Question 1

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?

Accepted Answer

A)  3.50 m/s 
B)  1.75 m/s 
C)  1.80 m/s 
D)  0.556 m/s 
E)  5.64 m/s 
A)  3.50 m/s 
B)  1.75 m/s 
C)  1.80 m/s 
D)  0.556 m/s 
E)  5.64 m/s

Question 2

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?

Accepted Answer

The answer of A centrifuge in a medical laboratory rotates...

Question 3

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  200 rev/s. Assuming all of this stored kinetic energy could be transferred to the linear speed of the  1500-kg car, find the maximum attainable speed of the car.

Accepted Answer

The answer of A futuristic design for a car is...

Question 4

A wheel having a moment of inertia of $5.00 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$ constant torque of $3.00 \mathrm {~N} \cdot \mathrm { m }$ 8.00 s?

Accepted Answer

A)  122 J 
B)  57.6 J 
C)  78.8 J 
D)  64.0 J 
A)  122 J 
B)  57.6 J 
C)  78.8 J 
D)  64.0 J

Question 5

Through how many degrees does a  33 rpm turntable rotate in  0.32 s?

Accepted Answer

A)  $35 ^ { \circ }$ 
B)  $46 ^ { \circ }$ 
C)  $74 ^ { \circ }$ 
D)  $63 ^ { \circ }$ 
A)  $35 ^ { \circ }$ 
B)  $46 ^ { \circ }$ 
C)  $74 ^ { \circ }$ 
D)  $63 ^ { \circ }$

Question 6

A uniform, solid, 100-kg cylinder with a diameter of  1.0 m is mounted so it is free to rotate about fixed, horizontal, frictionless axis that passes through the centers of its circular ends. A 10-kg block is hung from a very light thin cord wrapped around the cylinder's circumference. When the block is released, the cord unwinds and the block accelerates downward, as shown in the figure. What is the acceleration of the block?

Accepted Answer

The answer of A uniform, solid, 100-kg cylinder with a...

Question 7

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?

Accepted Answer

A)  $0.616 \mathrm { rad } / \mathrm { s } ^ { 2 }$ 
B)  $5.45 \mathrm { rad } / \mathrm { s } ^ { 2 }$ 
C)  $22.5 \mathrm { rad } / \mathrm { s } ^ { 2 }$ 
D)  $10.9 \mathrm { rad } / \mathrm { s } 2$ 
E)  $111 \mathrm { rad } / \mathrm { s } 2$ 
A)  $0.616 \mathrm { rad } / \mathrm { s } ^ { 2 }$ 
B)  $5.45 \mathrm { rad } / \mathrm { s } ^ { 2 }$ 
C)  $22.5 \mathrm { rad } / \mathrm { s } ^ { 2 }$ 
D)  $10.9 \mathrm { rad } / \mathrm { s } 2$ 
E)  $111 \mathrm { rad } / \mathrm { s } 2$

Question 8

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  58 rad/s. The wheel is run at that angular velocity for  30 s , and then power is shut off. The wheel slows down uniformly at $1.4 \mathrm { rad } / \mathrm { s } ^ { 2 }$ until the wheel stops. What is the total number of revolutions made by the wheel in this situation?

Accepted Answer

A)  320 
B)  510 
C)  750 
D)  470 
E)  280 
A)  320 
B)  510 
C)  750 
D)  470 
E)  280

Question 9

A man in a gym is holding an 8.0-kg weight at arm's length, a distance of 0.55 m from his shoulder joint. What is the torque about his shoulder joint due to the weight if his arm is held at 30° below
The horizontal?

Accepted Answer

A)  37 N · m 
B)  2.2 N · m 
C)  4.4 N · m 
D)  13 N · m 
E)  22 N · m 
A)  37 N · m 
B)  2.2 N · m 
C)  4.4 N · m 
D)  13 N · m 
E)  22 N · m

Question 10

A string is wrapped tightly around a fixed pulley that has a moment of inertia of $0.0352 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$ 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 ?

Accepted Answer

A)   4.95 m/s 
B)   1.97 m/s 
C)   2.00 m/s 
D)   3.94 m/s 
E)   2.28 m/s 
A)   4.95 m/s 
B)   1.97 m/s 
C)   2.00 m/s 
D)   3.94 m/s 
E)   2.28 m/s

Question 11

What is the angular speed, in  rad/s, of a flywheel turning at  813.0 rpm?

Accepted Answer

A)   13.53 rad/s 
B)   95.33 rad/s 
C)   85.14 rad/s 
D)   63.84 rad/s 
A)   13.53 rad/s 
B)   95.33 rad/s 
C)   85.14 rad/s 
D)   63.84 rad/s

Question 12

A uniform 135-g meter stick rotates about an axis perpendicular to the stick passing through its center with an angular speed of  3.50 rad/s. What is the magnitude of the angular momentum of the stick?

Accepted Answer

A)  $0.473 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$ 
B)  $0.158 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$ 
C)  $0.0236 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$ 
D)  $0.0739 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$ 
E)  $0.0394 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$ 
A)  $0.473 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$ 
B)  $0.158 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$ 
C)  $0.0236 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$ 
D)  $0.0739 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$ 
E)  $0.0394 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$

Question 13

A torque of $12 \mathrm {~N} \cdot \mathrm { m }$ is applied to a solid, uniform disk of radius  0.50 m. If the disk accelerates at $1.6 \mathrm { rad } / \mathrm { s } ^ { 2 }$ what is the mass of the disk?

Accepted Answer

A)   15 kg 
B)   30 kg 
C)   45 kg 
D)   60 kg 
A)   15 kg 
B)   30 kg 
C)   45 kg 
D)   60 kg

Question 14

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?

