Deck 10: Rotation

Question 1

If ,then

A)the magnitude of is always greater than the magnitude of
and the magnitude of
.
B)the magnitude of is always less than the magnitude of
and the magnitude of
.
C)the direction of is always equal to either the direction of
or the direction of
.
D)the direction of is always exactly half way between the direction of
and the direction of
.
E)None are correct.

Answer 1

None are correct.

Question 2

Two children balance on a seesaw,which consists of a 70-kg thin 5-m long steel rod that pivots about its center on a fulcrum.The first child has a mass of 22 kg and sits 2.5 m from the fulcrum while the second child with mass 31 kg sits on the opposite side,1.8 m from the fulcrum.The moment of inertia of the seesaw/children system about the fulcrum is

A)238 kg m².
B)1990 kg m².
C)183 kg m².
D)384 kg m².
E)265 kg m².

Answer 2

384 kg m².

Question 3

What is the moment of inertia of a solid sphere of mass m and radius r about a line parallel to another line passing through the center of the sphere? The distance between the lines is half the radius of the sphere.

A)mr²/5
B)2mr²/5
C)9mr²/10
D)13mr²/20

Answer 3

13mr²/20

Question 4

In opening a door,a person pushes at a point on the door 65 cm away from the hinges with a force of 50 N that is directed at an angle of 75 ^$\circ$ with respect to the surface of the door.The torque on the door about its hinges is

A)32.5 Nm.
B)8.41 Nm.
C)40.2 Nm.
D)48.3 Nm.
E)31.4 Nm.

Question 5

A thin uniform rod (length = 75.0 cm,mass = 1.0 kg)is pivoted about a horizontal frictionless pin through one end of the rod.The moment of inertia of the rod through this axis is (1/3)mL².The rod is released when it is below the horizontal and it makes the angle $\theta$ with the horizontal.If the angular acceleration of the rod at the instant it is released is 15.0 rad/s²,what is the angle $\theta$ ?

A)50 ^$\circ$
B)40 ^$\circ$
C)20 ^$\circ$
D)70 ^$\circ$
E)60 ^$\circ$

Question 6

A thin uniform rod (length = 125 cm,mass = 250 g)is pivoted about a horizontal frictionless pin through one end of the rod.The moment of inertia of the rod through this axis is (1/3)mL².The rod is released when it is 20^o below the horizontal.What is the angular acceleration of the rod at the instant it is released?

A)7.36 rad/s²
B)14.7 rad/s²
C)11.1 rad/s²
D)22.1 rad/s²
E)16.7 rad/s²

Question 7

A playground carousel is rotating about its center.The radius of the carousel is 1.50 m,its initial angular speed is 3.14 rad/s and its moment of inertia is 125 kg m².A 40.0-kg person climbs onto the carousel near its outer edge.What is the angular speed of the carousel after the person climbs aboard?

A)1.41 rad/s
B)1.57 rad/s
C)1.83 rad/s
D)3.14 rad/s

Question 8

In first gear,a motorcycle engine produces 902 Nm of torque on the rear wheel.If the rear wheel is lifted off the road and free to spin without friction,how long will it take the engine to spin the wheel from rest to 200 revolutions per minute (corresponding to the outer part of the wheel moving at approximately 24 km/h)if the wheel were on the road? Treat the rear wheel as a hollow cylinder with inner diameter 50 cm and outer diameter 64 cm,with a mass of 13 kg.

A)0.025 s
B)0.015 s
C)0.031 s
D)0.013 s
E)0.040 s

Question 9

A meter stick,sitting on a frictionless table top,is struck by a wad of clay with a force,F = 4.0 N at an angle of as shown.The meter stick will rotate in the plane of the table.Determine the magnitude of the torque about the axis of rotation located at the pivot point at the center of the stick.

A)0.31 Nm
B)1.3 Nm
C)2.4 Nm
D)4.0 Nm

Question 10

The torque required to screw a nut completely onto bolt using a wrench is 0.300 Nm.If the nut is completely secure in 20.3 turns and the diameter of the screw is 0.90 cm,what is the constant frictional force between the bolt and the nut?

