Question 1

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 2

A rod of length L is hinged at one end.The moment of inertia as the rod rotates around that hinge is ML2/3.Suppose a 2.00-m rod with a mass of 3.00 kg is hinged at one end and is held in a horizontal position.The rod is released as the free end is allowed to fall.What is the angular acceleration as it is released?

Accepted Answer

A) 3.70 rad/s2 
B) 7.35 rad/s2 
C) 2.45 rad/s2 
D) 4.90 rad/s2

Question 3

A woman who weighs 500 N stands on an 8.0-m-long board that weighs 100 N.The board is supported at each end.The support force at the right end is 3 times the support force at the left end.How far from the right end is the woman standing?

Accepted Answer

A) 4.0 m 
B) 2.0 m 
C) 2.7 m 
D) 1.6 m

Question 4

An object of mass m and moment of inertia I has rotational kinetic energy KR.Its angular momentum is:

Accepted Answer

A) 0.5 I/m. 
B) (2 IKR)1/2. 
C) (2 mKR)1/2. 
D) not given above.

Question 5

An automobile accelerates from zero to 30 m/s in 6.0 s.The wheels have a diameter of 0.40 m.What is the average angular acceleration of each wheel?

Accepted Answer

A) 5.0 rad/s2 
B) 15 rad/s2 
C) 25 rad/s2 
D) 35 rad/s2

Question 6

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 angular momentum will it have 8.0 s later?

Accepted Answer

A) 0.88 kg*m2/s 
B) 0.97 kg*m2/s 
C) 2.0 kg*m2/s 
D) 3.25 kg*m2/s

Question 7

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 8

A 4.2-kg mass is placed at (3.0,4.0)m.Where can an 8.4-kg mass be placed so that the moment of inertia about the z-axis is zero?

Accepted Answer

A) (-3.0,-4.0)m 
B) (-6.0,-8.0)m 
C) (-1.5,-2.0)m 
D) There is no position giving this result.

Question 9

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.The bucket is raised to the top of the well and released.The bucket is moving with a speed of 8.0 m/s upon hitting the water surface in the well.What is the angular speed of the cylinder at this instant?

Accepted Answer

A) 39 rad/s 
B) 79 rad/s 
C) 120 rad/s 
D) 160 rad/s

Question 10

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 11

Masses are distributed in the x,y-plane as follows: 6.0 kg at (0.0,0.0)m,4.0 kg at (2.0,0.0)m,and 5.0 kg at (2.0,3.0)m.What is the x-coordinate of the center of gravity of this system of masses?

Accepted Answer

A) 18 m 
B) 2.0 m 
C) 1.2 m 
D) 1.0 m

Question 12

A solid sphere with mass,M,and radius,R,rolls along a level surface without slipping with a linear speed,v.What is the ratio of rotational to linear kinetic energy? (For a solid sphere,I = 0.4 MR2)

Accepted Answer

A) 1/4 
B) 1/2 
C) 1/1 
D) 2/5

Question 13

A turntable has a moment of inertia of 3.00 x 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 14

An object consists of a rod (of length 3.0 m and negligible moment of inertia)to which four small 2.0-kg masses are attached,one at each end and one at each point on the rod 1.0 m from each end.(The masses are one meter apart. )The moment of inertia of this object about an axis perpendicular to the rod and through one of the inner masses:

Accepted Answer

A) is 72 kg*m2. 
B) is 12 kg*m2. 
C) is 4 kg*m2. 
D) cannot be uniquely determined until it is stated which inner mass the axis goes through.

Question 15

A uniform beam of length 4.0 m and weight 100 N is mounted on an axle at one end perpendicular to the length of the beam.A rope is attached to the end of the beam at the other end from the axle and the beam is lifted by the rope so that the beam makes an angle of 30 $\degree$ with the horizontal.What is the tension in the rope if it is straight up?

Accepted Answer

A) 50 N 
B) 87 N 
C) 100 N 
D) 200 N

Question 16

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 17

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 18

A figure skater on ice with arms extended,spins at a rate of 2.5 rev/s.After he draws his arms in,he spins at 6.0 rev/s.By what factor does the skater's kinetic energy change when he draws his arms in?

Accepted Answer

A) 2.4 
B) 1.0 
C) 0.42 
D) 0.12

Question 19

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 formed by one of the batons?

