Question 1

A uniform rod of length L and mass M is pivoted about one end.Attached to the rod is a mass M at its midpoint and at the end opposite the pivot is another mass M.What is the moment of inertia of this configuration about the pivot?

Accepted Answer

A)  3ML2
B)  7ML2/12
C)  4ML2/3
D)  19ML2/12 D

Question 2

A 2.00-kg mass is placed at (3.00,4.00)m,and a 3.50-kg mass is placed at (3.00,−4.00)m.What is the moment of inertia of this system of masses about the z axis?

Accepted Answer

A)  138 kg·m2
B)  16.5 kg·m2
C)  88.0 kg·m2
D)  49.5 kg·m2
E)  22.0 kg·m2 A

Question 3

Three disks have the same mass and the same total kinetic energy.Disk #1 has radius R,disk #2 has radius 2R,and disk #3 has radius 3R.Which one has the highest vtranslational?

Accepted Answer

A)  disk #1
B)  disk #2
C)  disk #3
D)  The all have the same vtranslational. D

Question 4

A meter stick is hinged at its lower end and allowed to fall from a vertical position.If its moment of inertia is ML2/3,with what angular speed does it hit the table?

Accepted Answer

A)  5.42 rad/s
B)  2.71 rad/s
C)  1.22 rad/s
D)  7.67 rad/s

Question 5

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 6

A bucket filled with water has a mass of 20.0 kg and is attached to a rope,which in turn,is wound around a 0.050-m radius cylinder at the top of a well.What torque does the weight of water and bucket produce on the cylinder if the cylinder is not permitted to rotate? (g = 9.80 m/s2)

Accepted Answer

A)  19.6 N·m
B)  9.8 N·m
C)  1.00 N·m
D)  400 N·m
E)  196 N·m

Question 7

A solid sphere of radius R is placed on an incline that makes an angle ​θ with the horizontal.The sphere rolls down the incline without slipping.What is its acceleration?

Accepted Answer

A)   
B)   
C)   
D)

Question 8

Tasha has mass 20 kg and wants to use a 5.0-m board of mass 12 kg as a seesaw.Her friends are busy,so Tasha seesaws by herself by putting the support at the system's center of gravity when she sits on one end of the board.How far is she from the support point?

Accepted Answer

A)  1.9 m
B)  0.94 m
C)  4.1 m
D)  3.1 m

Question 9

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 0.600-kg ball of putty is dropped vertically on the turntable and sticks at a point 0.100 m from the center.By what factor does the angular momentum of the system change after the putty is dropped onto the turntable?

Accepted Answer

A)  1.22
B)  1.00 (no change) 
C)  0.820
D)  1.20

Question 10

Two hoops or rings (I = MR2)are centered,lying on a turntable.The smaller ring has radius = 0.05 m;the larger has radius = 0.10 m.Both have a mass of 5.0 kg.What is the total moment of inertia as the turntable spins? Ignore the mass of the turntable.

Accepted Answer

A)  7.5E-1 kg·m2
B)  1.1E-1 kg·m2
C)  1.3E-2 kg·m2
D)  6.3E-2 kg·m2
E)  5.0E-2 kg·m2

Question 11

A 60-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 25 kg and it makes an angle of 60° with the ground,find the force of friction of the ground on the foot of the ladder.

Accepted Answer

A)  1.4E+1 N
B)  1.6E+2 N
C)  2.4E+2 N
D)  2.7E+2 N
E)  ​4.2E+3 N

Question 12

A baseball pitcher,loosening up his arm before a game,tosses a 0.140-kg ball using only the rotation of his forearm,0.290 m in length,to accelerate the ball.If the ball starts at rest and is released with a speed of 24.0 m/s in a time of 0.450 s,what is the average angular acceleration of the arm and ball?

Accepted Answer

A)  3.13 rad/s2
B)  37.2 rad/s2
C)  15.5 rad/s2
D)  184 rad/s2
E)  25.7 rad/s2

Question 13

A rod system with a uniform linear density of $\lambda$ = 4.40 kg/m has the shape shown in the figure,with rod 1 the vertical rod and rod 2 the horizontal rod.Rod 1 has length LS1U1B11S1U1B0 = 8.00 m,and rod 2 has length LS1U1B12S1U1B0 = 7.50 m.Neglect the diameter of the rods.  ​
-What is the center of mass of each rod?

Accepted Answer

A)  rod 1: (35.20 m,0) ,rod 2: (0,11.73 m) 
B)  rod 1: (17.60 m,0) ,rod 2: (0,16.50 m) 
C)  rod 1: (2.50,4.00) ,rod 2: (3.75 m,0 m) 
D)  rod 1: (10.20 m,0) ,rod 2: (0,9.70 m)  ​

Question 14

A figure skater with arms initially extended starts spinning on the ice at 3 rad/s.She then pulls her arms in close to her body.Which of the following results?

