Deck 10: Rotational Kinematics and Energy

Question 1

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.

Answer 1

Jacques and Ahmed have the same angular speed.
Ahmed has a greater tangential speed than Jacques.

Question 2

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)hoop,disk,sphere

Answer 2

sphere,disk,hoop

Question 3

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.

Answer 3

They all have the same angular speed.
They all have the same angular acceleration.

Question 4

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.

Question 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.

Question 6

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.

Question 7

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

Question 8

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

Question 9

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.

Question 10

Through how many degrees does a 33 rpm turntable rotate in

A)63°
B)35°
C)46°
D)74°

Question 11

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

Question 12

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.

Question 13

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.

Question 14

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.

Question 15

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.

Question 16

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

Question 17

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.

Question 18

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.

Question 19

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.

Question 20

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.

Question 21

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

Question 22

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

Question 23

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

Question 24

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

Question 25

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

Question 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

Question 27

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

Question 28

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

Question 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 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

Question 30

An electrical motor spins at a constant
If the rotor radius is
What is the linear acceleration of the edge of the rotor?

A)5,707 m/s²
B)281.6 m/s²
C)572,400 m/s²
D)28.20 m/s²

Question 31

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

Question 32

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.

Question 33

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/

Question 34

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

Question 35

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

Question 36

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

Question 37

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

Question 38

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

Question 39

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

Question 40

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

Question 41

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

Question 42

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

Question 43

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

Question 44

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

Question 45

A solid uniform cylinder is rolling without slipping.What fraction of its kinetic energy is rotational?

A)1/3
B)2/3
C)1/2
D)1/4
E)3/4

Question 46

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

Question 47

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

Question 48

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

Question 49

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

Question 50

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

Question 51

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

Question 52

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.

Question 53

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

Question 54

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

Question 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

Question 56

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

Question 57

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

Question 58

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.

Question 59

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

Question 60

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