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Rotational kinematics with constant angular acceleration: A 1.15-kg grinding wheel 22.0 cm in diameter is spinning counterclockwise at a rate of 20.0 revolutions per second. When the power to the grinder is turned off, the grinding wheel slows with constant angular acceleration and takes 80.0 s to come to a rest. (a) What was the angular acceleration (in rad/s2) of the grinding wheel as it came to rest if we take a counterclockwise rotation as positive? (b) How many revolutions did the wheel make during the time it was coming to rest?

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(a) -1.57 ...

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Equilibrium: A solid uniform brick is placed on a sheet of wood. When one end of the sheet is raised (see figure) , you observe that the maximum that the angle θ can be without tipping over the brick is 49.6°. There is enough friction to prevent the brick from sliding. What is the width w of the brick? Equilibrium: A solid uniform brick is placed on a sheet of wood. When one end of the sheet is raised (see figure) , you observe that the maximum that the angle θ can be without tipping over the brick is 49.6°. There is enough friction to prevent the brick from sliding. What is the width w of the brick? A) 5.18 cm B) 6.09 cm C) 6.81 cm D) 9.40 cm E) 10.5 cm


A) 5.18 cm
B) 6.09 cm
C) 6.81 cm
D) 9.40 cm
E) 10.5 cm

F) B) and E)
G) A) and B)

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Angular momentum: A bicycle is traveling north at 5.0 m/s. The mass of the wheel, 2.0 kg, is uniformly distributed along the rim, which has a radius of 20 cm. What are the magnitude and direction of the angular momentum of the wheel about its axle?


A) 2.0 kg ∙ m2/s towards the west
B) 5.0 kg ∙ m2/s vertically upwards
C) 2.0 kg ∙ m2/s towards the east
D) 5.0 kg ∙ m2/s towards the east
E) 5.0 kg ∙ m2/s towards the west

F) C) and E)
G) C) and D)

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Torque: A 95 N force exerted at the end of a Torque: A 95 N force exerted at the end of a torque wrench gives rise to a torque of What is the angle (assumed to be less than 90°) between the wrench handle and the direction of the applied force? A) 18° B) 14° C) 22° D) 25° torque wrench gives rise to a torque of Torque: A 95 N force exerted at the end of a torque wrench gives rise to a torque of What is the angle (assumed to be less than 90°) between the wrench handle and the direction of the applied force? A) 18° B) 14° C) 22° D) 25° What is the angle (assumed to be less than 90°) between the wrench handle and the direction of the applied force?


A) 18°
B) 14°
C) 22°
D) 25°

E) A) and B)
F) A) and C)

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Conservation of angular momentum: The angular momentum of a system remains constant


A) when the total kinetic energy is constant.
B) when no net external force acts on the system.
C) when the linear momentum and the energy are constant.
D) when no torque acts on the system.
E) all the time since it is a conserved quantity.

F) A) and B)
G) All of the above

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Rotational dynamics about a moving axis: A uniform solid cylindrical log begins rolling without slipping down a ramp that rises 28.0° above the horizontal. After it has rolled 4.20 m along the ramp, what is the magnitude of the linear acceleration of its center of mass?


A) 9.80 m/s2
B) 4.60 m/s2
C) 3.29 m/s2
D) 3.07 m/s2
E) 2.30 m/s2

F) A) and E)
G) None of the above

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Equilibrium: A 3.00-kg ball rests in a frictionless groove as shown in the figure. Equilibrium: A 3.00-kg ball rests in a frictionless groove as shown in the figure. (a) What is the magnitude of the force that the left side of the groove exerts on the ball? (b) What is the magnitude of the force that the right side of the groove exerts on the ball? (a) What is the magnitude of the force that the left side of the groove exerts on the ball? (b) What is the magnitude of the force that the right side of the groove exerts on the ball?

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(a) 26.4 N...

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Equilibrium: A 120-kg refrigerator, 2.00 m tall and 85.0 cm wide, has its center of mass at its geometrical center. You are attempting to slide it along the floor by pushing horizontally on the side of the refrigerator. The coefficient of static friction between the floor and the refrigerator is 0.300. Depending on where you push, the refrigerator may start to tip over before it starts to slide along the floor. What is the highest distance above the floor that you can push the refrigerator so that it won't tip before it begins to slide?


A) 0.710 m
B) 1.00 m
C) 1.21 m
D) 1.42 m
E) 1.63 m

F) A) and E)
G) B) and C)

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Rolling: A uniform solid disk of radius 1.60 m and mass 2.30 kg rolls without slipping to the bottom of an inclined plane. If the angular velocity of the disk is Rolling: A uniform solid disk of radius 1.60 m and mass 2.30 kg rolls without slipping to the bottom of an inclined plane. If the angular velocity of the disk is at the bottom, what is the height of the inclined plane? A) 5.61 m B) 4.21 m C) 4.94 m D) 6.73 m at the bottom, what is the height of the inclined plane?