Accepted Answer

A)  a smaller rotational rate
B)  a greater rotational rate
C)  a greater angular momentum
D)  a smaller angular momentum

Question 15

A figure skater on ice with arms extended,spins at a rate of 3.5 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)  1.7
C)  0.58
D)  0.12

Question 16

A rod system with a uniform linear density of $\lambda$ = 4.40 kg/m has the shape shown in the figure,with rod 1 the vertical rod and rod 2 the horizontal rod.Rod 1 has length LS1U1B11S1U1B0 = 8.00 m,and rod 2 has length LS1U1B12S1U1B0 = 7.50 m.Neglect the diameter of the rods.  ​
-What is the mass of each rod?

Accepted Answer

A)  rod 1: 12.4 kg,rod 2: 11.9 kg
B)  rod 1: 4.69 kg,rod 2: 4.13 kg
C)  rod 1: 0.550 kg,rod 2: 0.587 kg
D)  rod 1: 35.2 kg,rod 2: 33.0 kg

Question 17

An ice skater spins at 3.5 rev/s with his arms are extended.He draws his arms in and spins at 8.3 rev/s.By what factor does his moment of inertia change in the process?

Accepted Answer

A)  2.4
B)  0.58
C)  0.42
D)  0.12

Question 18

A rotating flywheel can be used as a method to store energy.If it has 2.00 × 106 J of kinetic energy when rotating at 400 rad/s,and if a frictional torque of 4.00 N 
M acts on the system,in what interval of time would the flywheel come to rest?

Accepted Answer

A)  2 500 min
B)  41.7 min
C)  25.0 min
D)  167 min

Question 19

A meterstick is supported by a knife-edge at the 50.0-cm mark.Doug hangs masses of 0.48 and 0.76 kg from the 10-cm and 80-cm marks,respectively.Where should Doug hang a third mass of 0.25 kg to keep the stick balanced?

Accepted Answer

A)  64.4 cm
B)  25.6 cm
C)  74.4 cm
D)  35.6 cm
E)  50 cm

Question 20

A uniform bridge span weighs 70.0 kN and is 40.0 m long.An automobile weighing 15.0 kN is parked with its center of gravity located 15.0 m from the right pier.What upward support force does the right pier provide?

Accepted Answer

A)  40.6 kN
B)  51.3 kN
C)  25.6 kN
D)  44.4 kN
E)  42.5 kN

Exam 8: Rotational Equilibrium and Dynamics

A uniform rod of length L and mass M is pivoted about one end.Attached to the rod is a mass M at its midpoint and at the end opposite the pivot is another mass M.What is the moment of inertia of this configuration about the pivot?

A 2.00-kg mass is placed at (3.00,4.00) m,and a 3.50-kg mass is placed at (3.00,−4.00) m.What is the moment of inertia of this system of masses about the z axis?

Three disks have the same mass and the same total kinetic energy.Disk #1 has radius R,disk #2 has radius 2R,and disk #3 has radius 3R.Which one has the highest v_{translational}?

A meter stick is hinged at its lower end and allowed to fall from a vertical position.If its moment of inertia is ML²/3,with what angular speed does it hit the table?

A bucket filled with water has a mass of 20.0 kg and is attached to a rope,which in turn,is wound around a 0.050-m radius cylinder at the top of a well.What torque does the weight of water and bucket produce on the cylinder if the cylinder is not permitted to rotate? (g = 9.80 m/s²)

A solid sphere of radius R is placed on an incline that makes an angle θ with the horizontal.The sphere rolls down the incline without slipping.What is its acceleration?

Tasha has mass 20 kg and wants to use a 5.0-m board of mass 12 kg as a seesaw.Her friends are busy,so Tasha seesaws by herself by putting the support at the system's center of gravity when she sits on one end of the board.How far is she from the support point?

Two hoops or rings (I = MR²) are centered,lying on a turntable.The smaller ring has radius = 0.05 m;the larger has radius = 0.10 m.Both have a mass of 5.0 kg.What is the total moment of inertia as the turntable spins? Ignore the mass of the turntable.

A 60-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 25 kg and it makes an angle of 60° with the ground,find the force of friction of the ground on the foot of the ladder.

A figure skater with arms initially extended starts spinning on the ice at 3 rad/s.She then pulls her arms in close to her body.Which of the following results?

A figure skater on ice with arms extended,spins at a rate of 3.5 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?

An ice skater spins at 3.5 rev/s with his arms are extended.He draws his arms in and spins at 8.3 rev/s.By what factor does his moment of inertia change in the process?

A rotating flywheel can be used as a method to store energy.If it has 2.00 × 10⁶ J of kinetic energy when rotating at 400 rad/s,and if a frictional torque of 4.00 N M acts on the system,in what interval of time would the flywheel come to rest?

