Filters
Question type
Study Flashcards

Rotational dynamics about a fixed axis: In the figure, a mass of 31.77 kg is attached to a light string that is wrapped around a cylindrical spool of radius 10.0 cm and moment of inertia 4.00 kg · m2. The spool is suspended from the ceiling, and the mass is then released from rest a distance 5.70 m above the floor. How long does it take to reach the floor? Rotational dynamics about a fixed axis: In the figure, a mass of 31.77 kg is attached to a light string that is wrapped around a cylindrical spool of radius 10.0 cm and moment of inertia 4.00 kg · m<sup>2</sup>. The spool is suspended from the ceiling, and the mass is then released from rest a distance 5.70 m above the floor. How long does it take to reach the floor? A) 3.98 s B) 3.83 s C) 1.14 s D) 5.59 s E) 7.89 s


A) 3.98 s
B) 3.83 s
C) 1.14 s
D) 5.59 s
E) 7.89 s

Correct Answer

verifed

verified

Conservation of angular momentum: A potter's wheel, with rotational inertia Conservation of angular momentum: A potter's wheel, with rotational inertia is spinning freely at 40 rpm. The potter drops a lump of clay onto the wheel, where it sticks a distance 1.2 m from the rotational axis. If the subsequent angular speed of the wheel and clay is 32 rpm what is the mass of the clay? A) 8.0 kg B) 5.4 kg C) 7.0 kg D) 8.8 kg is spinning freely at 40 rpm. The potter drops a lump of clay onto the wheel, where it sticks a distance 1.2 m from the rotational axis. If the subsequent angular speed of the wheel and clay is 32 rpm what is the mass of the clay?


A) 8.0 kg
B) 5.4 kg
C) 7.0 kg
D) 8.8 kg

Correct Answer

verifed

verified

Conservation of angular momentum: A turntable has a radius of 0.80 m and a moment of inertia of 2.0 kg · m2. The turntable is rotating with an angular velocity of 1.5 rad/s about a vertical axis though its center on frictionless bearings. A very small 0.40-kg ball is projected horizontally toward the turntable axis with a velocity of 3.0 m/s. The ball is caught by a very small and very light cup-shaped mechanism on the rim of the turntable (see figure) . What is the angular velocity of the turntable just after the ball is caught? Conservation of angular momentum: A turntable has a radius of 0.80 m and a moment of inertia of 2.0 kg · m<sup>2</sup>. The turntable is rotating with an angular velocity of 1.5 rad/s about a vertical axis though its center on frictionless bearings. A very small 0.40-kg ball is projected horizontally toward the turntable axis with a velocity of 3.0 m/s. The ball is caught by a very small and very light cup-shaped mechanism on the rim of the turntable (see figure) . What is the angular velocity of the turntable just after the ball is caught? A) 2.1 rad/s B) 1.3 rad/s C) 0.94 rad/s D) 0.75 rad/s E) 0.30 rad/s


A) 2.1 rad/s
B) 1.3 rad/s
C) 0.94 rad/s
D) 0.75 rad/s
E) 0.30 rad/s

Correct Answer

verifed

verified

Rolling: A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii and are of uniform density. If the three are released simultaneously at the top of an inclined plane and roll without slipping, which one will reach the bottom first?


A) solid sphere
B) hollow pipe
C) solid cylinder
D) They all reach the bottom at the same time.

Correct Answer

verifed

verified

Conservation of angular momentum: A uniform disk has a mass of 3.7 kg and a radius of 0.40 m. The disk is mounted on frictionless bearings and is used as a turntable. The turntable is initially rotating at 30 rpm. A thin-walled hollow cylinder has the same mass and radius as the disk. It is released from rest, just above the turntable, and on the same vertical axis. The hollow cylinder slips on the turntable for 0.20 s until it acquires the same final angular velocity as the turntable. What is the final angular momentum of the system?


