world history
3.84 × 108 m
1) The diameter of the Moon is 3.47 × 106 m, and it subtends an angle of 0.00904 rad when viewed from the surface of Earth. How far is the Moon from Earth?
A, C
1) When a rigid object rotates about a fixed axis, what is true about all the points in the object? (There could be more than one correct choice.) A) They all have the same angular speed. B) They all have the same tangential speed. C) They all have the same angular acceleration. D) They all have the same tangential acceleration. E) They all have the same radial acceleration.
40 cm
10) A bicycle wheel has an outside diameter of 66 cm. Through what distance does a point on the rim move as the wheel rotates through an angle of 70°?
C
10) A disk, a hoop, and a solid sphere are released at the same time at the top of an inclined plane. They are all uniform and roll without slipping. In what order do they reach the bottom? A) disk, hoop, sphere B) hoop, sphere, disk C) sphere, disk, hoop D) sphere, hoop, disk E) hoop, disk, sphere
D
11) A small uniform disk and a small uniform sphere are released simultaneously at the top of a high inclined plane, and they roll down without slipping. Which one will reach the bottom first? A) the one of smallest diameter B) the one of greatest mass C) the disk D) the sphere E) They will reach the bottom at the same time.
(a) 0.627 rad/s (b) 1.18 m/s2
11) When Mary is 3.00 m from the center of a merry-go-round, her tangential speed is a constant 1.88 m/s. (a) What is her angular speed in rad/s? (b) What is the magnitude of her linear acceleration?
140°
12) A cylinder of radius 8.0 cm rolls 20 cm in 5.0 s without slipping. Through how many degrees does the cylinder turn during this time?
D
12) Suppose a uniform solid sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on A) the mass of the sphere. B) the radius of the sphere. C) both the mass and the radius of the sphere. D) neither the mass nor the radius of the sphere.
(a) 1.0 m/s (b) 2.9 rad/s
13) A wheel of diameter 0.70 m rolls on the floor without slipping. A point at the top of the wheel moves with a speed 2.0 m/s relative to the floor. (a) At what speed is the central axis of the wheel moving relative to the floor? (b) What is the angular speed of the wheel?
B
13) Suppose a solid uniform sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on A) the mass of the sphere. B) the radius of the sphere. C) both the mass and the radius of the sphere. D) neither the mass nor the radius of the sphere.
B
14) A child is riding a merry-go-round that is turning at 7.18 rpm. If the child is standing 4.65 m from the center of the merry-go-round, how fast is the child moving? A) 5.64 m/s B) 3.50 m/s C) 0.556 m/s D) 1.75 m/s E) 1.80 m/s
B
14) A uniform ball is released from rest on a no-slip surface, as shown in the figure. After reaching its lowest point, the ball begins to rise again, this time on a frictionless surface. When the ball reaches its maximum height on the frictionless surface, it is A) higher than when it was released. B) lower than when it was released. C) at the same height from which it was released. D) It is impossible to tell without knowing the mass of the ball. E) It is impossible to tell without knowing the radius of the ball.
A
15) An electrical motor spins at a constant If the rotor radius is what is the linear acceleration of the edge of the rotor? A) 5707 m/s2 B) 281.6 m/s2 C) 572,400 m/s2 D) 28.20 m/s2
B
15) Two uniform solid balls, one of radius R and mass M, the other of radius 2R and mass 8M, roll down a high incline. They start together from rest at the top of the incline. Which one will reach the bottom of the incline first? A) The small sphere arrives first. B) Both reach the bottom at the same time. C) The large sphere arrives first.
A
16) A string is wound tightly around a fixed pulley having a radius of 5.0 cm. As the string is pulled, the pulley rotates without any slipping of the string. What is the angular speed of the pulley when the string is moving at 5.0 m/s? A) 100 rad/s B) 50 rad/s C) 25 rad/s D) 20 rad/s E) 10 rad/s
A
16) Two forces produce equal torques on a door about the door hinge. 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 has a greater magnitude? A) the first force (at the midpoint) B) the second force (at the doorknob) C) The two forces are equal.