A)33 N
B)45 N
C)67 N
D)86 N
E)92 N

Question 11

A solid cylinder rolls without slipping down an incline starting from rest.At the same time a box starts from rest at the same altitude and slides down the same incline with negligible friction.Which arrives at the bottom first?

A)the box
B)the cylinder
C)Both arrive at the same time.
D)It is impossible to determine.

Question 12

A 0.80-kg bead slides on a wire bent into a circle of radius 0.40 m.You pluck the bead with a force tangent to the circle.What force is needed to give the bead an angular acceleration of 3.0 rad/s²?

A)4.40 N
B)0.71 N
C)0.83 N
D)0.96 N
E)1.2 N

Question 13

Angular momentum is defined as

A)mass multiplied by velocity.
B)mass multiplied by speed.
C)moment of inertia multiplied by angular velocity.
D)moment of inertia multiplied by angular speed.

Question 14

A force (in N)of is applied to an object at a location (in m)of (the origin is the pivot point).Find the magnitude of the torque produced {assume that each number has three significant digits}.

A)9.00 N^. m
B)51.1 N^. m
C)45.3 N^. m
D)50.3 N^. m
E)None are correct.

Question 15

A 1.7-kg hoop rolls across the floor without slipping.The hoop has a diameter of 1.1 m.The ratio the translational to rotational kinetic energy of the hoop is

A)0.50.
B)0.75.
C)1.0.
D)1.8.
E)Insufficient information is provided to determine this ratio.

Question 16

Two children weighing 60.0 kg and 45.0 kg,respectively,are sitting at different points on the edge of a rotating merry-go-round which has a radius of 4.0 m.What is the rotational inertia for the children?

A)0.420 * 10³ kgm²
B)1.00 * 10³ kgm²
C)1.68 * 10³ kgm²
D)2.12 * 10³ kgm²
E)3.36 * 10³ kgm²

Question 17

A solid cylinder of mass m,radius r,and length L starts from rest and rolls without slipping down an inclined plane.Its vertical position decreases by a distance h.What is the final linear speed of its center of mass?

A)
B)
C)
D)

Question 18

A bowling ball,which can be treated as a solid sphere with a diameter of 21.6 cm and a weight of 33 kg,rolls down a bowling lane at a speed of 21 km/h.The kinetic energy of the bowling ball is

A)785 J.
B)225 J.
C)561 J.
D)1120 J.
E)1430 J.

Question 19

A force (in N)of is applied to an object at a location (in m)of (the origin is the pivot point).Find the magnitude of the torque produced {assume that each number has three significant digits}.

A)9.00 N^. m
B)51.1 N^. m
C)45.3 N^. m
D)53.0 N^. m
E)None are correct.

Question 20

The Earth can be treated as a sphere of radius 6.38 x 10⁶ m and mass 5.98 * 10²⁴kg.Find the angular momentum of the Earth in its orbit around the sun (R = 1.50 * 10¹¹m).

A)2.42 * 10³¹ kg m/s²
B)7.18 * 10³³ kg m/s²
C)1.77 * 10³³ kg m/s²
D)1.07 * 10⁴⁰ kg m/s²
E)2.68 * 10⁴⁰ kg m/s²

Question 21

The tangential force F shown in figure below is applied to a 2-kg disc with a 30-cm diameter which is allowed to rotate about an axis through its center.The magnitude of this tangential force is given in the graph of F vs.Angular Position.With the disc at rest initially and ignoring frictional torque,determine the disc's angular velocity after one full rotation

A)-20.5 rad/s
B)+20.5 rad/s
C)0 rad/s
D)-420 rad/s
E)+420 rad/s

Question 22

A uniform 1-kg disk with a radius of 25 cm rolls 2 m down an incline plane angled at 25 ^$\circ$ .What is the speed of the disk at the bottom of the plane?

A)4.07 m/s
B)3.32 m/s
C)5.43 m/s
D)6.26 m/s
E)1.24 m/s

Question 23

A yo-yo is made by wrapping a 2-m long string around a 500-g 10-cm diameter uniform disk.The string is fastened to the ceiling,and the yo-yo is released.What is the tension in the string as the yo-yo falls?

A)9.8 N
B)1.6 N
C)4.9 N
D)0.49 N
E)3.3 N

Question 24

A 2-kg thin hoop with a 50-cm radius rolls down a 30-degree slope without slipping.If the hoop starts at rest at the top of the slope,what is its translational velocity after it rolls 10 m along the slope?

