Question 1

Equilibrium: In the figure, a 10.0-m long bar is attached by a frictionless hinge to a wall and held horizontal by a rope that makes an angle θ of 53° with the bar. The bar is uniform and weighs 39.9 N. How far from the hinge should a 10.0-kg mass be suspended for the tension T in the rope to be 125 N?

Accepted Answer

The answer of Equilibrium: In the figure, a 10.0-m long...

Question 2

Rotational dynamics about a fixed axis: In the figure, a very light rope is wrapped around a wheel of radius R = 2.0 meters and does not slip. The wheel is mounted with frictionless bearings on an axle through its center. A block of mass 14 kg is suspended from the end of the rope. When the system is released from rest it is observed that the block descends 10 meters in 2.0 seconds. What is the moment of inertia of the wheel?

Accepted Answer

The answer of Rotational dynamics about a fixed axis: In...

Question 3

Equilibrium: In the figure, a uniform rectangular crate 0.40 m wide and 1.0 m tall rests on a horizontal surface. The crate weighs 930 N, and its center of gravity is at its geometric center. A horizontal force F is applied at a distance h above the floor. If  what minimum value of F is required to make the crate start to tip over? Static friction is large enough that the crate does not start to slide.

Accepted Answer

The answer of Equilibrium: In the figure, a uniform rectangular...

Question 4

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

Question 5

Rolling: A tire is rolling along a road, without slipping, with a velocity v. A piece of tape is attached to the tire. When the tape is opposite the road (at the top of the tire), its velocity with respect to the road is

Accepted Answer

A)  2v. 
B)  v. 
C)  1.5v. 
D)  zero. 
E)  The velocity depends on the radius of the tire.

Question 6

Rotational dynamics about a moving axis: A uniform hollow spherical ball of mass 1.75 kg and radius 40.0 cm rolls without slipping up a ramp that rises at 30.0° above the horizontal. The speed of the ball at the base of the ramp is 2.63 m/s. While the ball is moving up the ramp, find
(a) the acceleration (magnitude and direction) of its center of mass and
(b) the friction force (magnitude and direction) acting on it due to the surface of the ramp.

Accepted Answer

The answer of Rotational dynamics about a moving axis: A...

Question 7

Rotational kinetic energy: While spinning down from 500.0 rpm to rest, a solid uniform flywheel does  of work. If the radius of the disk is  what is its mass?

Accepted Answer

A)  5.2 kg 
B)  4.4 kg 
C)  6.0 kg 
D)  6.8 kg

Question 8

Rolling: Consider a uniform solid sphere of radius R and mass M rolling without slipping. Which form of its kinetic energy is larger, translational or rotational?

Accepted Answer

A)  Its translational kinetic energy is larger than its rotational kinetic energy. 
B)  Its rotational kinetic energy is larger than its translational kinetic energy. 
C)  Both forms of energy are equal. 
D)  You need to know the speed of the sphere to tell.

Question 9

Rotational kinematics with constant angular acceleration: In the figure, point P is at rest when it is on the x-axis. The time t, when P returns to the original position on the x-axis, is closest to

Accepted Answer

A)  13 s. 
B)  18 s. 
C)  25 s. 
D)  35 s. 
E)  50 s.

Question 10

Rotational dynamics about a fixed axis: For the apparatus shown in the figure, there is no slipping between the cord and the surface of the pulley. The blocks have mass of 3.0 kg and 5.7 kg, and the pulley has a radius of 0.12 m and a mass of 10.3 kg. At the instant the 5.7 kg mass has fallen 1.5 m starting from rest, find the speed of each block. (Assume the pulley is in the shape of a uniform solid disk and has no friction in its axle.)

Accepted Answer

The answer of Rotational dynamics about a fixed axis: For...

Question 11

Equilibrium: 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. Under maximum load, find the magnitude of the x component of the force exerted on the beam by the pivot at P.

Accepted Answer

A)  13,800 N 
B)  12,800 N 
C)  11,200 N 
D)  14,400 N 
E)  16,000 N

Question 12

Rotational dynamics about a fixed axis: A string is wrapped around a pulley with a radius of 2.0 cm and no appreciable friction in its axle. The pulley is initially not turning. A constant force of 50 N is applied to the string, which does not slip, causing the pulley to rotate and the string to unwind. If the string unwinds 1.2 m in 4.9 s, what is the moment of inertia of the pulley?