A) 0.93 Conservation of angular momentum: A uniform disk has a mass of 3.7 kg and a radius of 0.40 m. The disk is mounted on frictionless bearings and is used as a turntable. The turntable is initially rotating at 30 rpm. A thin-walled hollow cylinder has the same mass and radius as the disk. It is released from rest, just above the turntable, and on the same vertical axis. The hollow cylinder slips on the turntable for 0.20 s until it acquires the same final angular velocity as the turntable. What is the final angular momentum of the system? A) 0.93 /s B) 1.1 /s C) 1.3 /s D) 1.6 /s E) 1.9 /s /s
B) 1.1 Conservation of angular momentum: A uniform disk has a mass of 3.7 kg and a radius of 0.40 m. The disk is mounted on frictionless bearings and is used as a turntable. The turntable is initially rotating at 30 rpm. A thin-walled hollow cylinder has the same mass and radius as the disk. It is released from rest, just above the turntable, and on the same vertical axis. The hollow cylinder slips on the turntable for 0.20 s until it acquires the same final angular velocity as the turntable. What is the final angular momentum of the system? A) 0.93 /s B) 1.1 /s C) 1.3 /s D) 1.6 /s E) 1.9 /s /s
C) 1.3 Conservation of angular momentum: A uniform disk has a mass of 3.7 kg and a radius of 0.40 m. The disk is mounted on frictionless bearings and is used as a turntable. The turntable is initially rotating at 30 rpm. A thin-walled hollow cylinder has the same mass and radius as the disk. It is released from rest, just above the turntable, and on the same vertical axis. The hollow cylinder slips on the turntable for 0.20 s until it acquires the same final angular velocity as the turntable. What is the final angular momentum of the system? A) 0.93 /s B) 1.1 /s C) 1.3 /s D) 1.6 /s E) 1.9 /s /s
D) 1.6 Conservation of angular momentum: A uniform disk has a mass of 3.7 kg and a radius of 0.40 m. The disk is mounted on frictionless bearings and is used as a turntable. The turntable is initially rotating at 30 rpm. A thin-walled hollow cylinder has the same mass and radius as the disk. It is released from rest, just above the turntable, and on the same vertical axis. The hollow cylinder slips on the turntable for 0.20 s until it acquires the same final angular velocity as the turntable. What is the final angular momentum of the system? A) 0.93 /s B) 1.1 /s C) 1.3 /s D) 1.6 /s E) 1.9 /s /s
E) 1.9 Conservation of angular momentum: A uniform disk has a mass of 3.7 kg and a radius of 0.40 m. The disk is mounted on frictionless bearings and is used as a turntable. The turntable is initially rotating at 30 rpm. A thin-walled hollow cylinder has the same mass and radius as the disk. It is released from rest, just above the turntable, and on the same vertical axis. The hollow cylinder slips on the turntable for 0.20 s until it acquires the same final angular velocity as the turntable. What is the final angular momentum of the system? A) 0.93 /s B) 1.1 /s C) 1.3 /s D) 1.6 /s E) 1.9 /s /s

Correct Answer

verifed

verified

A

Angular momentum: Three solid, uniform, cylindrical flywheels, each of mass 65.0 kg and radius 1.47 m rotate independently around a common axis. Two of the flywheels rotate in one direction at Angular momentum: Three solid, uniform, cylindrical flywheels, each of mass 65.0 kg and radius 1.47 m rotate independently around a common axis. Two of the flywheels rotate in one direction at the other rotates in the opposite direction at 3.42 rad/s. Calculate the magnitude of the net angular momentum of the system. A) 298 kg ∙ m<sup>2</sup>/s B) 778 kg ∙ m<sup>2</sup>/s C) 257 kg ∙ m<sup>2</sup>/s D) 222 kg ∙ m<sup>2</sup>/s the other rotates in the opposite direction at 3.42 rad/s. Calculate the magnitude of the net angular momentum of the system.