A)14.5 m/s
B)3.22 m/s
C)7.00 m/s
D)44.8 m/s
E)20.5 m/s

Question 25

The tangential force F shown in figure below is applied to a disc is allowed to rotate about an axis through its center.The diameter of the disc is 24.0 cm.The magnitude of this tangential force is given in the graph of F vs.Angular Position.With the disc at rest initially and ignoring frictional torque,the disc's angular velocity after one full rotation is -31.4 rad/sec.What is the mass of the disk?

A)1.06 kg
B)1.21 kg
C)2.00 kg
D)33.4 kg
E)5.64 kg

Question 26

The tangential force F shown in figure below is applied to a 2-kg disc is allowed to rotate about an axis through its center.The magnitude of this tangential force is given in the graph of F vs.Angular Position.With the disc at rest initially and ignoring frictional torque,the disc's angular velocity after one full rotation is -31.4 rad/sec.What is the diameter of the disk?

A)12.7 cm
B)200 cm
C)400 cm
D)9.65 cm
E)19.2 cm

Question 27

A meter stick and a two-meter stick have the same thicknesses and density.They are both placed upright and balancing on one end.They are then disturbed slightly from this unstable equilibrium and fall to the floor.Which one hits the ground first?

A)the meter stick
B)the two meter stick
C)They both hit the floor at about the same time.
D)It depends how far the initial displacement is.

Question 28

A uniform solid sphere of mass M and radius R is rolling without slipping along a level plane with an initial speed of v = 4.00 m/s when it encounters a ramp that is at an angle of $\theta$ = 32.0^o above horizontal.Find the maximum distance that the sphere rolls without slipping up the ramp before (instantaneously)stopping.

A)0.54 m
B)1.35 m
C)1.54 m
D)2.15 m
E)None are correct.

Question 29

In loosening a nut with a wrench,which of the following methods exerts the most torque?

A)exerting a 200 N force perpendicular to the wrench 25 cm from the nut
B)exerting a 300 N force perpendicular to the wrench 15 cm from the nut
C)exerting a 400 N force at an angle of 45 ^$\circ$ with respect to the wrench at a distance of 25 cm from the nut
D)exerting a 500 N force at an angle of 45 ^$\circ$ with respect to the wrench at a distance of 15 cm from the nut
E)exerting a 600 N force parallel to the wrench at a distance of 25 cm from the nut

Question 30

Which of the following has the largest moment of inertia?

A)A cylinder of mass M with a radius R rotating about its central axis.
B)A hoop of mass M with a radius R rotating about the axis perpendicular to the plane of the hoop and passing through its center.
C)A hoop of mass M with a radius R rotating about a line through its diameter and parallel to the plane of the hoop.
D)A cube of mass M and sides 2R rotating about a line passing through the center of two opposite sides.
E)A rod of mass M and length 2R rotating about a line passing through the center and perpendicular to the rod.

Question 31

The Crab Pulsar, radius is a neutron star located in the Crab Nebula.The rotation of the Crab Pulsar is currently approximately 30 rotations per second,or 60 rad/s.The rotation rate of the star,however,is decreasing such that each year the rotation period increases by 10^-5 s.Estimate the amount of energy the pulsar looses each year.

A)4 * 10³¹ J
B)2 * 10³⁵ J
C)1 * 10³⁹ J
D)6 * 10⁴² J

Question 32

A uniform solid sphere of mass M and radius R is rolling without slipping along a level plane when it encounters a ramp that is at an angle of $\theta$ = 32.0^o above horizontal.The maximum distance that the sphere rolls without slipping up the ramp before (instantaneously)stopping and rolling back down is 3.15 m.What was the linear speed of the sphere before it encountered the ramp?

A)3.69 m/s
B)4.84 m/s
C)6.12 m/s
D)7.86 m/s
E)None are correct.

Question 33

A wheel of radius R rolls without slipping with angular speed $\omega$ ,the linear speed of its center is A.The masses and the radii of discs A and B are respectively 2 kg and 0.2 kg,and 25 cm and 2.5 cm.What is the moment of inertia of the composite object?

