
(a) 1.71 kN downwards
(b) 2.51 kN upwards
Diff: 2 Var: 1 Page Ref: Sec. 8.2
7) A 20.0-kg mass is supported by two strings as shown in Fig. 8-3. The left string is 2.00 m long and the right string is 5.00 m long. The attachment points for the two strings are 6.00 m apart on the ceiling.
(a) What is the tension in the left side string?
(b) What is the tension in the right side string?
Answer:
(a) 199 N
(b) 131 N
Diff: 2 Var: 1 Page Ref: Sec. 8.2
8) 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?
Answer:
(a) 956. N
(b) 653. N
Diff: 3 Var: 5 Page Ref: Sec. 8.2
Skill: Algorithmic
9) A majorette fastens two batons together at their centers to form an X shape. What is the moment of inertia of the combination about an axis through the center of the X if each baton was 1.2 m long and each ball at the end of each baton has a mass of 0.25 kg (assume negligible mass in the rods)?
Answer: 0.36 kg∙ m2
Diff: 2 Var: 1 Page Ref: Sec. 8.3
10) Consider a bicycle wheel to be a ring of radius 30. cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20. N is applied tangentially to a sprocket of radius 4.0 cm for 4.0 s, what linear speed does the wheel achieve, assuming it rolls without slipping?
Answer: 7.11 m/s
Diff: 2 Var: 1 Page Ref: Sec. 8.3
11) A triatomic molecule is modeled as follows: mass m is at the origin, mass 2m is at x = a, and mass 3m is at x = 2a.
(a) What is the amount of inertia about the origin?
(b) What is the moment of inertia about the center of mass?
Answer:
(a) 14 ma2
(b) 3.3 ma2
Diff: 2 Var: 1 Page Ref: Sec. 8.3
12) A 1.8 kg solid disk pulley of radius 0.11 m rotates about an axis through its center.
(a) What is its moment of inertia?
(b) Starting from rest, a torque of 0.22 m-N will produce what angular acceleration?
Answer:
(a) 1.1 × 10-2 kg ∙ m2
(b) 20. rad/s2
Diff: 3 Var: 5 Page Ref: Sec. 8.3
Skill: Algorithmic
13) A cylinder of radius R and mass M rolls without slipping down a plane inclined at an angle θ above horizontal.
(a) What is the torque about the point of contact with the plane?
(b) What is the moment of inertia about the point of contact?
(c) What is the linear speed of the cylinder t seconds after it is released from rest?
Answer:
(a) MgR sin θ
(b) 3MR2 / 2
(c) 3 2 g t sin θ
Diff: 3 Var: 1 Page Ref: Sec. 8.3
14) Consider a bus designed to obtain its motive power from a large rotating flywheel (1400. kg of diameter 1.5 m) that is periodically brought up to its maximum speed of 3600. rpm by an electric motor at the terminal. If the bus requires an average power of 12. kilowatts, how long will it operate between recharges?
Answer: 39. minutes
Diff: 2 Var: 1 Page Ref: Sec. 8.4
15) Consider a motorcycle of mass 150. kg, one wheel of which has a mass of 10. kg and a radius of 30. cm. What is the ratio of the rotational kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.
Answer: 0.13 : 1
Diff: 2 Var: 1 Page Ref: Sec. 8.4
16) A uniform solid cylinder (mass 100. kg and radius 50.0 cm) is mounted so it is free to rotate about fixed horizontal axis that passes through the centers of its circular ends. A 10.0 kg block is hung from a massless cord wrapped around the cylinder's circumference. When the block is released, the cord unwinds and the block accelerates downward, as shown in Fig. 8-4. What is the block's acceleration?
Answer: 1.63 m/s2
Diff: 2 Var: 1 Page Ref: Sec. 8.4
17) Two children, each of mass 20.0 kg, ride on the perimeter of a small merry-go-round that is rotating at the rate of 1.0 revolution every 4.0 s. The merry-go-round is a disk of mass 30. kg and radius 3.0 m. The children now both move halfway in toward the center to positions 1.5 m from the axis of rotation. Calculate the kinetic energy before and after, and the final rate of rotation. Explain any changes in energy.
Answer:
Ko = 0.61 kJ
Kf = 1.3 kJ
f = 0.55 Hz
Children do work moving inward.
Diff: 3 Var: 1 Page Ref: Sec. 8.4
18) 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?
