Question 1

A gyroscope has a moment of inertia of 0.140 kg*m2 and has an initial angular speed of 15.0 rad/s.If a lubricant is applied to the bearings of the gyroscope so that frictional torque is reduced to 2.00 * 10-2 N*m, then in what time interval will the gyroscope coast from 15.0 rad/s to zero?

Accepted Answer

A) 150 s 
B) 105 s 
C) 90.0 s 
D) 180 s

Question 2

The torque caused by a force F applied at a distance r from the axis of rotation, is given by  , where q is the angle between  and  .If the magnitudes r and F remain the same, what other angle q¢ will produce the same torque as was produced at angle q if q was less than 90$\degree$?

Accepted Answer

A)   
B)   
C)   
D) None of the above.

Question 3

An 80-kg man is one fourth of the way up a 10-m ladder that is resting against a smooth, frictionless wall.If the ladder has a mass of 20 kg and it makes an angle of 60$\degree$with the ground, find the force of friction of the ground on the foot of the ladder.

Accepted Answer

A) 7.8 * 102 N 
B) 2.0 * 102 N 
C) 50 N 
D) 1.7 * 102 N

Question 4

A uniform solid sphere rolls down an incline of height 3 m after starting from rest.In order to calculate its speed at the bottom of the incline, one needs to know:

Accepted Answer

A) the mass of the sphere. 
B) the radius of the sphere. 
C) the mass and the radius of the sphere. 
D) no more than is given in the problem.

Question 5

A rod of length L is pivoted about its left end and has a force F applied perpendicular to the other end.The force F is now removed and another force F' is applied at the midpoint of the rod.If F' is at an angle of 30$\degree$ with respect to the rod, what is its magnitude if the resulting torque is the same as when F was applied?

Accepted Answer

A) F 
B) 2F 
C) 3F 
D) 4F

Question 6

A baseball pitcher, loosening up his arm before a game, tosses a 0.15-kg ball using only the rotation of his forearm, 0.32 m in length, to accelerate the ball.If the ball starts at rest and is released with a speed of 12 m/s in a time of 0.40 s, what is the average angular acceleration of the arm and ball?

Accepted Answer

A) 0.067 rad/s2 
B) 94 rad/s2 
C) 15 rad/s2 
D) 37 rad/s2

Question 7

A majorette takes two batons and fastens them together in the middle at right angles to make an "x" shape.Each baton was 0.80 m long and each ball on the end is 0.20 kg.(Ignore the mass of the rods.) What is the moment of inertia if the arrangement is spun around an axis through the center perpendicular to both rods?

Accepted Answer

A) 0.064 kg*m2 
B) 0.096 kg*m2 
C) 0.13 kg*m2 
D) 0.32 kg*m2

Question 8

A ventilation fan with a moment of inertia of 0.034 kg*m2 has a net torque of 0.11 N*m applied to it.If it starts from rest, what kinetic energy will it have 8.0 s later?

Accepted Answer

A) 31 J 
B) 17 J 
C) 11 J 
D) 6.6 J

Question 9

A cylinder (I = MR2/2) is rolling along the ground at 7.0 m/s.It comes to a hill and starts going up.Assuming no losses to friction, how high does it get before it stops?

Accepted Answer

A) 1.2 m 
B) 3.7 m 
C) 4.2 m 
D) 5.9 m

Question 10

A 3.0-m rod is pivoted about its left end.A force of 6.0 N is applied perpendicular to the rod at a distance of 1.2 m from the pivot causing a ccw torque, and a force of 5.2 N is applied at the end of the rod 3.0 m from the pivot.The 5.2 N is at an angle of 30$\degree$to the rod and causes a cw torque.What is the net torque about the pivot?

Accepted Answer

A) 15 N*m 
B) 0 N*m 
C) -6.3 N*m 
D) -0.6 N*m

Question 11

A gyroscope has a moment of inertia of 0.14 kg*m2 and an initial angular speed of 15 rad/s.Friction in the bearings causes its speed to reduce to zero in 30 s.What is the value of the average frictional torque?

Accepted Answer

A) 3.3 * 10-2 N*m 
B) 8.1 * 10-2 N*m 
C) 14 * 10-2 N*m 
D) 7.0 * 10-2 N*m

Question 12

A 4.0-kg mass is placed at (3.0, 4.0) m, and a 6.0-kg mass is placed at (3.0, -4.0) m.What is the moment of inertia of this system of masses about the x-axis?

Accepted Answer

A) 160 kg*m2 
B) 90 kg*m2 
C) 250 kg*m2 
D) 32 kg*m2

Question 13

A box slides down a frictionless incline, and a hoop rolls down another incline.Both inclines have the same height, and both the box and the hoop have the same mass.If both objects start from rest, upon reaching the bottom of the incline which one will have the greater kinetic energy and which one will have the greater speed?