A)0.
B) $\omega$ /R.
C) $\omega$ R.
D) $\omega$ R².

Question 34

An object made of two disc shaped sections A and B,as shown in the figure is rotating about an axis through the center of disc A)The masses and the radii of discs A and B are respectively 2 kg and 0.2 kg,and 25 cm and 2.5 cm.If the axial frictional torque is 0.2 Nm,how long will it take for the object to come to a stop if it is rotating with an angular velocity of -2 $\pi$ rad/s?

A)0.36 s
B)2.28 s
C)0.73 s
D)1.14 s

Question 35

The tangential force F shown in figure below is applied to a disc is allowed to rotate about an axis through its center.The diameter of the disc is 24.0 cm.The magnitude of this tangential force is given in the graph of F vs.Angular Position.With the disc at rest initially and ignoring frictional torque,the disc's angular velocity after one full rotation is -31.4 rad/sec.What is the moment of inertia of the disk?

A)3.14 * 10^-3 kg m²
B)7.65 * 10^-3 kg m²
C)2.40 * 10^-1 kg m²
D)6.32 * 10^-3 kg m²
E)1.28 * 10^-3 kg m²

Question 36

The tangential force F shown in figure below is applied to a disc is allowed to rotate about an axis through its center.The diameter of the disc is 24.0 cm.The magnitude of this tangential force is given in the graph of F vs.Angular Position.With the disc at rest initially and ignoring frictional torque,find the disc's kinetic energy after one full rotation.

A)4.89 J
B)7.50 J
C)15.1 J
D)3.77 J
E)not enough information is given to determine the kinetic energy

Question 37

A composite object is made of two disc shaped sections A and B,as shown in the figure,and is rotating about an axis through the center of disc

A)0.0145 kg m²
B)1.45 kg m²
C)7.27 kg m²
D)0.727 kg m²
E) 0.0727 kg m²

Question 38

A 100-g hockey puck hits the end of a 1.5-m 1-kg stick lying on the ice at a velocity of 4 m/s perpendicular to the stick and bounces back at a speed of a 2 m/s.What is the rotational speed of the stick after the collision?

A)2.4 rad/s
B)3.2 rad/s
C)0.8 rad/s
D)1.6 rad/s
E)1.8 rad/s

Question 39

A uniform solid sphere of mass M and radius R is rolling without slipping along a level plane with an initial speed of v = 5.00 m/s when it encounters a ramp that is at an angle above horizontal.The maximum distance that the sphere rolls without slipping up the ramp before (instantaneously)stopping and rolling back down is 2.15 m.

A)34.0^o
B)39.7^o
C)56.0^o
D)66.5^o
E)None are correct.

Question 40

An extended object comprises two point masses m₁ and m₂ connected via a rigid massless rod of length L.The object is rotating at a constant angular velocity about an axis perpendicular to the page through the midpoint along the rod.Two time varying tangential forces F₁ and F₂ are applied to m₁ and m₂ respectively as shown in the figure.After the shown forces have been applied,the angular velocity of the object

A)increases.
B)decreases.
C)remains unchanged.
D)There is not enough information to make a determination.

Question 41

Two masses are hung by a massless cord over a disk with radius R and mass M as shown.If the angular velocity of the disk is 2 rad/s counterclockwise and is not changing,which one of the following statements is true?

A)T₂ > m₂g
B)T₂ > T₁
C)The net torque on the disk must be zero.
D)The angular acceleration of the disk is counterclockwise.
E)T₁m₁ + T₂m₂ = Mg

Question 42

A sphere rolls without slipping down an inclined plane that makes an angle 30 ^$\circ$ from the horizontal.The vertical height change is h.Which one of the following statements concerning the velocity when it reaches the bottom is true?

A)The velocity would be equal to .
B)The velocity would be zero.
C)The velocity would be less than if the sphere were sliding without friction and not rolling.
D)The velocity would be greater than if the sphere were sliding without friction and not rolling.
E)The velocity does not depend on the moment of inertia of the sphere.

Question 43

A flat disk with a radius of 0.71 m is attached to a string with tension 7.3 N.If it takes 12 seconds to reach 100 radians/sec from rest,what is the moment of inertia of the disk in kg-m²?