B
17) A scooter has wheels with a diameter of 120 mm. What is the angular speed of the wheels when the scooter is moving forward at 6.00 m/s? A) 47.7 rpm B) 955 rpm C) 72.0 rpm D) 50.0 rpm E) 100 rpm
A
17) Two equal-magnitude forces are applied to a door at the doorknob. The first force is applied perpendicular to the door, and the second force is applied at 30° to the plane of the door. Which force exerts the greater torque about the door hinge? A) the first force (applied perpendicular to the door) B) the second force (applied at an angle) C) Both forces exert equal non-zero torques. D) Both forces exert zero torque.
D
18) A bicycle has wheels that are 60 cm in diameter. What is the angular speed of these wheels when it is moving at 4.0 m/s? A) 1.2 rad/s B) 4.8 rad/s C) 0.36 rad/s D) 13 rad/s E) 7.6 rad/s
A
18) As shown in the figure, a given force is applied to a rod in several different ways. In which case is the torque about the pivot P due to this force the greatest? A) 1 B) 2 C) 3 D) 4 E) 5
(a) 110 rad (b) 48 rad/s (c) 210 m/s2 (d) 0 m/s2
19) A bowling ball of mass 7.5 kg and diameter 18 cm rolls without slipping down a 10-m bowling lane with a constant speed 4.3 m/s. (a) Through what angle does the bowling ball turn as it travels the length of the lane? (b) What is the angular speed of the bowling ball? (c) Calculate the maximum radial acceleration that a point on the surface of the bowling ball could have. (d) Calculate the tangential acceleration of a point on the surface of the bowling ball.
C
19) Five forces act on a rod that is free to pivot at point P, as shown in the figure. Which of these forces is producing a counter-clockwise torque about point P? (There could be more than one correct choice.) A) force A B) force B C) force C D) force D E) force E
1.4 × 109 m
2) The sun subtends an angle of 0.00928 rad when viewed from the surface of the earth, and its distance from Earth is 1.5 × 1011 m. What is the diameter of the sun?
B, D
2) Two children, Ahmed and Jacques, ride on a merry-go-round. Ahmed is at a greater distance from the axis of rotation than Jacques. Which of the following are true statements? (There could be more than one correct choice.) A) Jacques has a greater angular speed than Ahmed. B) Jacques and Ahmed have the same angular speed. C) Jacques has a smaller angular speed than Ahmed. D) Ahmed has a greater tangential speed than Jacques. E) Jacques and Ahmed have the same tangential speed.
B
20) A rolling wheel of diameter of 68 cm slows down uniformly from 8.4 m/s to rest over a distance of 115 m. What is the magnitude of its angular acceleration if there was no slipping? A) 1.8 rad/s2 B) 0.90 rad/s2 C) 5.7 rad/s2 D) 11 rad/s2
B
20) The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left), or a distance r/2 from the axis of rotation (right). If you release the hanging blocks simultaneously from rest, A) the block at the left lands first. B) the block at the right lands first. C) both blocks land at the same time.
A
21) A child is riding a merry-go-round that has an instantaneous angular speed of 1.25 rad/s and an angular acceleration of 0.745 rad/s2. The child is standing 4.65 m from the center of the merry-go-round. What is the magnitude of the linear acceleration of the child? A) 8.05 m/s2 B) 7.27 m/s2 C) 2.58 m/s2 D) 3.46 m/s2 E) 4.10 m/s2
D
21) A person sits on a freely spinning lab stool that has no friction in its axle. When this person extends her arms, A) her moment of inertia decreases and her angular speed increases. B) her moment of inertia decreases and her angular speed decreases. C) her moment of inertia increases and her angular speed increases. D) her moment of inertia increases and her angular speed decreases. E) her moment of inertia increases and her angular speed remains the same.
A
22) A merry-go-round spins freely when Diego moves quickly to the center along a radius of the merry-go-round. As he does this, it is true to say that A) the moment of inertia of the system decreases and the angular speed increases. B) the moment of inertia of the system decreases and the angular speed decreases. C) the moment of inertia of the system decreases and the angular speed remains the same. D) the moment of inertia of the system increases and the angular speed increases. E) the moment of inertia of the system increases and the angular speed decreases.
(a) 0.63 rad/s2 (b) 1.5 rev
22) When an old LP turntable was revolving at 33 rpm, it was shut off and uniformly slowed down and stopped in 5.5 seconds. (a) What was the magnitude of its angular acceleration (in rad/s2) as it slowed down? (b) Through how many revolutions did it turn while stopping?
