Question 1

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 2

Two children seat themselves on a seesaw.The one on the left has a weight of 400 N while the one on the right weighs 300 N.The fulcrum is at the midpoint of the seesaw.If the child on the left is not at the end but is 1.50 m from the fulcrum and the seesaw is balanced, what is the torque provided by the weight of the child on the right?

Accepted Answer

A) 600 N*m 
B) 450 N*m 
C) -600 N*m 
D) -450 N*m

Question 3

According to Newton's second law, the angular acceleration experienced by an object is directly proportional to:

Accepted Answer

A) its moment of inertia. 
B) the net applied torque. 
C) the object's size. 
D) choices a and b above are both valid.

Question 4

Two hoops or rings (I = MR2) are centered, lying on a turntable.The smaller ring has radius = 0.050 m; the larger has radius = 0.10 m.Both have a mass of 3.0 kg.What is the total moment of inertia as the turntable spins? Ignore the mass of the turntable.

Accepted Answer

A) 0.030 kg*m2 
B) 0.007 5 kg*m2 
C) 0.038 kg*m2 
D) 0.075 kg*m2

Question 5

Two spheres, one with the center core up to r = R/2 hollow and the other solid, have the same mass M and same outer radius R.If they are both rolling at the same linear speed, which one has the greater kinetic energy?

Accepted Answer

A) The both have the same kinetic energy. 
B) The hollow one has the greater kinetic energy. 
C) The solid one has the greater kinetic energy. 
D) More information is needed to choose an answer.

Question 6

A bowling ball has a mass of 7.0 kg, a moment of inertia of 2.8 * 10-2 kg*m2 and a radius of 0.10 m.If it rolls down the lane without slipping at a linear speed of 4.0 m/s, what is its angular speed?

Accepted Answer

A) 0.80 rad/s 
B) 10 rad/s 
C) 0.050 rad/s 
D) 40 rad/s

Question 7

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 8

A solid sphere of mass 4.0 kg and radius 0.12 m starts from rest at the top of a ramp inclined 15$\degree$, and rolls to the bottom.The upper end of the ramp is 1.2 m higher than the lower end.What is the linear speed of the sphere when it reaches the bottom of the ramp? (Note: I = 0.4MR2 for a solid sphere and g = 9.8 m/s2)

Accepted Answer

A) 4.7 m/s 
B) 4.1 m/s 
C) 3.4 m/s 
D) 2.4 m/s

Question 9

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 10

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 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) 1.50

Question 11

Tasha has mass 20 kg and wants to use a 4.0-m board of mass 10 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) 2.0 m 
B) 1.0 m 
C) 0.67 m 
D) 0.33 m

Question 12

A cylinder with its mass concentrated toward the center has a moment of inertia of 0.1 MR2.If this cylinder is rolling without slipping along a level surface with a linear speed v, what is the ratio of its rotational kinetic energy to its linear kinetic energy?

Accepted Answer

A) 1/l0 
B) 1/5 
C) 1/2 
D) 1/1

Question 13

Masses are distributed in the xy-plane as follows: 10 kg at (2.0, 6.0) m, 4.0 kg at (2.0, 0.0) m, and 6.0 kg at (0.0, 3.0) m.Where would a 20-kg mass need to be positioned so that the center of gravity of the resulting four mass system would be at the origin?

Accepted Answer

A) (1.4, 3.9) m 
B) (3.9, 1.4) m 
C) (-1.4, -3.9) m 
D) (-3.9, -1.4) m

Question 14

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 15

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

Question 16

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 17

A vault is opened by applying a force of 300 N perpendicular to the plane of the door, 0.80 m from the hinges.Find the torque due to this force about an axis through the hinges.

Accepted Answer

A) 120 N*m 
B) 240 N*m 
C) 300 N*m 
D) 360 N*m

Question 18

A solid cylinder of mass 3.0 kg and radius 0.2 m starts from rest at the top of a ramp, inclined 15$\degree$, and rolls to the bottom without slipping.(For a cylinder I = 0.5MR2) The upper end of the ramp is 1.2 m higher than the lower end.Find the linear speed of the cylinder when it reaches the bottom of the ramp.(g = 9.8 m/s2)

Accepted Answer

A) 4.7 m/s 
B) 4.3 m/s 
C) 4.0 m/s 
D) 2.4 m/s

Question 19

An initially installed flywheel can store 106 J of kinetic energy when rotating at 300 rad/s.It is replaced by another flywheel of the same size but made of a lighter and stronger material.If its mass is half that of the original and it is now capable of achieving a rotational speed of 600 rad/s, what maximum energy can be stored?

Accepted Answer

A) 40 * 105 J 
B) 20 * 105 J 
C) 10 * 105 J 
D) 5.0 * 105 J

Question 20

A 100-N uniform ladder, 8.0 m long, rests against a smooth vertical wall.The coefficient of static friction between ladder and floor is 0.40.What minimum angle can the ladder make with the floor before it slips?

Accepted Answer

A) 22$\degree$ 
B) 51$\degree$ 
C) 18$\degree$ 
D) 42$\degree$

Exam 8: Rotational Equilibrium and Rotational Dynamics

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)

According to Newton's second law, the angular acceleration experienced by an object is directly proportional to:

Two hoops or rings (I = MR²) are centered, lying on a turntable.The smaller ring has radius = 0.050 m; the larger has radius = 0.10 m.Both have a mass of 3.0 kg.What is the total moment of inertia as the turntable spins? Ignore the mass of the turntable.