Accepted Answer

A)  cylinder 
B)  sphere 
C)  pipe 
D)  The pipe and cylinder arrive together before the sphere. 
E)  They all reach the bottom at the same time. 
A)  cylinder 
B)  sphere 
C)  pipe 
D)  The pipe and cylinder arrive together before the sphere. 
E)  They all reach the bottom at the same time.

Question 15

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?

Accepted Answer

A)  4.13 s 
B)  4.77 s 
C)  2.07 s 
D)  8.26 s 
E)  118 s 
A)  4.13 s 
B)  4.77 s 
C)  2.07 s 
D)  8.26 s 
E)  118 s

Question 16

A pulley has an initial angular speed of  12.5 rad/s and a constant angular acceleration of  3.41  $\mathrm { rad } / \mathrm { s } ^ { 2 }$ Through what angle does the pulley turn in  5.26 s?

Accepted Answer

A)   19.3 rad 
B)   22.6 rad 
C)   113 rad 
D)   160 rad 
E)   42.6 rad 
A)   19.3 rad 
B)   22.6 rad 
C)   113 rad 
D)   160 rad 
E)   42.6 rad

Question 17

A 95-N force exerted at the end of a 0.32-m long torque wrench produces a torque of 15 N · m. What is the angle (less than 90°) between the wrench handle and the direction of the applied force?

Accepted Answer

A)  $42 ^ { \circ }$ 
B)  $24 ^ { \circ }$ 
C)  $30 ^ { \circ }$ 
D)  $36 ^ { \circ }$ 
A)  $42 ^ { \circ }$ 
B)  $24 ^ { \circ }$ 
C)  $30 ^ { \circ }$ 
D)  $36 ^ { \circ }$

Question 18

When an old LP turntable was revolving at $33 \frac { 1 } { 3 } \mathrm { rpm }$ it was shut off and uniformly
slowed down and stopped in  5.5  seconds.
(a) What was the magnitude of its angular acceleration $\left( \text { in } \mathrm { rad } / \mathrm { s } ^ { 2 } \right)$
as it slowed down?
(b) Through how many revolutions did it turn while stopping?

Accepted Answer

The answer of When an old LP turntable was revolving...

Question 19

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?

Accepted Answer

(a)  0.627

Question 20

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 2 $25 ^ { \circ }$ 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?

Accepted Answer

A)  22 J 
B)  34 J 
C)  45 J 
D)  62 J 
E)  This question cannot be answered without knowing the radius of the hoop. 
A)  22 J 
B)  34 J 
C)  45 J 
D)  62 J 
E)  This question cannot be answered without knowing the radius of the hoop.

Exam 8: Rotational Motion

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 wheel having a moment of inertia of 5.00 kg⋅m25.00 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }5.00 kg⋅m2 constant torque of 3.00 N⋅m3.00 \mathrm {~N} \cdot \mathrm { m }3.00 N⋅m 8.00 s?

Through how many degrees does a 33 rpm turntable rotate in 0.32 s?

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 man in a gym is holding an 8.0-kg weight at arm's length, a distance of 0.55 m from his shoulder joint. What is the torque about his shoulder joint due to the weight if his arm is held at 30° below The horizontal?

What is the angular speed, in rad/s, of a flywheel turning at 813.0 rpm?

A uniform 135-g meter stick rotates about an axis perpendicular to the stick passing through its center with an angular speed of 3.50 rad/s. What is the magnitude of the angular momentum of the stick?

A torque of 12 N⋅m12 \mathrm {~N} \cdot \mathrm { m }12 N⋅m is applied to a solid, uniform disk of radius 0.50 m. If the disk accelerates at 1.6rad/s21.6 \mathrm { rad } / \mathrm { s } ^ { 2 }1.6rad/s2 what is the mass of the disk?

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 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 pulley has an initial angular speed of 12.5 rad/s and a constant angular acceleration of 3.41 rad/s2\mathrm { rad } / \mathrm { s } ^ { 2 }rad/s2 Through what angle does the pulley turn in 5.26 s?

A 95-N force exerted at the end of a 0.32-m long torque wrench produces a torque of 15 N · m. What is the angle (less than 90°) between the wrench handle and the direction of the applied force?

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?

Introduction, Measurement, Estimating

Describing Motion: Kinematics in One Dimension

Kinematics in Two Dimensions; Vectors

Dynamics: Newtons Laws of Motion

Circular Motion; Gravitation

Work and Energy

Linear Momentum

Static Equilibrium; Elasticity and Fracture

Fluids

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Sound

Temperature and Kinetic Theory

Heat

The Laws of Thermodynamics

Electric Charge and Electric Field

Electric Potential

Electric Currents

Dc Circuits

Magnetism

Electromagnetic Induction and Faradays Law

Electromagnetic Waves

Light: Geometric Optics

The Wave Nature of Light

Optical Instruments

The Special Theory of Relativity

Early Quantum Theory and Models of the Atom

Quantum Mechanics of Atoms

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Nuclear Energy; Effects and Uses of Radiation

Elementary Particles

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Filters

A wheel having a moment of inertia of $5.00 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$ constant torque of $3.00 \mathrm {~N} \cdot \mathrm { m }$ 8.00 s?

A torque of $12 \mathrm {~N} \cdot \mathrm { m }$ is applied to a solid, uniform disk of radius 0.50 m. If the disk accelerates at $1.6 \mathrm { rad } / \mathrm { s } ^ { 2 }$ what is the mass of the disk?

A pulley has an initial angular speed of 12.5 rad/s and a constant angular acceleration of 3.41 $\mathrm { rad } / \mathrm { s } ^ { 2 }$ Through what angle does the pulley turn in 5.26 s?