A) 5.61 m
B) 4.21 m
C) 4.94 m
D) 6.73 m

E) A) and B)
F) C) and D)

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Equilibrium: A child is trying to stack two uniform wooden blocks, 12 cm in length, so they will protrude as much as possible over the edge of a table, without tipping over, as shown in the figure. What is the maximum possible overhang distance d? Equilibrium: A child is trying to stack two uniform wooden blocks, 12 cm in length, so they will protrude as much as possible over the edge of a table, without tipping over, as shown in the figure. What is the maximum possible overhang distance d? A) 5 cm B) 6 cm C) 7 cm D) 8 cm E) 9 cm


A) 5 cm
B) 6 cm
C) 7 cm
D) 8 cm
E) 9 cm

F) C) and D)
G) A) and D)

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Equilibrium: A light board, 10 m long, is supported by two sawhorses, one at one edge of the board and a second at the midpoint. A small 40-N weight is placed between the two sawhorses, 3.0 m from the edge and 2.0 m from the center. What forces are exerted by the sawhorses on the board?

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16 N at th...

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Rotational kinematics with constant angular acceleration: In the figure, point P is at rest when it is on the x-axis. The linear speed of point P when it reaches the y-axis is closest to Rotational kinematics with constant angular acceleration: In the figure, point P is at rest when it is on the x-axis. The linear speed of point P when it reaches the y-axis is closest to A) 0.18 m/s. B) 0.24 m/s. C) 0.35 m/s. D) 0.49 m/s. E) 0.71 m/s.


A) 0.18 m/s.
B) 0.24 m/s.
C) 0.35 m/s.
D) 0.49 m/s.
E) 0.71 m/s.

F) A) and B)
G) All of the above

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Rolling: A uniform solid cylinder of radius R and a thin uniform spherical shell of radius R both roll without slipping. If both objects have the same mass and the same kinetic energy, what is the ratio of the linear speed of the cylinder to the linear speed of the spherical shell?


A) Rolling: A uniform solid cylinder of radius R and a thin uniform spherical shell of radius R both roll without slipping. If both objects have the same mass and the same kinetic energy, what is the ratio of the linear speed of the cylinder to the linear speed of the spherical shell? A) /2 B) /2 C) D) 4/ E) 4/3 /2
B) Rolling: A uniform solid cylinder of radius R and a thin uniform spherical shell of radius R both roll without slipping. If both objects have the same mass and the same kinetic energy, what is the ratio of the linear speed of the cylinder to the linear speed of the spherical shell? A) /2 B) /2 C) D) 4/ E) 4/3 /2
C) Rolling: A uniform solid cylinder of radius R and a thin uniform spherical shell of radius R both roll without slipping. If both objects have the same mass and the same kinetic energy, what is the ratio of the linear speed of the cylinder to the linear speed of the spherical shell? A) /2 B) /2 C) D) 4/ E) 4/3
D) 4/ Rolling: A uniform solid cylinder of radius R and a thin uniform spherical shell of radius R both roll without slipping. If both objects have the same mass and the same kinetic energy, what is the ratio of the linear speed of the cylinder to the linear speed of the spherical shell? A) /2 B) /2 C) D) 4/ E) 4/3
E) 4/3

F) All of the above
G) B) and D)

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Equilibrium: An 82.0 kg-diver stands at the edge of a light 5.00-m diving board, which is supported by two narrow pillars 1.60 m apart, as shown in the figure. Find the magnitude and direction of the force exerted on the diving board (a) by pillar A. (b) by pillar B. Equilibrium: An 82.0 kg-diver stands at the edge of a light 5.00-m diving board, which is supported by two narrow pillars 1.60 m apart, as shown in the figure. Find the magnitude and direction of the force exerted on the diving board (a) by pillar A. (b) by pillar B.

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(a) 1.71 k...

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Rolling: A uniform disk, a uniform hoop, and a uniform solid sphere are released at the same time at the top of an inclined ramp. They all roll without slipping. In what order do they reach the bottom of the ramp?


