Question 1

If two forces of equal magnitude act on an object that is hinged at a pivot, the force acting farther from the pivot must produce the greater torque about the pivot.

Accepted Answer

A)  true 
B)  false 
C)  unable to decide without knowing the shape of the object 
A)  true 
B)  false 
C)  unable to decide without knowing the shape of the object

Question 2

What is the torque about the origin on a particle located at      = 3 m   + 4 m   - 2 m   if a force   = 5 N   - 2 N   + 3 N   acts on the particle?

Accepted Answer

A)  (8   +   - 26   ) N ∙ m 
B)  (8   - 19   - 26   ) N ∙ m 
C)  (8   + 2   +   ) N ∙ m 
D)  (16   - 19   - 26   ) N ∙ m 
E)  (8   - 2   +   ) N ∙ m 
A)  (8   +   - 26   ) N ∙ m 
B)  (8   - 19   - 26   ) N ∙ m 
C)  (8   + 2   +   ) N ∙ m 
D)  (16   - 19   - 26   ) N ∙ m 
E)  (8   - 2   +   ) N ∙ m

Question 3

A 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg ∙ m2 is rotating freely with an angular speed of 1.0 rad/s. Two people, each having a mass of 60 kg, are standing right outside the edge of the merry-go-round and step on it with negligible speed. What is the angular speed of the merry-go-round right after the two people have stepped on?

Accepted Answer

A)  0.20 rad/s 
B)  0.40 rad/s 
C)  0.60 rad/s 
D)  0.80 rad/s 
E)  0.67 rad/s 
A)  0.20 rad/s 
B)  0.40 rad/s 
C)  0.60 rad/s 
D)  0.80 rad/s 
E)  0.67 rad/s

Question 4

A 5.0-m long, 12-kg uniform ladder rests against a smooth vertical wall with the bottom of the ladder 3.0 m from the wall. The coefficient of static friction between the floor and the ladder is 0.28. What distance, measured along the ladder from the bottom, can a 60-kg person climb before the ladder starts to slip?

Accepted Answer

A)  4.0 m 
B)  3.7 m 
C)  1.7 m 
D)  1.3 m 
E)  3.3 m 
A)  4.0 m 
B)  3.7 m 
C)  1.7 m 
D)  1.3 m 
E)  3.3 m

Question 5

A 500-g particle is located at the point   = 4m   + 3m   - 2m   and is moving with a velocity   = 5 m/s   -2 ms   + 4 m/s   . What is the angular momentum of this particle about the origin?

Accepted Answer

A)  (24   - 6   - 8   ) kg ∙ m2/s 
B)  (12   - 3   - 4   ) kg ∙ m2/s 
C)  (8   + 14   - 13   ) kg ∙ m2/s 
D)  (10   -   + 2   ) kg ∙ m2/s 
E)  (4   - 13   - 11.5   ) kg ∙ m2/s 
A)  (24   - 6   - 8   ) kg ∙ m2/s 
B)  (12   - 3   - 4   ) kg ∙ m2/s 
C)  (8   + 14   - 13   ) kg ∙ m2/s 
D)  (10   -   + 2   ) kg ∙ m2/s 
E)  (4   - 13   - 11.5   ) kg ∙ m2/s

Question 6

In an experiment, a student brings up the rotational speed of a piece of laboratory apparatus to 30.0 rpm. She then allows the apparatus to slow down uniformly on its own, and counts 240 revolutions before the apparatus comes to a stop. The moment of inertia of the apparatus is known to be 0.0850 kg∙m2. What is the magnitude of the retarding torque on the apparatus?

Accepted Answer

A)  0.0425 N ∙ m 
B)  0.159 N ∙ m 
C)  0.0787 N ∙ m 
D)  0.000278 N ∙ m 
E)  0.0000136 N ∙ m 
A)  0.0425 N ∙ m 
B)  0.159 N ∙ m 
C)  0.0787 N ∙ m 
D)  0.000278 N ∙ m 
E)  0.0000136 N ∙ m

Question 7

A uniform solid sphere of mass 1.5 kg and diameter 30.0 cm starts from rest and rolls without slipping down a 35° incline that is 7.0 m long.
(a) Calculate the linear speed of the center of the sphere when it reaches the bottom of the incline.
(b) Determine the angular speed of the sphere about its center at the bottom of the incline.
(c) Through what angle (in radians) does this sphere turn as it rolls down the incline?
(d) Does the linear speed in (a) depend on the radius or mass of the sphere? Does the angular speed in (b) depend on the radius or mass of the sphere?