A) 298 kg ∙ m2/s
B) 778 kg ∙ m2/s
C) 257 kg ∙ m2/s
D) 222 kg ∙ m2/s

Correct Answer

verifed

verified

Torque: A force Torque: A force = 3.00 N - 2.00 N acts as a location = 1.00 m + 2.00 m on an object. What is the torque that this force applies about an axis through the origin perpendicular to the xy-plane? A) -1.00 N ∙ m B) 7.00 N ∙ m C) -3.00 N ∙ m D) 5.00 N ∙ m E) -8.00 N ∙ m = 3.00 N Torque: A force = 3.00 N - 2.00 N acts as a location = 1.00 m + 2.00 m on an object. What is the torque that this force applies about an axis through the origin perpendicular to the xy-plane? A) -1.00 N ∙ m B) 7.00 N ∙ m C) -3.00 N ∙ m D) 5.00 N ∙ m E) -8.00 N ∙ m - 2.00 N Torque: A force = 3.00 N - 2.00 N acts as a location = 1.00 m + 2.00 m on an object. What is the torque that this force applies about an axis through the origin perpendicular to the xy-plane? A) -1.00 N ∙ m B) 7.00 N ∙ m C) -3.00 N ∙ m D) 5.00 N ∙ m E) -8.00 N ∙ m acts as a location Torque: A force = 3.00 N - 2.00 N acts as a location = 1.00 m + 2.00 m on an object. What is the torque that this force applies about an axis through the origin perpendicular to the xy-plane? A) -1.00 N ∙ m B) 7.00 N ∙ m C) -3.00 N ∙ m D) 5.00 N ∙ m E) -8.00 N ∙ m = 1.00 m Torque: A force = 3.00 N - 2.00 N acts as a location = 1.00 m + 2.00 m on an object. What is the torque that this force applies about an axis through the origin perpendicular to the xy-plane? A) -1.00 N ∙ m B) 7.00 N ∙ m C) -3.00 N ∙ m D) 5.00 N ∙ m E) -8.00 N ∙ m + 2.00 m Torque: A force = 3.00 N - 2.00 N acts as a location = 1.00 m + 2.00 m on an object. What is the torque that this force applies about an axis through the origin perpendicular to the xy-plane? A) -1.00 N ∙ m B) 7.00 N ∙ m C) -3.00 N ∙ m D) 5.00 N ∙ m E) -8.00 N ∙ m on an object. What is the torque that this force applies about an axis through the origin perpendicular to the xy-plane?


A) -1.00 N ∙ m Torque: A force = 3.00 N - 2.00 N acts as a location = 1.00 m + 2.00 m on an object. What is the torque that this force applies about an axis through the origin perpendicular to the xy-plane? A) -1.00 N ∙ m B) 7.00 N ∙ m C) -3.00 N ∙ m D) 5.00 N ∙ m E) -8.00 N ∙ m
B) 7.00 N ∙ m Torque: A force = 3.00 N - 2.00 N acts as a location = 1.00 m + 2.00 m on an object. What is the torque that this force applies about an axis through the origin perpendicular to the xy-plane? A) -1.00 N ∙ m B) 7.00 N ∙ m C) -3.00 N ∙ m D) 5.00 N ∙ m E) -8.00 N ∙ m
C) -3.00 N ∙ m Torque: A force = 3.00 N - 2.00 N acts as a location = 1.00 m + 2.00 m on an object. What is the torque that this force applies about an axis through the origin perpendicular to the xy-plane? A) -1.00 N ∙ m B) 7.00 N ∙ m C) -3.00 N ∙ m D) 5.00 N ∙ m E) -8.00 N ∙ m
D) 5.00 N ∙ m Torque: A force = 3.00 N - 2.00 N acts as a location = 1.00 m + 2.00 m on an object. What is the torque that this force applies about an axis through the origin perpendicular to the xy-plane? A) -1.00 N ∙ m B) 7.00 N ∙ m C) -3.00 N ∙ m D) 5.00 N ∙ m E) -8.00 N ∙ m
E) -8.00 N ∙ m Torque: A force = 3.00 N - 2.00 N acts as a location = 1.00 m + 2.00 m on an object. What is the torque that this force applies about an axis through the origin perpendicular to the xy-plane? A) -1.00 N ∙ m B) 7.00 N ∙ m C) -3.00 N ∙ m D) 5.00 N ∙ m E) -8.00 N ∙ m