A meterstick is supported by a knife-edge at the 50.0-cm mark.Doug hangs masses of 0.48 and 0.76 kg from the 10-cm and 80-cm marks,respectively.Where should Doug hang a third mass of 0.25 kg to keep the stick balanced?

A uniform bridge span weighs 70.0 kN and is 40.0 m long.An automobile weighing 15.0 kN is parked with its center of gravity located 15.0 m from the right pier.What upward support force does the right pier provide?

Exam 8: Rotational Equilibrium and Dynamics

A uniform rod of length L and mass M is pivoted about one end.Attached to the rod is a mass M at its midpoint and at the end opposite the pivot is another mass M.What is the moment of inertia of this configuration about the pivot?

A 2.00-kg mass is placed at (3.00,4.00) m,and a 3.50-kg mass is placed at (3.00,−4.00) m.What is the moment of inertia of this system of masses about the z axis?

Three disks have the same mass and the same total kinetic energy.Disk #1 has radius R,disk #2 has radius 2R,and disk #3 has radius 3R.Which one has the highest vtranslational?

A meter stick is hinged at its lower end and allowed to fall from a vertical position.If its moment of inertia is ML2/3,with what angular speed does it hit the table?

A bucket filled with water has a mass of 20.0 kg and is attached to a rope,which in turn,is wound around a 0.050-m radius cylinder at the top of a well.What torque does the weight of water and bucket produce on the cylinder if the cylinder is not permitted to rotate? (g = 9.80 m/s2)

A solid sphere of radius R is placed on an incline that makes an angle ​θ with the horizontal.The sphere rolls down the incline without slipping.What is its acceleration?

Tasha has mass 20 kg and wants to use a 5.0-m board of mass 12 kg as a seesaw.Her friends are busy,so Tasha seesaws by herself by putting the support at the system's center of gravity when she sits on one end of the board.How far is she from the support point?

Two hoops or rings (I = MR2) are centered,lying on a turntable.The smaller ring has radius = 0.05 m;the larger has radius = 0.10 m.Both have a mass of 5.0 kg.What is the total moment of inertia as the turntable spins? Ignore the mass of the turntable.

A 60-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 25 kg and it makes an angle of 60° with the ground,find the force of friction of the ground on the foot of the ladder.

A figure skater with arms initially extended starts spinning on the ice at 3 rad/s.She then pulls her arms in close to her body.Which of the following results?

A figure skater on ice with arms extended,spins at a rate of 3.5 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 rod system with a uniform linear density of λ\lambdaλ = 4.40 kg/m has the shape shown in the figure,with rod 1 the vertical rod and rod 2 the horizontal rod.Rod 1 has length L1 = 8.00 m,and rod 2 has length L2 = 7.50 m.Neglect the diameter of the rods. ​ -What is the mass of each rod?

An ice skater spins at 3.5 rev/s with his arms are extended.He draws his arms in and spins at 8.3 rev/s.By what factor does his moment of inertia change in the process?

A rotating flywheel can be used as a method to store energy.If it has 2.00 × 106 J of kinetic energy when rotating at 400 rad/s,and if a frictional torque of 4.00 N M acts on the system,in what interval of time would the flywheel come to rest?

A meterstick is supported by a knife-edge at the 50.0-cm mark.Doug hangs masses of 0.48 and 0.76 kg from the 10-cm and 80-cm marks,respectively.Where should Doug hang a third mass of 0.25 kg to keep the stick balanced?

A uniform bridge span weighs 70.0 kN and is 40.0 m long.An automobile weighing 15.0 kN is parked with its center of gravity located 15.0 m from the right pier.What upward support force does the right pier provide?

Three disks have the same mass and the same total kinetic energy.Disk #1 has radius R,disk #2 has radius 2R,and disk #3 has radius 3R.Which one has the highest v_{translational}?

A meter stick is hinged at its lower end and allowed to fall from a vertical position.If its moment of inertia is ML²/3,with what angular speed does it hit the table?

A bucket filled with water has a mass of 20.0 kg and is attached to a rope,which in turn,is wound around a 0.050-m radius cylinder at the top of a well.What torque does the weight of water and bucket produce on the cylinder if the cylinder is not permitted to rotate? (g = 9.80 m/s²)

A solid sphere of radius R is placed on an incline that makes an angle θ with the horizontal.The sphere rolls down the incline without slipping.What is its acceleration?

Two hoops or rings (I = MR²) are centered,lying on a turntable.The smaller ring has radius = 0.05 m;the larger has radius = 0.10 m.Both have a mass of 5.0 kg.What is the total moment of inertia as the turntable spins? Ignore the mass of the turntable.

A rotating flywheel can be used as a method to store energy.If it has 2.00 × 10⁶ J of kinetic energy when rotating at 400 rad/s,and if a frictional torque of 4.00 N M acts on the system,in what interval of time would the flywheel come to rest?