Accepted Answer

(a) 7.5 m/s (b) 50 rad/s (c) 4

Question 8

The angular acceleration of a wheel is given in   by   where t is in seconds. If the wheel starts from rest at   when is the next time the wheel is at rest?

Accepted Answer

A)  5.1 s 
B)  8.4 s 
C)  6.9 s 
D)  3.6 s 
A)  5.1 s 
B)  8.4 s 
C)  6.9 s 
D)  3.6 s

Question 9

A uniform 300-kg beam, 6.00 m long, is freely pivoted at P, as shown in the figure. The beam is supported in a horizontal position by a light strut, 5.00 m long, which is freely pivoted at Q and is loosely pinned to the beam at R. A load of mass is suspended from the end of the beam at S. A maximum compression of 23,000 N in the strut is permitted, due to safety. The maximum mass M of the load is closest to

Accepted Answer

A)  789 kg. 
B)  554 kg. 
C)  1020 kg. 
D)  1090 kg. 
E)  1320 kg. 
A)  789 kg. 
B)  554 kg. 
C)  1020 kg. 
D)  1090 kg. 
E)  1320 kg.

Question 10

A uniform solid sphere has a moment of inertia I about an axis tangent to its surface. What is the moment of inertia of this sphere about an axis through its center?

Accepted Answer

A)  1/7 I 
B)  2/7 I 
C)  2/5 I 
D)  3/5 I 
E)  7/5 I 
A)  1/7 I 
B)  2/7 I 
C)  2/5 I 
D)  3/5 I 
E)  7/5 I

Question 11

A force   = 3.00 N   - 2.00 N   acts at a location   = 1.00 m   + 2.00 m   on an object. What is the torque that this force applies about an axis through the origin perpendicular to the xy-plane?

Accepted Answer

A)  -1.00 N ∙ m   
B)  7.00 N ∙ m   
C)  -3.00 N ∙ m   
D)  5.00 N ∙ m   
E)  -8.00 N ∙ m   
A)  -1.00 N ∙ m   
B)  7.00 N ∙ m   
C)  -3.00 N ∙ m   
D)  5.00 N ∙ m   
E)  -8.00 N ∙ m

Question 12

A 1.25-kg ball begins rolling from rest with constant angular acceleration down a hill. If it takes 3.60 s for it to make the first complete revolution, how long will it take to make the next complete revolution?

Accepted Answer

The answer of A 1.25-kg ball begins rolling from rest...

Question 13

A 72.0-kg person pushes on a small doorknob with a force of 5.00 N perpendicular to the surface of the door. The doorknob is located 0.800 m from axis of the frictionless hinges of the door. The door begins to rotate with an angular acceleration of 2.00 rad/s2. What is the moment of inertia of the door about the hinges?

Accepted Answer

A)  4.28 kg ∙ m2 
B)  7.52 kg ∙ m2 
C)  1.88 kg ∙ m2 
D)  0.684 kg ∙ m2 
E)  2.74 kg ∙ m2 
A)  4.28 kg ∙ m2 
B)  7.52 kg ∙ m2 
C)  1.88 kg ∙ m2 
D)  0.684 kg ∙ m2 
E)  2.74 kg ∙ m2

Question 14

A slender uniform rod 100.00 cm long is used as a meter stick. Two parallel axes that are perpendicular to the rod are considered. The first axis passes through the 50-cm mark and the second axis passes through the 30-cm mark. What is the ratio of the moment of inertia through the second axis to the moment of inertia through the first axis?

Accepted Answer

A)  I2/I1 = 1.5 
B)  I2/I1 = 1.7 
C)  I2/I1 = 1.9 
D)  I2/I1 = 2.1 
E)  I2/I1 = 2.3 
A)  I2/I1 = 1.5 
B)  I2/I1 = 1.7 
C)  I2/I1 = 1.9 
D)  I2/I1 = 2.1 
E)  I2/I1 = 2.3

Question 15

A very thin horizontal, 2.00-m long, 5.00-kg uniform beam that lies along the east-west direction is acted on by two forces. At the east end of the beam, a 200-N force pushes downward. At the west end of the beam, a 200-N force pushes upward. What is the angular acceleration of the beam?

Accepted Answer

A)  240 rad/s2 north 
B)  1.33 × 102 rad/s2 north 
C)  zero 
D)  240 rad/s2 south 
E)  1.33 × 102 rad/s2 south 
A)  240 rad/s2 north 
B)  1.33 × 102 rad/s2 north 
C)  zero 
D)  240 rad/s2 south 
E)  1.33 × 102 rad/s2 south

Question 16

A bicycle is traveling north at 5.0 m/s. The mass of the wheel, 2.0 kg, is uniformly distributed along the rim, which has a radius of 20 cm. What are the magnitude and direction of the angular momentum of the wheel about its axle?