Accepted Answer

A)  0.17 kg ∙ m2 
B)  17 kg ∙ m2 
C)  14 kg ∙ m2 
D)  0.20 kg ∙ m2 
E)  0.017 kg ∙ m2

Question 13

Conservation of angular momentum: A metal bar is hanging from a hook in the ceiling when it is suddenly struck by a ball that is moving horizontally (see figure). The ball is covered with glue, so it sticks to the bar. During this collision

Accepted Answer

A)  the angular momentum of the system (ball and bar) is conserved about the hook because only gravity is acting on the system. 
B)  the angular momentum of the system (ball and bar) is not conserved because the hook exerts a force on the bar. 
C)  the angular momentum of the system (ball and bar) is conserved about the hook because neither the hook nor gravity exerts any torque on this system about the hook. 
D)  both the angular momentum of the system (ball and bar) and its kinetic energy are conserved. 
E)  both the linear momentum and the angular momentum of the system (ball and bar) are conserved.

Question 14

Rotational dynamics about a fixed axis: 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)  2.00 kg ∙ m2 
D)  0.684 kg ∙ m2 
E)  2.74 kg ∙ m2

Question 15

Conservation of angular momentum: A figure skater rotating at 5.00 rad/s with arms extended has a moment of inertia of 2.25 kg ∙ m2. If the arms are pulled in so the moment of inertia decreases to 1.80 kg ∙ m2, what is the final angular speed?

Accepted Answer

A)  2.25 rad/s 
B)  4.60 rad/s 
C)  6.25 rad/s 
D)  1.76 rad/s 
E)  0.810 rad/s

Question 16

Equilibrium: 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.

Question 17

Rotational dynamics about a fixed axis: 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

Question 18

Rotational kinematics: The angular velocity of a 755-g wheel 15.0 cm in diameter is given by the equation ω(t) = (2.00 rad/s²)t + (1.00 rad/s⁴)t³. (a) Through how many radians does the wheel turn during the first 2.00 s of its motion? (b) What is the angular acceleration (in rad/s²) of the wheel at the end of the first 2.00 s of its motion?

Accepted Answer

The answer of Rotational kinematics: The angular velocity of a...

Question 19

Equilibrium: A uniform sign is supported against a wall at point P as shown in the figure. If the sign is a square  on a side and its mass is  what is the magnitude of the horizontal force that the wall at P experiences?

Accepted Answer

A)  20 N 
B)  0.00 N 
C)  7.8 N 
D)  98 N

Question 20

Equilibrium: In the figure, the horizontal lower arm has a mass of 2.8 kg and its center of gravity is 12 cm from the elbow joint pivot. How much force FM must the vertical extensor muscle in the upper arm exert on the lower arm to hold a 7.5 kg shot put?

Accepted Answer

A)  100 N 
B)  500 N 
C)  750 N 
D)  1000 N 
E)  1500 N

Exam 8: Momentum, Impulse, and Collisions

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

Rolling: A tire is rolling along a road, without slipping, with a velocity v. A piece of tape is attached to the tire. When the tape is opposite the road (at the top of the tire) , its velocity with respect to the road is

Rotational kinetic energy: While spinning down from 500.0 rpm to rest, a solid uniform flywheel does of work. If the radius of the disk is what is its mass?

Rolling: Consider a uniform solid sphere of radius R and mass M rolling without slipping. Which form of its kinetic energy is larger, translational or rotational?

Rotational kinematics with constant angular acceleration: In the figure, point P is at rest when it is on the x-axis. The time t, when P returns to the original position on the x-axis, is closest to

Conservation of angular momentum: A metal bar is hanging from a hook in the ceiling when it is suddenly struck by a ball that is moving horizontally (see figure) . The ball is covered with glue, so it sticks to the bar. During this collision

Conservation of angular momentum: A figure skater rotating at 5.00 rad/s with arms extended has a moment of inertia of 2.25 kg ∙ m². If the arms are pulled in so the moment of inertia decreases to 1.80 kg ∙ m², what is the final angular speed?

Equilibrium: A uniform sign is supported against a wall at point P as shown in the figure. If the sign is a square on a side and its mass is what is the magnitude of the horizontal force that the wall at P experiences?

Equilibrium: In the figure, the horizontal lower arm has a mass of 2.8 kg and its center of gravity is 12 cm from the elbow joint pivot. How much force F_M must the vertical extensor muscle in the upper arm exert on the lower arm to hold a 7.5 kg shot put?