A)1.23 * 10^-2
B)0.622
C)23.2
D)763.1
E)1094

Question 44

A massless string is wrapped around a cylinder of mass 0.400 kg and radius 0.100 m.The string is attached to the ceiling.The cylinder is released.As it falls,the string unwinds.What is the magnitude of the acceleration of the cylinder as it falls in m/s²?

A)3.27
B)4.91
C)6.54
D)7.61
E)9.81

Question 45

A child pedaling a bicycle with 33-cm diameter tires notices that the bike moves forward 1.9 m with each cycle of pedaling.If the front gear has 22 teeth,how many teeth does the back gear have?

A)6
B)12
C)24
D)55
E)127

Question 46

The mass of a star is 4.05 * 10³¹ kg and it performs one rotation in 15.00 days.Find its new period (in days)if the diameter suddenly expands to 1.450 times its original size.Assume a uniform spherical mass before the collapse and a uniform spherical mass distribution after the expansion.

A)21.75
B)38.25
C)7.134
D)31.54
E)10.34

Question 47

A baton consists of a nearly massless rod of length L and two spheres attached to the ends of the rod,whose masses are each M and whose centers are separated by L.The spheres have radius R.If the sphere radius R is not negligible compared to the length L,what is the moment of inertia of the baton about an axis perpendicular to its length and passing through its center?

A)2MR²
B)2ML²
C)2ML² + 2MR²
D)(1/2)ML²
E)(1/2)ML² + 2MR²

Question 48

A massless string is wrapped around a cylinder of mass 0.500 kg and radius 0.100 m.The string is attached to the ceiling.The cylinder is released.As it falls,the string unwinds.What is the magnitude of the tension in the string as the cylinder falls in N?

A)0
B)4.91
C)1.64
D)3.13
E)1.12

Question 49

The mass of a star is 4.05 * 10³¹ kg and it performs one rotation in 15.00 days.Find its new period (in days)if the diameter suddenly shrinks to 0.450 times its original size.Assume a uniform spherical mass before the collapse and a uniform spherical mass distribution after the collapse.

A)1.8965
B)2.2189
C)2.5962
D)3.0375
E)3.5539

Question 50

A flywheel has mass 150 kg and radius 1.2 m,and is accelerated uniformly from rest to an angular speed of 125 radians per second in 12 seconds.What torque is required in order to accomplish this?

A)1.1 * 10³ Nm
B)2.2 * 10³ Nm
C)1.9 * 10² Nm
D)3.8 * 10² Nm

Question 51

A solid cylinder rolls without slipping on a horizontal surface such that its center of mass moves at 5.0 m/s.If it has a total kinetic energy is 1.7 kJ,what is its mass?

A)140 kg
B)91 kg
C)68 kg
D)58 kg
E)45 kg

Question 52

A solid ball of mass 2 kg and diameter 20 cm is rotating about its diameter at 100 rev/min.The kinetic energy of rotation is

A)2.59 J.
B)1.76 J.
C)0.91 J.
D)0.44 J.
E)0.22 J.

Question 53

Two solid steel balls,one small and one large,are on an incline plane.The large ball has a diameter of 3.0 cm and the small ball has a diameter of 1.0 cm.Starting from rest,the two balls roll without slipping down the incline plane until their centers of mass are 1 m below their starting positions.If it takes the large ball 2.0 seconds to roll down the inclined plane,how long will it take the small ball to roll down the inclined plane?

A)0.67 s
B)1.2 s
C)2.0 s
D)3.5 s
E)6.0 s

Question 54

A boy of mass 55 kg runs on a line tangent to the edge of a merry-go-round,whose mass is 125 kg and radius 1.2 m.He jumps onto the merry-go-round,and the angular speed of the merry-go-round becomes 2.2 radians per second.How fast was the boy running before he landed on the merry-go-round?

A)5.6 m/s
B)6.8 m/s
C)8.6 m/s
D)3.2 m/s

Question 55

A cyclist exerts a vertical force of 150 N on one end of a pedal rod of length 18 cm than is inclined at an angle 45 ^$\circ$ to the horizontal.The magnitude of the torque about the fixed end of the pedal rod is

A)19 Nm.
B)24 Nm.
C)27 Nm.
D)32 Nm
E)56 Nm.