(a) 11 rad (b) 10 rad/s
23) A wheel accelerates with a constant angular acceleration of 4.5 rad/s2 from an initial angular speed of 1.0 rad/s. (a) Through what angle does the wheel turn in the first 2.0 s, and (b) what is its angular speed at that time?
C
23) If the answer to your calculation has units of kg ∙ m2/s, what type of quantity could it be? (There could be more than one correct choice). A) force B) work C) angular momentum D) linear momentum E) power F) rotational kinetic energy G) moment of inertia H) torque
0.73 s
24) A wheel starts from rest and has a uniform angular acceleration of 4.0 rad/s2. After the wheel completes its first revolution, how long does it take for it to make its second complete revolution?
B, F, H
24) If the answer to your calculation has units of kg ∙ m2/s2 , what type of quantity could it be? (There could be more than one correct choice.) A) force B) work C) angular momentum D) linear momentum E) power F) rotational kinetic energy G) moment of inertia H) torque
A, B, C, D, E, G
25) A ballet dancer is spinning in the middle of a horizontal frictionless stage. Which of the following things could he change by moving parts of his body or his whole body? (There could be more than one correct choice.) A) his total kinetic energy B) his translational kinetic energy C) his rotational kinetic energy D) his angular momentum E) his moment of inertia F) the horizontal component of his linear momentum G) the location of his center of mass (or center of gravity)
0.67 s
25) A bicycle wheel has an initial angular speed of 7.2 rad/s. After turning through of a revolution, the angular speed is reduced to 2.2 rad/s. If the angular acceleration of the wheel was constant during the motion, how long will it take the wheel to make the revolution?
A
26) A spinning ice skater on extremely smooth ice is able to control the rate at which she rotates by pulling in her arms. Which of the following statements are true about the skater during this process? (There could be more than one correct choice.) A) Her angular momentum remains constant. B) Her moment of inertia remains constant. C) Her kinetic energy remains constant. D) She is subject to a constant non-zero torque.
B
26) How long does it take for a rotating object to speed up from 15.0 rad/s to 33.3 rad/s if it has a uniform angular acceleration of 3.45 rad/s2? A) 4.35 s B) 5.30 s C) 9.57 s D) 10.6 s E) 63.1 s
A
27) A wheel accelerates from rest to at a uniform rate of Through what angle (in radians) did the wheel turn while accelerating? A) 30 rad B) 24 rad C) 60 rad D) 38 rad
D
27) When is the angular momentum of a system constant? A) Only when its total kinetic energy is constant. B) Only when no net external force acts on the system. C) Only when the linear momentum and the energy are constant. D) Only when no net external torque acts on the system. E) Only when the moment of inertia is constant.
A
28) A machinist turns on the power to a grinding wheel at time t = 0 s. The wheel accelerates uniformly from rest for 10 s and reaches the operating angular speed of The wheel is run at that angular speed for 30 s and then power is shut off. The wheel slows down uniformly at until the wheel stops. In this situation, what is the angular acceleration of the wheel between and A) 3.8 rad/ B) 4.6 rad/ C) 5.3 rad/ D) 6.1 rad/ E) 6.8 rad/
B
28) 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? A) up B) down C) to your left D) to your right E) forwards
A
29) A machinist turns on the power on to a grinding wheel at time t = 0 s. The wheel accelerates uniformly from rest for 10 s and reaches the operating angular speed of The wheel is run at that angular velocity for 30 s, and then power is shut off. The wheel slows down uniformly at until the wheel stops. What is the total number of revolutions made by the wheel in this situation? A) 510 B) 280 C) 320 D) 470 E) 750
A
29) When you ride a bicycle, in what direction is the angular velocity of the wheels? A) to your left B) to your right C) forwards D) backwards E) up
(a) 130 mph (b) 0 mps (c) 65 mph
3) A car is traveling along a freeway at 65 mph. What is the linear speed, relative to the highway, of each of the following points on one of its tires? (a) the highest point on the tire (b) the lowest point on a tire (c) the center of the tire
A
3) What is the angular speed, in rad/s, of a flywheel turning at 813.0 rpm? A) 85.14 rad/s B) 13.53 rad/s C) 63.84 rad/s D) 95.33 rad/s
A
30) A machinist turns on the power on to a grinding wheel at time t = 0 s. The wheel accelerates uniformly from rest for 10 s and reaches the operating angular speed of The wheel is run at that angular velocity for 40 s and then power is shut off. The wheel slows down uniformly at until the wheel stops. For how long a time after the power is shut off does it take the wheel to stop? A) 64 s B) 62 s C) 66 s D) 68 s E) 70 s
(a) 0.020 m/s2 (b) 0.35 m/s (c) 0.066 m/s2 (d) 35 s
31) In the figure, point P is on the rim of a wheel of radius 2.0 m. At time t = 0, the wheel is at rest, and P is on the x-axis. The wheel undergoes a uniform counterclockwise angular acceleration of 0.010 rad/s2 about the center O. (a) At time t = 0, what is the tangential acceleration of P? (b) What is the linear speed of P when it reaches the y-axis? (c) What is the magnitude of the net linear acceleration of P when it reaches the y-axis? (d) How long after starting does it take for P to return to its original position on the x-axis?