Correct Answer

verifed

verified

Precession: An object is rotating with an angular momentum 4.00 kg ∙ m2/s while being acted on by a constant torque 3.00 N∙m . What is the angular speed of precession of the angular velocity of the object?


A) 1.33 rad/s
B) 0.750 rad/s
C) 12.0 rad/s
D) zero
E) It depends on the moment of inertia of the object.

Correct Answer

verifed

verified

Rotational dynamics about a fixed axis: 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) . You release the hanging blocks simultaneously from rest, and call tL the time taken by the block on the left and tR the time taken by the block on the right to reach the bottom, respectively. The bar, pulley, and rope have negligible mass, the rope does not slip, and there is no friction in the axle of the pulley. Under these conditions Rotational dynamics about a fixed axis: 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) . You release the hanging blocks simultaneously from rest, and call t<sub>L</sub> the time taken by the block on the left and t<sub>R</sub> the time taken by the block on the right to reach the bottom, respectively. The bar, pulley, and rope have negligible mass, the rope does not slip, and there is no friction in the axle of the pulley. Under these conditions A) tL = tR. B) t<sub>L</sub> = t<sub>R</sub>. C) tL = tR. D) t<sub>L</sub> = 2t<sub>R</sub>. E) t<sub>l</sub> = 4t<sub>R</sub>.


A) tL = Rotational dynamics about a fixed axis: 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) . You release the hanging blocks simultaneously from rest, and call t<sub>L</sub> the time taken by the block on the left and t<sub>R</sub> the time taken by the block on the right to reach the bottom, respectively. The bar, pulley, and rope have negligible mass, the rope does not slip, and there is no friction in the axle of the pulley. Under these conditions A) tL = tR. B) t<sub>L</sub> = t<sub>R</sub>. C) tL = tR. D) t<sub>L</sub> = 2t<sub>R</sub>. E) t<sub>l</sub> = 4t<sub>R</sub>. tR.
B) tL = tR.
C) tL = Rotational dynamics about a fixed axis: 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) . You release the hanging blocks simultaneously from rest, and call t<sub>L</sub> the time taken by the block on the left and t<sub>R</sub> the time taken by the block on the right to reach the bottom, respectively. The bar, pulley, and rope have negligible mass, the rope does not slip, and there is no friction in the axle of the pulley. Under these conditions A) tL = tR. B) t<sub>L</sub> = t<sub>R</sub>. C) tL = tR. D) t<sub>L</sub> = 2t<sub>R</sub>. E) t<sub>l</sub> = 4t<sub>R</sub>. tR.
D) tL = 2tR.
E) tl = 4tR.

Correct Answer

verifed

verified

Rotational dynamics about a fixed axis: In an experiment, a student brings up the rotational speed of a piece of laboratory apparatus to 30.0 rpm. She then allows the apparatus to slow down uniformly on its own, and counts 240 revolutions before the apparatus comes to a stop. The moment of inertia of the apparatus is known to be 0.0850 kg ∙ m2. What is the magnitude of the retarding torque on the apparatus?


A) 0.0425 N ∙ m
B) 0.159 N ∙ m
C) 0.0787 N ∙ m
D) 0.000278 N ∙ m
E) 0.0000136 N ∙ m

Correct Answer

verifed

verified

Rotational kinematics with constant angular acceleration: A 4.50-kg wheel that is 34.5 cm in diameter 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

Correct Answer

verifed

verified

Basic rotational quantities: A horizontal disk rotates about a vertical axis through its center. Point P is midway between the center and the rim of the disk, and point Q is on the rim. If the disk turns with constant angular velocity, which of the following statements about it are true? (There may be more than one correct choice.)