Answer: 4 Hz
Diff: 2 Var: 1 Page Ref: Sec. 8.5
19) A ballerina spins initially at 1.5 revolutions/second when her arms are extended. She then draws in her arms to her body and her moment of inertia becomes 0.88 kg-m2 and her angular speed increases to 4.0 rev/s. Determine her initial moment of inertia.
Answer: 2.3 kg ∙ m2
Diff: 2 Var: 1 Page Ref: Sec. 8.5
20) A solid disk with diameter 2.00 meters and mass 4.0 kg freely rotates about a vertical axis at 36. rpm. A 0.50 kg hunk of bubblegum is dropped onto the disk and sticks to the disk at a distance d = 80. cm from the axis of rotation, as shown in Fig. 8-5.
(a) What was the moment of inertia before the gum fell?
(b) What was the moment of inertia after the gum stuck?
(c) What is the angular velocity after the gum fell onto the disk?
Answer:
(a) 2.0 kg ∙ m2
(b) 2.3 kg ∙ m2
(c) 31. rpm
Diff: 3 Var: 1 Page Ref: Sec. 8.5
21) NASA puts a satellite in space which consists of two (32. kg each) masses connected by a 12. meter long light cable, as shown in Fig. 8-6. The entire system initially is rotating 4.0 rpm about an axis (at the center of mass) perpendicular to the cable. Motors in each mass reel out more cable so that the masses double their separation (to 24. m).
(a) What is the final ROTATIONAL VELOCITY?
(b) The final KINETIC ENERGY is what fraction of the initial?
Answer:
(a) 1.0 rpm
(b) 1/4
Diff: 3 Var: 1 Page Ref: Sec. 8.5
22) A ball with diameter 10. cm rolls without slipping on a horizontal table top. The moment of inertia of the ball is 2.2 × 10-3 kg-m2 and its translational speed is 0.45 m/s.
(a) What is its angular speed about its center of mass?
(b) What is its rotational kinetic energy?
(c) What is its angular momentum?
Answer:
(a) 9.0 rad/s
(b) 0.089 J
(c) 0.020 J ∙ s
Diff: 3 Var: 5 Page Ref: Sec. 8.5
Skill: Algorithmic
23) A bicycle is moving 4.0 m/s. What is the angular speed of a wheel if its radius is 30.cm?
A) 4.8 rad/s
B) 7.6 rad/s
C) 0.36 rad/s
D) 1.2 rad/s
E) 13. rad/s
Answer: E
Diff: 2 Var: 1 Page Ref: Sec. 8.1
24) A 30.0-kg child sits on one end of a long uniform beam with a mass 20.0 kg and a 40.0-kg child sits on the other end. The beam balances when a fulcrum is placed below the beam a distance 1.10 m from the 30.0-kg child. How long is the beam?
A) 2.12 m
B) 1.98 m
C) 1.93 m
D) 2.07 m
E) 2.20 m
Answer: B
Diff: 1 Var: 1 Page Ref: Sec. 8.2
25) A seesaw made of a plank of mass 10.0 kg and length 3.00 m is balanced on a fulcrum 1.00 m from one end of the plank. A 20.0-kg mass rests on the end of the plank nearest the fulcrum. What mass must be on the other end if the plank remains balanced?
A) 6.67 kg
B) 7.50 kg
C) 10.0 kg
D) -10.0 kg
E) 5.00 kg
Answer: B
Diff: 1 Var: 1 Page Ref: Sec. 8.2
26) Two children are carrying a 2.00-m long uniform level board with a mass 5.00 kg, each supporting one end of the board. A 1.00-kg book is resting on the board a distance 1.20 m from one end of the board. What is the force applied by the child that is closer to the book to support the board?
A) 29.4 N downward
B) 58.9 N upward
C) 29.4 N upward
D) 30.4 N upward
E) 3.10 N upward
Answer: D
Diff: 1 Var: 1 Page Ref: Sec. 8.2
27) A uniform rod has a weight of 40. N and a length of 1.0 m. It is hinged to a wall (at the left end), and held in a horizontal position by a vertical massless string (at the right end), as shown in Fig. 8-7. What is the magnitude of the torque exerted by the string about a horizontal axis which passes through the hinge and is perpendicular to the rod?