E
32) An old LP record that is originally rotating at 33.3 rad/s is given a uniform angular acceleration of 2.15 rad/s2. Through what angle has the record turned when its angular speed reaches 72.0 rad/s? A) 83.2 rad B) 316 rad C) 697 rad D) 66.8 rad E) 948 rad
E
33) A wheel rotates through an angle of 13.8 rad as it slows down uniformly from 22.0 rad/s to 13.5 rad/s. What is the magnitude of the angular acceleration of the wheel? A) 0.616 rad/s2 B) 5.45 rad/s2 C) 111 rad/s2 D) 22.5 rad/s2 E) 10.9 rad/s2
A
34) A pulley has an initial angular speed of 12.5 rad/s and a constant angular acceleration of 3.41 rad/s2. Through what angle does the pulley turn in 5.26 s? A) 113 rad B) 22.6 rad C) 42.6 rad D) 19.3 rad E) 160 rad
B
35) An old 78 rpm record rotates through an angle of 320° as it slows down uniformly from 78.0 rpm to 22.8 rpm. What is the magnitude of the angular acceleration of the record? A) 2.34 rad/s2 B) 5.46 rad/s2 C) 6.50 rad/s2 D) 8.35 rad/s2 E) 10.9 rad/s2
1.4 s
36) A turntable 45 cm in diameter starts from rest and makes its first complete revolution in 3.4 s with constant angular acceleration. If it maintains the same acceleration, how long will it take the turntable to make its second complete revolution?
C
37) A Ferris wheel rotating at 20 rad/s slows down with a constant angular acceleration of magnitude 5.0 rad/s2. How many revolutions does it make while slowing down before coming to rest? A) 40 B) 20 C) 6.4 D) 3.2
(a) 230 rad/s2 (b) 1.7 s
38) A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it makes 50 complete turns at a constant angular acceleration before coming to rest. (a) What was the magnitude of the angular acceleration of the centrifuge as it slowed down? (d) How long did it take for the centrifuge to come to rest after being turned off?
0.36 kg ∙ m2
39) A majorette fastens two batons together at their centers to form an X shape. Each baton consists of an extremely light 1.2-m bar with small 0.25-kg balls at each end. What is the moment of inertia of this baton about an axis through the center of the X?
B
4) The figure shows scale drawings of four objects, each of the same mass and uniform thickness, with the mass distributed uniformly. Which one has the greatest moment of inertia when rotated about an axis perpendicular to the plane of the drawing at point P? A) A B) B C) C D) D E) The moment of inertia is the same for all of these objects.
A
4) Through how many degrees does a 33 rpm turntable rotate in A) 63° B) 35° C) 46° D) 74°
D
40) A triatomic molecule is oriented as follows along the x-axis: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia of this molecule about the y-axis? A) 2ma2 B) 3ma2 C) 12ma2 D) 14ma2
E
41) 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 about a central axis to that of the smaller sphere is A) 4/5. B) 8/5. C) 1/2. D) 2. E) 4.
(a) 6.48 kg ∙ m2 (b) 32.7 kg ∙ m2
42) The L-shaped object shown in the figure consists of three small masses connected by extremely light rods. Assume that the masses shown are accurate to three significant figures. What is the moment of inertia of this object (a) about the x-axis, and (b) about the y-axis?