Question 56

In a water molecule the angle between the two H-O bonds is 105 ^$\circ$ and the distance between the oxygen and hydrogen atoms is 9 * 10^-11 m.The mass of the hydrogen atom m_H is 1.67 * 10^-27 kg and that of the oxygen atom m_O = 16 m_H.The moment of inertia of the water molecule about an axis along one of the H-O bonds is

A)1.35 * 10^-47 kg m².
B)1.26 * 10^-47 kg m².
C)0.89 * 10^-47 kg m².
D)0.15 * 10^-47 kg m².

Question 57

A torque of 2.2 *10³ Nm on a flywheel causes it to accelerate uniformly from rest to an angular speed of 125 radians per second in 12 seconds.If the radius of the flywheel is 1.20 m,what is the mass of the flywheel?

A)161 kg
B)176 kg
C)323 kg
D)293 kg
E)352 kg

Question 58

A torque of 2.2 * 10³ Nm on a flywheel causes it to accelerate uniformly from rest to an angular speed of 125 radians per second in 12 seconds.What is the moment of inertia of the flywheel?

A)211 kgm²
B)183 kgm²
C)17.6 kgm²
D)2.29 * 10⁴ kgm²
E)0.682 kgm²

Question 59

A rigid body of moment of inertia 0.5 kg m² rotates with constant angular velocity about a fixed axis.It has kinetic energy of 1.5 J.The magnitude of the angular momentum of the rigid body is

A)7.9 kg m²/s.
B)5.6 kg m²/s.
C)3.0 kg m²/s.
D)1.5 kg m²/s.
E)1.22 kg m²/s.

Question 60

A baton consists of a nearly massless rod of length L and two spheres attached to the ends of the rod,whose masses are each M and whose centers are separated by L.The spheres have radius R.If the sphere radius R is negligible compared to the length L,what is the moment of inertia of the baton about an axis perpendicular to its length and passing through its center?

A)2ML²
B)ML²
C)(1/2)ML²
D)(1/4)ML²

Question 61

Which of the following statements is the one that is correct?

A)If all the forces on a body act through the axis of rotation,the angular acceleration will be zero.
B)If two bodies have the same moment of inertia about their centers of mass and the same mass,they must be identical.
C)Two disks roll down an inclined plane without slipping.The one with a smaller radius will always reach the bottom first independent of their masses.
D)Two disks roll down an inclined plane without slipping.The one with a bigger radius will always reach the bottom first independent of their masses.
E)Two disks roll down an inclined plane without slipping.The one with a bigger mass will always reach the bottom first.

Question 62

A basketball is moving at 14.0 m/s at the base of a hill.Over what vertical distance does the basketball roll before it temporarily comes to rest at its highest elevation? Ignore friction and air resistance.

A)20.0 m
B)14.0 m
C)1.43 m
D)9.99 m

Question 63

A bug (2 grams)crawls from the edge to the center of a disk that is freely turning at 20 rpm.The disk has a mass of 11 grams and a radius of 26 cm.What is the disk's new angular speed?

A)10.3 rpm
B)12.6 rpm
C)27.7 rpm
D)33.0 rpm
E)14.7 rpm

Question 64

An 18-wheeler travels down the highway with a speed of 50 km/hr.Each wheel has a 30 cm radius and a mass of 16 kg.What is the total kinetic energy (translational and rotational)of all 18 wheels? (The moment of inertia of a wheel is .)

A)27.7 kJ
B)83.3 kJ
C)72.5 kJ
D)55.5 kJ
E)41.7 kJ

Question 65

A massless string is wrapped around a cylinder of radius 0.100 m.A force of 100 N acts on the string.If it takes 1.2 seconds to reach an angular speed of 100 radians/s starting from rest,what is the moment of inertia of the cylinder?

A)0.15 kgm²
B)0.053 kgm²
C)0.12 kgm²
D)0.020 kgm²
E)0.015 kgm²

Question 66

Three objects,a hoop,a disk,and a solid sphere start from the top of a hill and roll without slipping down to the bottom.Which one of the following statements is true?

A)The sphere reaches the bottom first.
B)The disk reaches the bottom first.
C)The object with the greatest mass reaches the bottom first.
D)All three reach the bottom at the same time.
E)The hoop reaches the bottom first.