A) 40 m ∙ N
B) 10 m ∙ N
C) 5.0 m ∙ N
D) 20 m ∙ N
E) 30 m ∙ N
Answer: D
Diff: 2 Var: 1 Page Ref: Sec. 8.2
28) A force is applied to the end of a 2.0 ft long uniform board weighing 50. lb, in order to keep it horizontal, while it pushes against a wall at the left. If the angle the force makes with the board is 30° in the direction shown in Fig. 8-8, what is the applied force F?
A) 58. lb
B) 50. lb
C) 29. lb
D) 90. lb
E) 32. lb
Answer: B
Diff: 2 Var: 1 Page Ref: Sec. 8.2
29) A boy and a girl are balanced on a massless seesaw. The boy has a mass of 60 kg and the girl's mass is 50 kg. If the boy sits 1.5 m from the pivot point on one side of the seesaw, where must the girl sit on the other side for equilibrium?
A) 3.0 m
B) 1.3 m
C) 2.5 m
D) 1.8 m
E) 1.2 m
Answer: D
Diff: 2 Var: 1 Page Ref: Sec. 8.2
30) What is the rotational inertia (moment of inertia) of a 12-kg uniform rod, 0.30 m long, rotating about an axis perpendicular to the rod and passing through the center of the rod?
A) 0.27 kg m2
B) 0.18 kg m2
C) 0.090 kg m2
D) 0.54 kg m2
E) 0.36 kg m2
Answer: C
Diff: 1 Var: 1 Page Ref: Sec. 8.3
31) A 10.0-kg rod has a Varying linear density that is symmetric about the midpoint of the rod. The moment of inertia about an axis perpendicular to the rod that passes through the rod
30.0 cm from its midpoint is 5.00 kg∙m2. What is the moment of inertia about an axis perpendicular to the rod that passes through the rod 20.0 cm from its midpoint?
A) 7.50 kg∙m2
B) 4.50 kg∙m2
C) 5.10 kg∙m2
D) 4.90 kg∙m2
E) Answer depends on whether the new axis is on the same side of the midpoint as the 30.0 cm distant axis or if its on the opposite side of the midpoint.
Answer: B
Diff: 1 Var: 1 Page Ref: Sec. 8.3
32) A thin hoop with a radius of 10 cm and a mass of 3.0 kg is rotating about its center with an angular speed of 3.5 rad/s. What is its kinetic energy?
A) 0.18 J
B) 0.092 J
C) 0.96 J
D) 1.05 J
E) 0.53 J
Answer: A
Diff: 1 Var: 1 Page Ref: Sec. 8.3
33) A solid cylinder with a radius of 10 cm and a mass of 3.0 kg is rotating about its center with an angular speed of 3.5 rad/s. What is its kinetic energy?
A) 0.18 J
B) 0.092 J
C) 0.96 J
D) 1.05 J
E) 0.53 J
Answer: B
Diff: 1 Var: 1 Page Ref: Sec. 8.3
34) The moment of inertia of a uniform rod (about its center) is given by I = ML2/12. What is the kinetic energy of a 120-cm rod with a mass of 450 g rotating about its center at 3.60 rad/s?
A) 0.350 J
B) 4.20 J
C) 0.700 J
D) 0.960 J
E) 2.10 J
Answer: A
Diff: 1 Var: 1 Page Ref: Sec. 8.3
35) Consider two uniform solid spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is
A) 10.
B) 8.
C) 2.
D) 6.
E) 4.
Answer: B
Diff: 2 Var: 1 Page Ref: Sec. 8.3
36) Two uniform solid spheres have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is
A) 9/5.
B) 8/5.
C) 4/5.
D) 4.
E) 2.
Answer: D
Diff: 2 Var: 1 Page Ref: Sec. 8.3
37) A 4.0 kg mass is hung from a string which is wrapped around a cylindrical pulley (a cylindrical shell), as shown in Fig. 8-9. If the mass accelerates downward at 4.90 m/s2, what is the mass of the pulley?
A) 10.0 kg
B) 4.0 kg
C) 8.0 kg
D) 2.0 kg
E) 6.0 kg
Answer: C
Diff: 2 Var: 1 Page Ref: Sec. 8.3
38) A uniform rod has a length of 2.0 m. It is hinged to a wall (at the left end), and held in a horizontal position by a vertical massless string (at the right end), as shown in Fig. 8-7. What is the angular acceleration of the rod at the moment the string is released?