Accepted Answer

A) The box will have both the greater kinetic energy and the greater speed. 
B) The hoop will have both the greater kinetic energy and the greater speed. 
C) Both will have the same kinetic energy but the hoop will have the greater speed. 
D) Both will have the same kinetic energy but the box will have the greater speed.

Question 14

A solid cylinder (I = MR2/2) has a string wrapped around it many times.When I release the cylinder, holding on to the string, the cylinder falls and spins as the string unwinds.What is the downward acceleration of the cylinder as it falls?

Accepted Answer

A) 0 
B) 4.9 m/s2 
C) 6.5 m/s2 
D) 9.8 m/s2

Question 15

A uniform 1.0-N meter stick is suspended horizontally by vertical strings attached at each end.A 2.0-N weight is suspended from the 10-cm position on the stick, another 2.0-N weight is suspended from the 50 cm position, and a 3.0-N weight is suspended from the 60 cm position.What is the tension in the string attached at the 100-cm end of the stick?

Accepted Answer

A) 1.9 N 
B) 3.0 N 
C) 3.5 N 
D) 4.0 N

Question 16

A turntable has a moment of inertia of 3.00 * 10-2 kg*m2 and spins freely on a frictionless bearing at 25.0 rev/min.A 0.300-kg ball of putty is dropped vertically onto the turntable and sticks at a point 0.100 m from the center.What is the new rate of rotation of the system?

Accepted Answer

A) 40.8 rev/min 
B) 22.7 rev/min 
C) 33.3 rev/min 
D) 27.2 rev/min

Question 17

An 800-N billboard worker stands on a 4.0-m scaffold supported by vertical ropes at each end.If the scaffold weighs 500 N and the worker stands 1.0 m from one end, what is the tension in the rope nearest the worker?

Accepted Answer

A) 450 N 
B) 500 N 
C) 800 N 
D) 850 N

Question 18

A bucket of water with total mass 23 kg is attached to a rope, which in turn, is wound around a 0.050-m radius cylinder at the top of a well.A crank with a turning radius of 0.25 m is attached to the end of the cylinder.What minimum force directed perpendicular to the crank handle is required to just raise the bucket? (Assume the rope's mass is negligible, that cylinder turns on frictionless bearings, and that g = 9.8 m/s2.)

Accepted Answer

A) 45 N 
B) 68 N 
C) 90 N 
D) 135 N

Question 19

A tetherball is attached to a pole with a 2.0-m rope.It is circling at 0.20 rev/s.As the rope wraps around the pole it shortens.How long is the rope when the ball is moving at 5.0 m/s?

Accepted Answer

A) 1.8 m 
B) 1.5 m 
C) 1.2 m 
D) 1.0 m

Question 20

The total kinetic energy of a baseball thrown with a spinning motion is a function of:

Accepted Answer

A) its linear speed but not rotational speed. 
B) its rotational speed but not linear speed. 
C) both linear and rotational speeds. 
D) neither linear nor rotational speed.

Exam 8: Rotational Equilibrium and Rotational Dynamics

A gyroscope has a moment of inertia of 0.140 kgm²and has an initial angular speed of 15.0 rad/s.If a lubricant is applied to the bearings of the gyroscope so that frictional torque is reduced to 2.00 10^-2 N*m, then in what time interval will the gyroscope coast from 15.0 rad/s to zero?

An 80-kg man is one fourth of the way up a 10-m ladder that is resting against a smooth, frictionless wall.If the ladder has a mass of 20 kg and it makes an angle of 60 $\degree$ with the ground, find the force of friction of the ground on the foot of the ladder.

A uniform solid sphere rolls down an incline of height 3 m after starting from rest.In order to calculate its speed at the bottom of the incline, one needs to know:

A ventilation fan with a moment of inertia of 0.034 kgm² has a net torque of 0.11 Nm applied to it.If it starts from rest, what kinetic energy will it have 8.0 s later?

A cylinder (I = MR²/2) is rolling along the ground at 7.0 m/s.It comes to a hill and starts going up.Assuming no losses to friction, how high does it get before it stops?

A gyroscope has a moment of inertia of 0.14 kg*m² and an initial angular speed of 15 rad/s.Friction in the bearings causes its speed to reduce to zero in 30 s.What is the value of the average frictional torque?

A 4.0-kg mass is placed at (3.0, 4.0) m, and a 6.0-kg mass is placed at (3.0, -4.0) m.What is the moment of inertia of this system of masses about the x-axis?

A solid cylinder (I = MR²/2) has a string wrapped around it many times.When I release the cylinder, holding on to the string, the cylinder falls and spins as the string unwinds.What is the downward acceleration of the cylinder as it falls?

A turntable has a moment of inertia of 3.00 * 10^-2 kg*m² and spins freely on a frictionless bearing at 25.0 rev/min.A 0.300-kg ball of putty is dropped vertically onto the turntable and sticks at a point 0.100 m from the center.What is the new rate of rotation of the system?