A) P and Q have the same linear acceleration.
B) Q is moving twice as fast as P.
C) The linear acceleration of Q is twice as great as the linear acceleration of P.
D) The linear acceleration of P is twice as great as the linear acceleration of Q.
E) The angular velocity of Q is twice as great as the angular velocity of P.

Correct Answer

verifed

verified

Conservation of angular momentum: A 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg ∙ m2 is rotating freely with an angular speed of 1.0 rad/s. Two people, each having a mass of 60 kg, are standing right outside the edge of the merry-go-round and step on it with negligible speed. What is the angular speed of the merry-go-round right after the two people have stepped on?


A) 0.20 rad/s
B) 0.40 rad/s
C) 0.60 rad/s
D) 0.80 rad/s
E) 0.67 rad/s

Correct Answer

verifed

verified

Moment of inertia: A slender uniform rod 100.00 cm long is used as a meter stick. Two parallel axes that are perpendicular to the rod are considered. The first axis passes through the 50-cm mark and the second axis passes through the 30-cm mark. What is the ratio of the moment of inertia through the second axis to the moment of inertia through the first axis?


A) I2/I1 = 1.5
B) I2/I1 = 1.7
C) I2/I1 = 1.9
D) I2/I1 = 2.1
E) I2/I1 = 2.3

Correct Answer

verifed

verified

A

Basic rotational quantities: 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

Correct Answer

verifed

verified

Rotational kinetic energy: A uniform solid sphere of mass M and radius R rotates with an angular speed ω about an axis through its center. A uniform solid cylinder of mass M, radius R, and length 2R rotates through an axis running through the central axis of the cylinder. What must be the angular speed of the cylinder so it will have the same rotational kinetic energy as the sphere?


A) 2ω/5
B) Rotational kinetic energy: A uniform solid sphere of mass M and radius R rotates with an angular speed ω about an axis through its center. A uniform solid cylinder of mass M, radius R, and length 2R rotates through an axis running through the central axis of the cylinder. What must be the angular speed of the cylinder so it will have the same rotational kinetic energy as the sphere? A) 2ω/5 B) ω C) 4ω/5 D) 2ω/ E) ω/ ω
C) 4ω/5
D) 2ω/ Rotational kinetic energy: A uniform solid sphere of mass M and radius R rotates with an angular speed ω about an axis through its center. A uniform solid cylinder of mass M, radius R, and length 2R rotates through an axis running through the central axis of the cylinder. What must be the angular speed of the cylinder so it will have the same rotational kinetic energy as the sphere? A) 2ω/5 B) ω C) 4ω/5 D) 2ω/ E) ω/
E) ω/ Rotational kinetic energy: A uniform solid sphere of mass M and radius R rotates with an angular speed ω about an axis through its center. A uniform solid cylinder of mass M, radius R, and length 2R rotates through an axis running through the central axis of the cylinder. What must be the angular speed of the cylinder so it will have the same rotational kinetic energy as the sphere? A) 2ω/5 B) ω C) 4ω/5 D) 2ω/ E) ω/

Correct Answer

verifed

verified

D

Precession: In the figure, the rotor of a gyroscope is a uniform disk that has a radius of 13.8 cm and a moment of inertia about its axis of 4.0 × 10-3 kg∙m2. The length of the rotor shaft is 6.9 cm. The ball pivot at P is frictionless. At a given instant, the rotor shaft is horizontal and the rotor is rotating with an angular velocity of 90 rad/s about its axis OP, as shown. The rotor is viewed from point Q on the axis. The precessional linear velocity of point O, including the direction seen from point Q, is closest to Precession: In the figure, the rotor of a gyroscope is a uniform disk that has a radius of 13.8 cm and a moment of inertia about its axis of 4.0 × 10<sup>-3</sup> kg∙m<sup>2</sup>. The length of the rotor shaft is 6.9 cm. The ball pivot at P is frictionless. At a given instant, the rotor shaft is horizontal and the rotor is rotating with an angular velocity of 90 rad/s about its axis OP, as shown. The rotor is viewed from point Q on the axis. The precessional linear velocity of point O, including the direction seen from point Q, is closest to A) 0.054 m/s, leftward B) 0.054 m/s, upward C) 0.054 m/s, rightward D) 0.11 m/s, downward E) 0.11 m/s, rightward