(a) 19.4 kg ∙ m2 (b) 76.2 kg ∙ m2
43) The L-shaped object shown in the figure consists of three small masses connected by thin uniform rods, each rod of mass 3.00 kg. Assume that the masses shown are accurate to three significant figures. What is the moment of inertia of this object (a) about the x-axis, and (b) about the y-axis?
24.9 kg ∙ m2
44) In the figure, a weightlifter's barbell consists of two identical small but dense spherical weights, each of mass 50 kg. These weights are connected by a thin 0.96-m rod with a mass of 24 kg. Find the moment of inertia of the barbell through the axis perpendicular to the rod at its center, assuming the two weights are small enough to be treated as point masses.
A
45) A potter's wheel has the shape of a solid uniform disk of mass and radius 0.65 m. It spins about an axis perpendicular to the disk at its center. A small 2.1 kg lump of very dense clay is dropped onto the wheel at a distance 0.41 m from the axis. What is the moment of inertia of the system about the axis of spin? A) 1.8 kg ∙ m2 B) 1.5 kg ∙ m2 C) 0.40 kg ∙ m2 D) 2.5 kg ∙ m2
B
46) A uniform 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 33.4 rpm. What is its kinetic energy? A) 0.18 J B) 0.092 J C) 0.96 J D) 1.1 J E) 17 J
A
47) What is the kinetic energy of a 120-cm thin uniform rod with a mass of 450 g that is 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
C
48) To drive a typical car at 40 mph on a level road for one hour requires about 3.2 × 107 J of energy. Suppose we tried to store this much energy in a spinning, solid, uniform, cylindrical flywheel. A large flywheel cannot be spun too fast or it will fracture. If we used a flywheel of diameter 1.2 m and mass 400 kg, what angular speed would be required to store 3.2 × 107 J? A) 1800 rad/s B) 3600 rad/s C) 940 rad/s D) 530 rad/s E) 5500 rad/s
(a) 34.2 J (b) 173 J
49) The L-shaped object shown in the figure consists of three small masses connected by extremely light rods. Assume that the masses shown are accurate to three significant figures. How much work must be done to accelerate the object from rest to an angular speed of 3.25 rad/s (a) about the x-axis, (b) about the y-axis?
C
5) Consider a uniform hoop of radius R and mass M rolling without slipping. Which is larger, its translational kinetic energy or its rotational kinetic energy? A) Translational kinetic energy is larger. B) Rotational kinetic energy is larger. C) Both are equal. D) You need to know the speed of the hoop to tell.
3.49 rad/s
5) Express the angular speed of an old 33 1/3 rpm LP in rad/s.
403 J
50) The L-shaped object shown in the figure consists of three small masses connected by thin uniform rods, each rod of mass 3.00 kg. Assume that the masses shown are accurate to three significant figures. How much work must be done to accelerate the object from rest to an angular speed of 3.25 rad/s about the y-axis?
221 m/s
51) A futuristic design for a car is to have a large flywheel within the car to store kinetic energy. The flywheel is a solid uniform disk of mass 370 kg with a radius of 0.50 m, and it can rotate up to Assuming all of this stored kinetic energy could be transferred to the linear speed of the car, find the maximum attainable speed of the car.
1.8 rad/s
52) A small ball is tied to one end of a light 2.5-m wire, and the other end of the wire is hooked to the ceiling. A person pulls the ball to the side until the wire makes an angle of 35° with the plane of the ceiling and then gently releases it. What is the angular speed of the ball, in rad/s, as it swings through its lowest point?