An 800-N billboard worker stands on a 4.0-m scaffold supported by vertical ropes at each end.If the scaffold weighs 500 N and the worker stands 1.0 m from one end, what is the tension in the rope nearest the worker?

A tetherball is attached to a pole with a 2.0-m rope.It is circling at 0.20 rev/s.As the rope wraps around the pole it shortens.How long is the rope when the ball is moving at 5.0 m/s?

The total kinetic energy of a baseball thrown with a spinning motion is a function of:

Exam 8: Rotational Equilibrium and Rotational Dynamics

A gyroscope has a moment of inertia of 0.140 kg*m2 and has an initial angular speed of 15.0 rad/s.If a lubricant is applied to the bearings of the gyroscope so that frictional torque is reduced to 2.00 * 10-2 N*m, then in what time interval will the gyroscope coast from 15.0 rad/s to zero?

The torque caused by a force F applied at a distance r from the axis of rotation, is given by , where q is the angle between and .If the magnitudes r and F remain the same, what other angle q¢ will produce the same torque as was produced at angle q if q was less than 90 °\degree° ?

An 80-kg man is one fourth of the way up a 10-m ladder that is resting against a smooth, frictionless wall.If the ladder has a mass of 20 kg and it makes an angle of 60 °\degree° with the ground, find the force of friction of the ground on the foot of the ladder.

A uniform solid sphere rolls down an incline of height 3 m after starting from rest.In order to calculate its speed at the bottom of the incline, one needs to know:

A ventilation fan with a moment of inertia of 0.034 kg*m2 has a net torque of 0.11 N*m applied to it.If it starts from rest, what kinetic energy will it have 8.0 s later?

A cylinder (I = MR2/2) is rolling along the ground at 7.0 m/s.It comes to a hill and starts going up.Assuming no losses to friction, how high does it get before it stops?

A gyroscope has a moment of inertia of 0.14 kg*m2 and an initial angular speed of 15 rad/s.Friction in the bearings causes its speed to reduce to zero in 30 s.What is the value of the average frictional torque?

A 4.0-kg mass is placed at (3.0, 4.0) m, and a 6.0-kg mass is placed at (3.0, -4.0) m.What is the moment of inertia of this system of masses about the x-axis?

A solid cylinder (I = MR2/2) has a string wrapped around it many times.When I release the cylinder, holding on to the string, the cylinder falls and spins as the string unwinds.What is the downward acceleration of the cylinder as it falls?

A turntable has a moment of inertia of 3.00 * 10-2 kg*m2 and spins freely on a frictionless bearing at 25.0 rev/min.A 0.300-kg ball of putty is dropped vertically onto the turntable and sticks at a point 0.100 m from the center.What is the new rate of rotation of the system?

An 800-N billboard worker stands on a 4.0-m scaffold supported by vertical ropes at each end.If the scaffold weighs 500 N and the worker stands 1.0 m from one end, what is the tension in the rope nearest the worker?

A tetherball is attached to a pole with a 2.0-m rope.It is circling at 0.20 rev/s.As the rope wraps around the pole it shortens.How long is the rope when the ball is moving at 5.0 m/s?

The total kinetic energy of a baseball thrown with a spinning motion is a function of:

A gyroscope has a moment of inertia of 0.140 kgm²and has an initial angular speed of 15.0 rad/s.If a lubricant is applied to the bearings of the gyroscope so that frictional torque is reduced to 2.00 10^-2 N*m, then in what time interval will the gyroscope coast from 15.0 rad/s to zero?

An 80-kg man is one fourth of the way up a 10-m ladder that is resting against a smooth, frictionless wall.If the ladder has a mass of 20 kg and it makes an angle of 60 $\degree$ with the ground, find the force of friction of the ground on the foot of the ladder.

A ventilation fan with a moment of inertia of 0.034 kgm² has a net torque of 0.11 Nm applied to it.If it starts from rest, what kinetic energy will it have 8.0 s later?

A cylinder (I = MR²/2) is rolling along the ground at 7.0 m/s.It comes to a hill and starts going up.Assuming no losses to friction, how high does it get before it stops?

A gyroscope has a moment of inertia of 0.14 kg*m² and an initial angular speed of 15 rad/s.Friction in the bearings causes its speed to reduce to zero in 30 s.What is the value of the average frictional torque?

A solid cylinder (I = MR²/2) has a string wrapped around it many times.When I release the cylinder, holding on to the string, the cylinder falls and spins as the string unwinds.What is the downward acceleration of the cylinder as it falls?

A turntable has a moment of inertia of 3.00 * 10^-2 kg*m² and spins freely on a frictionless bearing at 25.0 rev/min.A 0.300-kg ball of putty is dropped vertically onto the turntable and sticks at a point 0.100 m from the center.What is the new rate of rotation of the system?