A) disk, hoop, sphere
B) hoop, sphere, disk
C) sphere, disk, hoop
D) sphere, hoop, disk
E) hoop, disk, sphere

F) A) and B)
G) C) and E)

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Rotational kinetic energy: In the figure, two blocks, of masses 2.00 kg and 3.00 kg, are connected by a light string that passes over a frictionless pulley of moment of inertia 0.00400 kg · m2 and radius 5.00 cm. The coefficient of friction for the tabletop is 0.300. The blocks are released from rest. Using energy methods, find the speed of the upper block just as it has moved 0.600 m. Rotational kinetic energy: In the figure, two blocks, of masses 2.00 kg and 3.00 kg, are connected by a light string that passes over a frictionless pulley of moment of inertia 0.00400 kg · m<sup>2</sup> and radius 5.00 cm. The coefficient of friction for the tabletop is 0.300. The blocks are released from rest. Using energy methods, find the speed of the upper block just as it has moved 0.600 m. A) 1.22 m/s B) 5.44 m/s C) 3.19 m/s D) 1.95 m/s E) 1.40 m/s


A) 1.22 m/s
B) 5.44 m/s
C) 3.19 m/s
D) 1.95 m/s
E) 1.40 m/s

F) B) and E)
G) A) and B)

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Rotational dynamics about a moving axis: A thin cylindrical shell is released from rest and rolls without slipping down an inclined ramp that makes an angle of 30° with the horizontal. How long does it take it to travel the first 3.1 m?


A) 1.4 s
B) 1.1 s
C) 2.1 s
D) 1.6 s
E) 1.8 s

F) B) and D)
G) C) and D)

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Equilibrium: A 10.0-kg uniform ladder that is 2.50 m long is placed against a smooth vertical wall and reaches to a height of 2.10 m, as shown in the figure. The base of the ladder rests on a rough horizontal floor whose coefficient of static friction with the ladder is 0.800. An 80.0-kg bucket of concrete is suspended from the top rung of the ladder, right next to the wall, as shown in the figure. What is the magnitude of the friction force that the floor exerts on the ladder? Equilibrium: A 10.0-kg uniform ladder that is 2.50 m long is placed against a smooth vertical wall and reaches to a height of 2.10 m, as shown in the figure. The base of the ladder rests on a rough horizontal floor whose coefficient of static friction with the ladder is 0.800. An 80.0-kg bucket of concrete is suspended from the top rung of the ladder, right next to the wall, as shown in the figure. What is the magnitude of the friction force that the floor exerts on the ladder? A) 538 N B) 706 N C) 1290 N D) 833 N E) 601 N


A) 538 N
B) 706 N
C) 1290 N
D) 833 N
E) 601 N

F) All of the above
G) B) and D)

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Moment of inertia: A piece of thin uniform wire of mass m and length 3b is bent into an equilateral triangle. Find the moment of inertia of the wire triangle about an axis perpendicular to the plane of the triangle and passing through one of its vertices.


A) Moment of inertia: A piece of thin uniform wire of mass m and length 3b is bent into an equilateral triangle. Find the moment of inertia of the wire triangle about an axis perpendicular to the plane of the triangle and passing through one of its vertices. A) mb<sup>2</sup> B) mb<sup>2</sup> C) mb<sup>2</sup> D) mb<sup>2</sup> E) mb<sup>2</sup> mb2
B) Moment of inertia: A piece of thin uniform wire of mass m and length 3b is bent into an equilateral triangle. Find the moment of inertia of the wire triangle about an axis perpendicular to the plane of the triangle and passing through one of its vertices. A) mb<sup>2</sup> B) mb<sup>2</sup> C) mb<sup>2</sup> D) mb<sup>2</sup> E) mb<sup>2</sup> mb2
C) Moment of inertia: A piece of thin uniform wire of mass m and length 3b is bent into an equilateral triangle. Find the moment of inertia of the wire triangle about an axis perpendicular to the plane of the triangle and passing through one of its vertices. A) mb<sup>2</sup> B) mb<sup>2</sup> C) mb<sup>2</sup> D) mb<sup>2</sup> E) mb<sup>2</sup> mb2
D) Moment of inertia: A piece of thin uniform wire of mass m and length 3b is bent into an equilateral triangle. Find the moment of inertia of the wire triangle about an axis perpendicular to the plane of the triangle and passing through one of its vertices. A) mb<sup>2</sup> B) mb<sup>2</sup> C) mb<sup>2</sup> D) mb<sup>2</sup> E) mb<sup>2</sup> mb2
E) Moment of inertia: A piece of thin uniform wire of mass m and length 3b is bent into an equilateral triangle. Find the moment of inertia of the wire triangle about an axis perpendicular to the plane of the triangle and passing through one of its vertices. A) mb<sup>2</sup> B) mb<sup>2</sup> C) mb<sup>2</sup> D) mb<sup>2</sup> E) mb<sup>2</sup> mb2

F) B) and D)
G) A) and B)

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Rotational dynamics about a fixed axis: A solid uniform sphere of mass 1.85 kg and diameter 45.0 cm spins about an axle through its center. Starting with an angular velocity of 2.40 rev/s, it stops after turning through 18.2 rev with uniform acceleration. The net torque acting on this sphere as it is slowing down is closest to


A) 0.00593 N ∙ m.
B) 0.0372 N ∙ m.
C) 0.0466 N ∙ m.
D) 0.0620 N ∙ m.
E) 0.149 N ∙ m.

F) A) and E)
G) B) and D)

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