A
53) While spinning down from 500 rpm to rest, a flywheel does of work. This flywheel is in the shape of a solid uniform disk of radius 1.2 m. What is the mass of this flywheel? A) 4.0 kg B) 3.4 kg C) 4.6 kg D) 5.2 kg
A
54) A solid uniform sphere of mass 120 kg and radius 1.7 m starts from rest and rolls without slipping down an inclined plane of vertical height 5.3 m. What is the angular speed of the sphere at the bottom of the inclined plane? A) 5.1 rad/s B) 8.7 rad/s C) 9.7 rad/s D) 6.1 rad/s
A
55) A solid uniform disk of diameter 3.20 m and mass 42 kg rolls without slipping to the bottom of a hill, starting from rest. If the angular speed of the disk is 4.27 rad/s at the bottom, how high did it start on the hill? A) 3.57 m B) 2.68 m C) 3.14 m D) 4.28 m
A
56) A wheel having a 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) 64.0 J C) 78.8 J D) 122 J
E
57) As shown in the figure, two blocks are connected by a light string that passes over a frictionless pulley having a moment of inertia of 0.0040 kg ∙ m2 and diameter 10 cm. The coefficient of kinetic friction between the table top and the upper block is 0.30. The blocks are released from rest, and the string does not slip on the pulley. How fast is the upper block moving when the lower one has fallen 0.60 m? A) 1.2 m/s B) 5.4 m/s C) 3.2 m/s D) 2.0 m/s E) 1.4 m/s
A
58) A solid uniform ball with a mass of 125 g is rolling without slipping along the horizontal surface of a table with a speed of 4.5 m/s when it rolls off the edge and falls towards the floor, 1.1 m below. What is the rotational kinetic energy of the ball just before it hits the floor? A) 0.51 J B) 0.73 J C) 1.1 J D) 2.6 J E) This question cannot be answered without knowing the radius of the ball.
C
59) A string is wrapped tightly around a fixed pulley that has a moment of inertia of 0.0352 kg ∙ m2 and a radius of 12.5 cm. A mass of 423 g is attached to the free end of the string. With the string vertical and taut, the mass is gently released so it can descend under the influence of gravity. As the mass descends, the string unwinds and causes the pulley to rotate, but does not slip on the pulley. What is the speed of the mass after it has fallen through 1.25 m? A) 2.00 m/s B) 2.28 m/s C) 1.97 m/s D) 3.94 m/s E) 4.95 m/s
0.0011 rad/s
6) An artificial satellite in a low orbit circles the earth every 98 minutes. What is its angular speed in rad/s?
A
6) Consider a solid uniform sphere of radius R and mass M rolling without slipping. Which form of its kinetic energy is larger, translational or rotational? A) Translational kinetic energy is larger. B) Rotational kinetic energy is larger. C) Both are equal. D) You need to know the speed of the sphere to tell.
B
60) A string is wrapped tightly around a fixed frictionless pulley that has a moment of inertia of 0.0352 kg ∙ m2 and a radius of 12.5 cm. The string is pulled away from the pulley with a constant force of 5.00 N, causing the pulley to rotate. What is the speed of the string after it has unwound 1.25 m if the string does not slip on the pulley? A) 2.09 m/s B) 2.36 m/s C) 1.18m/s D) 3.18 m/s E) 4.95 m/s
B
61) An Atwood machine consists of a mass of 3.5 kg connected by a light string to a mass of 6.0 kg over a frictionless pulley with a moment of inertia of 0.0352 kg ∙ m2 and a radius of 12.5 cm. If the system is released from rest, what is the speed of the masses after they have moved through 1.25 m if the string does not slip on the pulley? A) 2.0 m/s B) 2.3 m/s C) 4.0 m/s D) 5.0 m/s E) 6.0 m/s
2.4 m/s
62) The figure shows two blocks connected by a light cord over a pulley. This apparatus is known as an Atwood's machine. There is no slipping between the cord and the surface of the pulley. The pulley itself has negligible friction and it has a radius of 0.12 m and a mass of 10.3 kg. We can model this pulley as a solid uniform disk. At the instant that the heavier block has descended 1.5 m starting from rest, what is the speed of the lighter block?