A) 15. rad/s2
B) It can't be calculated without knowing the rod's mass.
C) 7.4 rad/s2
D) 11. rad/s2
E) 3.3 rad/s2
Answer: C
Diff: 2 Var: 1 Page Ref: Sec. 8.3
39) A potter's wheel with a moment of inertia of 8.0 kg-m2 has 5.0 N-m applied to it. It starts from rest. 10. s later it has gained what kinetic energy?
A) 44. J
B) 0.12 kJ
C) 78. J
D) 1.6 kJ
E) 53. J
Answer: C
Diff: 2 Var: 1 Page Ref: Sec. 8.4
40) A wheel of moment of inertia of 5.00 kg-m2 starts from rest and accelerates under a constant torque of 3.00 N-m for 8.00 s. What is the wheel's rotational kinetic energy at the end of 8.00 s?
A) 57.6 J
B) 122.0 J
C) 91.9 J
D) 64.0 J
E) 78.8 J
Answer: A
Diff: 2 Var: 1 Page Ref: Sec. 8.4
41) The moment of inertia of a solid cylinder about its axis is given by 0.5MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is
A) 1:2
B) 1:3
C) 2:1
D) 1:1
E) 3:1
Answer: A
Diff: 2 Var: 1 Page Ref: Sec. 8.4
42) A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?
A) 7.7 m/s
B) 6.2 m/s
C) 5.4 m/s
D) 3.8 m/s
E) 2.2 m/s
Answer: C
Diff: 2 Var: 1 Page Ref: Sec. 8.4
43) An 8.0 kg-m2 wheel with 155. Joules of rotational kinetic energy requires what torque to bring it to rest in 4.0 s?
A) -1.6 N-m
B) -1.2 N-m
C) +0.88 N-m
D) -1.8 N-m
E) -1.0 N-m
Answer: E
Diff: 2 Var: 1 Page Ref: Sec. 8.4
44) An ice skater has a moment of inertia of 5.0 kg∙m2 when her arms are outstretched. At this time she is spinning at 3.0 revolutions per second (rps). If she pulls in her arms and decreases her moment of inertia to 2.0 kg∙m2, how fast will she be spinning?
A) 2.0 rps
B) 3.3 rps
C) 7.5 rps
D) 8.4 rps
E) 10 rps
Answer: C
Diff: 1 Var: 1 Page Ref: Sec. 8.5
45) A figure skater rotating at 5.00 rad/s with arms extended has a moment of inertia of 2.25 kg m2. If the arms are pulled in so the moment of inertia decreases to 1.80 kg∙m2, what is the final angular speed?
A) 2.25 rad/s
B) 4.60 rad/s
C) 6.25 rad/s
D) 1.76 rad/s
E) 0.81 rad/s
Answer: C
Diff: 2 Var: 1 Page Ref: Sec. 8.5
46) A proton of mass M rotates with an angular speed of 2 × 106 rad/s in a circle of radius 0.80 m in a cyclotron. What is the orbital angular momentum of the proton? (M = 1.67 × 10-27 kg)
A) 2.1 × 10-21 N-m-s
B) 1.1 × 10-20 N-m-s
C) 2.9 × 10-21 N-m-s
D) 5.3 × 10-21 N-m-s
E) 3.9 × 10-21 N-m-s
Answer: A
Diff: 2 Var: 1 Page Ref: Sec. 8.5
47) Initially, a 2.00-kg mass is whirling at the end of a string (in a circular path of radius 0.750 m) on a horizontal frictionless surface with a tangential speed of 5 m/s, as shown in Fig. 8-10. The string has been slowly winding around a vertical rod, and a few seconds later the length of the string has shortened to 0.250 m. What is the instantaneous speed of the mass at the moment the string reaches a length of 0.250 m?
A) 75 m/s
B) 15 m/s
C) 225 m/s
D) 3.9 m/s
E) 9.3 m/s
Answer: B
Diff: 2 Var: 1 Page Ref: Sec. 8.5
48) An object's angular momentum changes by 10 kg-m2/s in 2.0 s. What magnitude average torque acted on this object?
A) 2.5 N-m
B) 40 N-m
C) 10 N-m
D) 5 N-m
E) 20 N-m
Answer: D
Diff: 2 Var: 1 Page Ref: Sec. 8.5