A) 0.054 m/s, leftward
B) 0.054 m/s, upward
C) 0.054 m/s, rightward
D) 0.11 m/s, downward
E) 0.11 m/s, rightward

Correct Answer

verifed

verified

Rolling: A 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 as shown in the figure. When the ball reaches its maximum height on the frictionless surface, it is Rolling: A 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 as shown in the figure. When the ball reaches its maximum height on the frictionless surface, it is A) at a greater height than when it was released. B) at a lesser height than when it was released. C) at the same height as when 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) at a greater height than when it was released.
B) at a lesser height than when it was released.
C) at the same height as when 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.

Correct Answer

verifed

verified

Rolling: A uniform solid sphere is rolling without slipping along a horizontal surface with a 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 sphere after it has rolled 3.00 m up the ramp, measured along the surface of the ramp?


A) 4.01 m/s
B) 8.02 m/s
C) 1.91 m/s
D) 2.16 m/s
E) 3.53 m/s

Correct Answer

verifed

verified

Moment of inertia: A dumbbell-shaped object is composed by two equal masses, m, connected by a rod of negligible mass and length r. If I1 is the moment of inertia of this object with respect to an axis passing through the center of the rod and perpendicular to it and I2 is the moment of inertia with respect to an axis passing through one of the masses, it follows that


A) I1 = I2.
B) I1 > I2.
C) I2 > I1.

Correct Answer

verifed

verified

Showing 1 - 20 of 99

Related Exams

Exam 2

Motion Along a Straight Line

55 Questions

Exam 3

Motion in Two or Three Dimensions

59 Questions

Exam 4

Newtons Laws of Motion

50 Questions

Exam 5

Applying Newtons Laws

139 Questions

Exam 6

Work and Kinetic Energy

109 Questions

Exam 7

Potential Energy and Energy Conservation

50 Questions

Exam 9

Rotation of Rigid Bodies

26 Questions

Exam 10

Dynamics of Rotational Motion

49 Questions

Exam 11

Equilibrium and Elasticity

50 Questions

Exam 12

Fluid Mechanics

54 Questions

Exam 13

Gravitation

52 Questions

Exam 14

Periodic Motion

109 Questions

Exam 15

Mechanical Waves

50 Questions

Exam 16

Sound and Hearing

121 Questions

Exam 17

Temperature and Heat

60 Questions

Exam 18

Thermal Properties of Matter

41 Questions

Exam 19

The First Law of Thermodynamics

55 Questions

Exam 20

The Second Law of Thermodynamics

52 Questions

Exam 21

Electric Charge and Electric Field

54 Questions

Exam 22

Gausss Law

54 Questions

Exam 23

Electric Potential

88 Questions

Exam 24

Capacitance and Dielectrics

70 Questions

Exam 25

Current, Resistance, and Electromotive Force

44 Questions

Exam 26

Direct-Current Circuits

51 Questions

Exam 27

Magnetic Field and Magnetic Forces

105 Questions

Exam 28

Sources of Magnetic Field

82 Questions

Exam 29

Electromagnetic Induction

51 Questions

Exam 30

Inductance

88 Questions

Exam 31

Alternating Current

51 Questions

Exam 32

Electromagnetic Waves Optics

53 Questions

Exam 33

The Nature and Propagation of Light

31 Questions

Exam 34

Geometric Optics

89 Questions

Exam 35

Interference

59 Questions

Show Answer