Question 67

A spherical ball of material is rotating about its center at 35 rad/s.It has a mass of 2.0 kg and a radius of 0.11 m.If it suddenly expands to become a disk of 0.22-m radius,what will be its rate of rotation?

A)51 rad/s
B)7 rad/s
C)87 rad/s
D)29 rad/s
E)14 rad/s

Question 68

A bug crawls from the center to the edge of a uniform disk that is freely turning at 20 rpm.The disk has a mass of 11 grams and a radius of 26 cm.If the angular speed of the disk is 12.6 rpm when the bug reaches the disk's edge,what is the mass of the bug?

A)1.7 g
B)2.5 g
C)2.8 g
D)3.2 g
E)2.0 g

Question 69

A uniform solid cylinder,a hollow cylinder,and a uniform solid sphere are rolling at the same speed on a horizontal table without slipping.If they all have the same mass and radius,which statement is true?

A)They all have the same angular momentum.
B)The hollow cylinder has the most angular momentum.
C)The solid sphere has the most total kinetic energy.
D)The solid cylinder has the greatest rate of rotation.
E)They all have the same kinetic energy of rotation.

Question 70

A massless string is wrapped around a cylinder of mass 6.00 kg and radius 0.100 m.A force acts on the string,as shown in the diagram.If it takes 0.40 seconds to reach an angular speed of 100 radians/s starting from rest,what is the magnitude of the force,F?

A)120 N
B)75 N
C)100 N
D)65 N
E)30 N

Question 71

Which of the following statements is true?

A)When two hoops with different radii roll down an inclined plane without slipping,they reach the bottom at the same time.
B)If a body is rotating about an axis without any external torques,and its size doubles,it will speed up to double the angular velocity.
C)Two disks roll down an inclined plane without slipping.The one with a smaller radius will always reach the bottom first independent of their masses.
D)When two objects roll down an inclined plane without slipping,they have the same velocity when they reach the bottom only if they have the same mass.
E)The moment of inertia of an object would be different on the surface of the moon than it is on the surface of the Earth

Question 72

A person on a rotating stool with arms stretched out rotates at an angular speed of 5.00 rad/s.On bringing in his arms,the angular speed increases to 7.50 rad/s.By what factor does the moment of inertia change?

A)0.667
B)0.750
C)0.900
D)1.25
E)1.50

Question 73

A disk rotates about an axis perpendicular to the plane of the disk D = 0.593 m from the center of the disk.The disk has a mass of M = 2.6 kg and a radius of R = 1.22 m.What is the moment of inertia of the disk about this axis?

A)0 kg m²
B)1.93 kg m²
C)2.85 kg m²
D)3.87 kg m²
E)5.11 kg m²

Question 74

A massless string is wrapped around a cylinder of mass 0.400 kg and radius 0.200 m.The string is attached to the ceiling.The cylinder is released.As it falls,the string unwinds.What is the magnitude of the angular acceleration of the cylinder as it falls in rad/s²?

A)32.7
B)49.1
C)9.81
D)24.5
E)17.5

Question 75

A bug (2 grams)crawls from the center to the edge of a disk that is freely turning at 20 rpm.The disk has a mass of 11 grams and a radius of 26 cm.What is the disk's new angular speed?

A)8.7 rpm
B)10.3 rpm
C)12.6 rpm
D)14.7 rpm
E)22.3 rpm

Question 76

A solid cylinder of mass 1 kg and radius 5 cm is rolling without slipping on a horizontal surface.Its linear velocity is 0.2 m/s.What is its total kinetic energy?

A)0.03 J
B)0.02 J
C)0.01 J
D)0.2 J
E)2 J

Question 77

A massless string is wrapped around a cylinder of mass 4.00 kg and radius 0.100 m.A force of 100 N acts on the string.How long in seconds does it take to reach an angular speed of 100 radians/s starting from rest?

A)4000 s
B)1000 s
C)400 s
D)20 s
E)0.2 s

Question 78

A massless string is wrapped around a cylinder of radius 0.100 m.A force of 100 N acts on the string.If it takes 1.5 seconds to reach an angular speed of 100 radians/s starting from rest,what is the mass of the cylinder?

A)4.0 kg
B)24 kg
C)20 kg
D)10 kg
E)30 kg