Accepted Answer

A)  2.0 kg ∙ m2/s towards the west 
B)  5.0 kg ∙ m2/s vertically upwards 
C)  2.0 kg ∙ m2/s towards the east 
D)  5.0 kg ∙ m2/s towards the east 
E)  5.0 kg ∙ m2/s towards the west 
A)  2.0 kg ∙ m2/s towards the west 
B)  5.0 kg ∙ m2/s vertically upwards 
C)  2.0 kg ∙ m2/s towards the east 
D)  5.0 kg ∙ m2/s towards the east 
E)  5.0 kg ∙ m2/s towards the west

Question 17

A 20.0-kg uniform door has a width of 1.20 m and a height of 2.50 m. The door is mounted on a post by a pair of hinges, marked 1 and 2 in the figure, at the top and bottom of the door. An external force of 60.0 N, at an angle of 30.0° above the horizontal, is applied to the small doorknob, as shown in the figure. The doorknob is 1.00 m above the bottom of the door.
(a) Find the x component of the force that hinge 1 exerts on the door at the top.
(b) Find the SUM of the y components of the forces that hinges 1 and 2 together exert on the door.

Accepted Answer

(a) -53.4

Question 18

A solid, uniform sphere of mass 2.0 kg and radius 1.7 m rolls from rest without slipping down an inclined plane of height 7.0 m. What is the angular velocity of the sphere at the bottom of the inclined plane?

Accepted Answer

A)  5.8 rad/s 
B)  9.9 rad/s 
C)  11 rad/s 
D)  7.0 rad/s 
A)  5.8 rad/s 
B)  9.9 rad/s 
C)  11 rad/s 
D)  7.0 rad/s

Question 19

A 3.00-kg ball rests in a frictionless groove as shown in the figure.   (a) What is the magnitude of the force that the left side of the groove exerts on the ball?
(b) What is the magnitude of the force that the right side of the groove exerts on the ball?

Accepted Answer

(a) 26.4 N

Question 20

A dumbbell-shaped object is composed by two equal masses, m, connected by a rod of negligible mass and length r. If I1 is the moment of inertia of this object with respect to an axis passing through the center of the rod and perpendicular to it and I2 is the moment of inertia with respect to an axis passing through one of the masses, it follows that

Accepted Answer

A)  I1 = I2. 
B)  I1 > I2. 
C)  I2 > I1. 
A)  I1 = I2. 
B)  I1 > I2. 
C)  I2 > I1.

Exam 12: Rotation of a Rigid Body

If two forces of equal magnitude act on an object that is hinged at a pivot, the force acting farther from the pivot must produce the greater torque about the pivot.

What is the torque about the origin on a particle located at = 3 m + 4 m - 2 m if a force = 5 N - 2 N + 3 N acts on the particle?

A 500-g particle is located at the point = 4m + 3m - 2m and is moving with a velocity = 5 m/s -2 ms + 4 m/s . What is the angular momentum of this particle about the origin?

The angular acceleration of a wheel is given in by where t is in seconds. If the wheel starts from rest at when is the next time the wheel is at rest?

A uniform solid sphere has a moment of inertia I about an axis tangent to its surface. What is the moment of inertia of this sphere about an axis through its center?

A force = 3.00 N - 2.00 N acts at a location = 1.00 m + 2.00 m on an object. What is the torque that this force applies about an axis through the origin perpendicular to the xy-plane?

A 1.25-kg ball begins rolling from rest with constant angular acceleration down a hill. If it takes 3.60 s for it to make the first complete revolution, how long will it take to make the next complete revolution?

A very thin horizontal, 2.00-m long, 5.00-kg uniform beam that lies along the east-west direction is acted on by two forces. At the east end of the beam, a 200-N force pushes downward. At the west end of the beam, a 200-N force pushes upward. What is the angular acceleration of the beam?

A bicycle is traveling north at 5.0 m/s. The mass of the wheel, 2.0 kg, is uniformly distributed along the rim, which has a radius of 20 cm. What are the magnitude and direction of the angular momentum of the wheel about its axle?

A solid, uniform sphere of mass 2.0 kg and radius 1.7 m rolls from rest without slipping down an inclined plane of height 7.0 m. What is the angular velocity of the sphere at the bottom of the inclined plane?

A 3.00-kg ball rests in a frictionless groove as shown in the figure. (a) What is the magnitude of the force that the left side of the groove exerts on the ball? (b) What is the magnitude of the force that the right side of the groove exerts on the ball?

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