A
63) A pencil that is 15.7 cm long is released from a vertical position with the eraser end resting on a table. The eraser does not slip as it tips over. Treat the pencil like a uniform rod. What is the angular speed of the pencil just before it hits the table? A) 13.7 rad/s B) 7.23 rad/s C) 3.70 rad/s D) 24.5 rad/s E) 16.8 rad/s
C
64) A uniform solid disk is released from rest and rolls without slipping down an inclined plane that makes an angle of 25° with the horizontal. What is the forward speed of the disk after it has rolled 3.0 m, measured along the plane? A) 2.0 m/s B) 3.5 m/s C) 4.1 m/s D) 5.7 m/s E) 6.3 m/s
B
65) A solid uniform disk is rolling without slipping along a horizontal surface with a speed of 4.5 m/s when it starts up a ramp that makes an angle of 25° with the horizontal. What is the speed of the disk after it has rolled 3.0 m up as measured along the surface of the ramp? A) 4.0 m/s B) 1.9 m/s C) 2.1 m/s D) 6.8 m/s E) 8.0 m/s
E
66) A solid uniform sphere is rolling without slipping along a horizontal surface with a speed of 5.5 m/s when it starts up a ramp that makes an angle of 25° with the horizontal. What is the speed of the sphere after it has rolled 3.0 m up as measured along the surface of the ramp? A) 4.0 m/s B) 8.0 m/s C) 1.9 m/s D) 2.2 m/s E) 3.5 m/s
A
67) A hoop is rolling without slipping along a horizontal surface with a forward speed of 5.50 m/s when it starts up a ramp that makes an angle of 25.0° with the horizontal. What is the speed of the hoop after it has rolled 3.00 m up as measured along the surface of the ramp? A) 4.22 m/s B) 1.91 m/s C) 2.06 m/s D) 3.79 m/s E) 8.02 m/s
D
68) A hoop with a mass of 2.75 kg is rolling without slipping along a horizontal surface with a speed of 4.5 m/s when it starts down a ramp that makes an angle of 25° below the horizontal. What is the forward speed of the hoop after it has rolled 3.0 m down as measured along the surface of the ramp? A) 4.9 m/s B) 6.3 m/s C) 5.2 m/s D) 5.7 m/s E) 8.0 m/s
C
69) A hoop with a mass of 2.75 kg is rolling without slipping along a horizontal surface with a speed of 4.5 m/s when it starts down a ramp that makes an angle of 25° below the horizontal. What is the rotational kinetic energy of the hoop after it has rolled 3.0 m down as measured along the surface of the ramp? A) 34 J B) 22 J C) 45 J D) 62 J E) This question cannot be answered without knowing the radius of the hoop.
A
7) A chicken is running in a circular path with an angular speed of 1.52 rad/s. How long does it take the chicken to complete one revolution? A) 4.13 s B) 2.07 s C) 118 s D) 4.77 s E) 8.26 s
B
7) A solid sphere and a solid cylinder, both uniform and of the same mass and radius, roll without slipping at the same forward speed. It is correct to say that the total kinetic energy of the solid sphere is A) more than the total kinetic energy of the cylinder. B) less than the total kinetic energy of the cylinder. C) equal to the total kinetic energy of the cylinder.
(a) 5.42 m/s (b) 24.5 J
70) A solid uniform 3.33-kg disk has thin string of negligible mass wrapped around its rim, with one end of the string tied to the ceiling, as shown in the figure. The disk is released from rest, and as it falls, it turns as the string unwraps. At the instant its center has fallen 2.25 m, (a) how fast is the center moving, and (b) how much rotational kinetic energy does the disk have?
(a) 3.7 m/s (b) 4.4 m/s (c) With friction, some of the initial potential energy goes into rotational kinetic energy, leaving less for translational kinetic energy. Without friction, the ball does not rotate, so all the initial potential energy goes into translational kinetic energy.
71) A solid uniform ball of mass 1.0 kg and radius 1.0 cm starts from rest and rolls down a 1.0-m high ramp. There is enough friction on the ramp to prevent the ball from slipping as it rolls down. (a) What is the forward speed of the ball when it reaches the bottom of the ramp? (b) What would be the forward speed of the ball if there were no friction on the ramp? (c) Since the ball starts from the same height in both cases, why is the speed different?
B
8) A disk and a hoop of the same mass and radius are released at the same time at the top of an inclined plane. If both are uniform, which one reaches the bottom of the incline first if there is no slipping? A) The hoop B) The disk C) Both reach the bottom at the same time.
B
8) At a certain instant, a compact disc is rotating at 210 rpm. What is its angular speed in rad/s? A) 11 rad/s B) 22 rad/s C) 45 rad/s D) 69 rad/s E) 660 rad/s
A
9) A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii. If the three of them are released simultaneously at the top of an inclined plane and do not slip, which one will reach the bottom first? A) sphere B) pipe C) cylinder D) The pipe and cylinder arrive together before the sphere. E) They all reach the bottom at the same time.
B
9) When a fan is turned off, its angular speed decreases from 10 rad/s to 6.3 rad/s in 5.0 s. What is the magnitude of the average angular acceleration of the fan? A) 0.86 rad/s2 B) 0.74 rad/s2 C) 0.37 rad/s2 D) 11 rad/s2 E) 1.2 rad/s2