Accepted Answer

A) 0.048 kg*m2 
B) 0.064 kg*m2 
C) 0.19 kg*m2 
D) 0.32 kg*m2

Question 20

A disk has a moment of inertia of 3.0 ´ 10-4 kg*m2 and rotates with an angular speed of 3.5 rad/sec.What net torque must be applied to bring it to rest within 3 s?

Accepted Answer

A) 4.5 ´ 10-3 N*m 
B) 7.5 ´ 10-4 N*m 
C) 3.5 ´ 10-4 N*m 
D) 5.0 ´ 10-4 N*m

Exam 8: Rotational Equilibrium and Rotational Dynamics

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 woman who weighs 500 N stands on an 8.0-m-long board that weighs 100 N.The board is supported at each end.The support force at the right end is 3 times the support force at the left end.How far from the right end is the woman standing?

An object of mass m and moment of inertia I has rotational kinetic energy K_R.Its angular momentum is:

An automobile accelerates from zero to 30 m/s in 6.0 s.The wheels have a diameter of 0.40 m.What is the average angular acceleration of each wheel?

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 angular momentum will it have 8.0 s later?

A 4.2-kg mass is placed at (3.0,4.0) m.Where can an 8.4-kg mass be placed so that the moment of inertia about the z-axis is zero?

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?

Masses are distributed in the x,y-plane as follows: 6.0 kg at (0.0,0.0) m,4.0 kg at (2.0,0.0) m,and 5.0 kg at (2.0,3.0) m.What is the x-coordinate of the center of gravity of this system of masses?

A solid sphere with mass,M,and radius,R,rolls along a level surface without slipping with a linear speed,v.What is the ratio of rotational to linear kinetic energy? (For a solid sphere,I = 0.4 MR²)

A turntable has a moment of inertia of 3.00 x 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?

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 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?

A figure skater on ice with arms extended,spins at a rate of 2.5 rev/s.After he draws his arms in,he spins at 6.0 rev/s.By what factor does the skater's kinetic energy change when he draws his arms in?

A disk has a moment of inertia of 3.0 ´ 10^-4 kg*m² and rotates with an angular speed of 3.5 rad/sec.What net torque must be applied to bring it to rest within 3 s?

Exam 8: Rotational Equilibrium and Rotational Dynamics

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 woman who weighs 500 N stands on an 8.0-m-long board that weighs 100 N.The board is supported at each end.The support force at the right end is 3 times the support force at the left end.How far from the right end is the woman standing?

An object of mass m and moment of inertia I has rotational kinetic energy KR.Its angular momentum is:

An automobile accelerates from zero to 30 m/s in 6.0 s.The wheels have a diameter of 0.40 m.What is the average angular acceleration of each wheel?

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 angular momentum will it have 8.0 s later?

A 4.2-kg mass is placed at (3.0,4.0) m.Where can an 8.4-kg mass be placed so that the moment of inertia about the z-axis is zero?

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?

Masses are distributed in the x,y-plane as follows: 6.0 kg at (0.0,0.0) m,4.0 kg at (2.0,0.0) m,and 5.0 kg at (2.0,3.0) m.What is the x-coordinate of the center of gravity of this system of masses?

A solid sphere with mass,M,and radius,R,rolls along a level surface without slipping with a linear speed,v.What is the ratio of rotational to linear kinetic energy? (For a solid sphere,I = 0.4 MR2)

A turntable has a moment of inertia of 3.00 x 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?

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 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?

A figure skater on ice with arms extended,spins at a rate of 2.5 rev/s.After he draws his arms in,he spins at 6.0 rev/s.By what factor does the skater's kinetic energy change when he draws his arms in?

A disk has a moment of inertia of 3.0 ´ 10-4 kg*m2 and rotates with an angular speed of 3.5 rad/sec.What net torque must be applied to bring it to rest within 3 s?

An object of mass m and moment of inertia I has rotational kinetic energy K_R.Its angular momentum is:

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 angular momentum will it have 8.0 s later?

A solid sphere with mass,M,and radius,R,rolls along a level surface without slipping with a linear speed,v.What is the ratio of rotational to linear kinetic energy? (For a solid sphere,I = 0.4 MR²)

A turntable has a moment of inertia of 3.00 x 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?

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 disk has a moment of inertia of 3.0 ´ 10^-4 kg*m² and rotates with an angular speed of 3.5 rad/sec.What net torque must be applied to bring it to rest within 3 s?