Question 1

You throw a Frisbee of mass m and radius r so that it is spinning about a horizontal axis perpendicular to the plane of the Frisbee. Ignoring air resistance, the torque exerted about its center of mass by gravity is

Accepted Answer

A)  0. 
B)  mgr. 
C)  2mgr. 
D)  a function of the angular velocity. 
E)  small at first, then increasing as the Frisbee loses the torque given it by your hand.

Question 2

Identical particles are placed at the 50-cm and 80-cm marks on a meter stick of negligible mass. This rigid body is then mounted so as to rotate freely about a pivot at the 0-cm mark on the meter stick. If this body is released from rest in a horizontal position, what is the angular speed of the meter stick as it swings through its lowest position?

Accepted Answer

A)  4.2 rad/s 
B)  5.4 rad/s 
C)  4.6 rad/s 
D)  5.0 rad/s 
E)  1.7 rad/s

Question 3

The figure below shows a graph of angular velocity as a function of time for a car driving around a circular track. Through how many radians does the car travel in the first 10 minutes?

Accepted Answer

A)  30 
B)  50 
C)  70 
D)  90 
E)  100

Question 4

Exhibit 10-2
The figure below shows a graph of angular velocity versus time for a man bicycling around a circular track.  Use this exhibit to answer the following question(s).
-Refer to Exhibit 10-2. What is his average angular acceleration, in rad/s2, in the first 10 minutes?

Accepted Answer

A)  0 
B) 
 
C) 
 
D) 
 
E)

Question 5

A uniform solid sphere rolls without slipping along a horizontal surface. What fraction of its total kinetic energy is in the form of rotational kinetic energy about the CM?

Accepted Answer

The answer of A uniform solid sphere rolls without slipping...

Question 6

A rigid rod of length l rotates about an axis perpendicular to the rod, with one end of the rod fixed to the axis. Which of the following are equal at all points on the rod? 
I.The angular position
II.The angular velocity
III.The angular acceleration
IV.The centripetal acceleration
V.The tangential acceleration

Accepted Answer

A)  I and II 
B)  I, II, and III 
C)  I, II, III and IV 
D)  I, II, III, IV and V 
E)  I, II and IV.

Question 7

A small sphere attached to a light rigid rod rotates about an axis perpendicular to and fixed to the other end of the rod. Relative to the positive direction of the axis of rotation, the angular positions of the sphere are negative, its angular velocity is negative, and its angular acceleration is positive. The sphere is

Accepted Answer

A)  rotating clockwise and slowing down. 
B)  rotating counterclockwise and slowing down. 
C)  rotating clockwise and speeding up. 
D)  rotating counterclockwise and speeding up. 
E)  first rotating counterclockwise and then clockwise.

Question 8

A wheel starts from rest and rotates with a constant angular acceleration about a fixed axis. It completes the first revolution 6.0 s after it started. How long after it started will the wheel complete the second revolution?

Accepted Answer

A)  9.9 s 
B)  7.8 s 
C)  8.5 s 
D)  9.2 s 
E)  6.4 s

Question 9

When a wheel is rolling without slipping, the magnitude of its velocity relative to the ground is greatest at

Accepted Answer

A)  the point in contact with the ground. 
B)  the point at the center of the wheel. 
C)  the point at the top of the wheel opposite to the point in contact with the ground. 
D)  the point farthest forward from the center of mass of the wheel. 
E)  the point farthest behind the center of mass of the wheel.

Question 10

A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s2 starts from rest at t = 0. The wheel has a diameter of 20 cm. What is the magnitude of the total linear acceleration of a point on the outer edge of the wheel at t = 0.60 s?

Accepted Answer

A)  0.25 m/s2 
B)  0.50 m/s2 
C)  0.14 m/s2 
D)  0.34 m/s2 
E)  0.20 m/s2

Question 11

A uniform rod is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at the horizontal position. What is the angular acceleration of the rod at the instant the rod makes an angle of 70° with the horizontal?

Accepted Answer

A)  3.7 rad/s2 
B)  1.3 rad/s2 
C)  2.5 rad/s2 
D)  4.9 rad/s2 
E)  1.9 rad/s2

Question 12

The rigid body shown rotates about an axis through its center of mass and perpendicular to the paper. If M = 2.0 kg and L = 80 cm, what is the kinetic energy of this object when its angular speed about this axis is equal to 5.0 rad/s? Neglect the mass of the connecting rod and treat the masses as particles.

Accepted Answer

A)  18 J 
B)  15 J 
C)  12 J 
D)  23 J 
E)  26 J

Question 13

The angular speed of the hour hand of a clock, in rad/s, is

Accepted Answer

A) 
 . 
B) 
 . 
C) 
 . 
D)  1 800π. 
E)  7 200π.

Question 14

A uniform rod (length = 2.0 m) is mounted to rotate freely about a horizontal axis that is perpendicular to the rod and that passes through the rod at a point 0.50 m from one end of the rod. If the rod is released from rest in a horizontal position, what is the angular speed of the rod as it rotates through its lowest position?

Accepted Answer

A)  3.5 rad/s 
B)  3.8 rad/s 
C)  4.1 rad/s 
D)  2.0 rad/s 
E)  5.6 rad/s

Question 15

Particles (mass of each = 0.40 kg) are placed at the 60-cm and 100-cm marks of a meter stick of negligible mass. This rigid body is free to rotate about a frictionless pivot at the 0-cm end. The body is released from rest in the horizontal position. What is the magnitude of the initial linear acceleration of the end of the body opposite the pivot?

Accepted Answer

A)  15 m/s2 
B)  9.8 m/s2 
C)  5.8 m/s2 
D)  12 m/s2 
E)  4.7 m/s2

Question 16

Exhibit 10-3
The graph below shows a plot of angular velocity in rad/s versus time in s from t = 0 s to t = 7 s.  Use this exhibit to answer the following question(s).
-Refer to Exhibit 10-3. The change in angular position, Δθ, during the 7-second period is

Accepted Answer

A)  21 rad, CW. 
B)  21 rad, CCW. 
C)  30 rad, CW. 
D)  30 rad, CCW. 
E)  39 rad, CCW.

Question 17

Exhibit 10-3
The graph below shows a plot of angular velocity in rad/s versus time in s from t = 0 s to t = 7 s.  Use this exhibit to answer the following question(s).
-Refer to Exhibit 10-3. The angular position, θ, at t = 0 s is 3.0 rad, clockwise. The angular position, θ, at t = 7 s is

Accepted Answer

A)  27 rad, CW. 
B)  27 rad, CCW. 
C)  33 rad, CW. 
D)  33 rad, CCW. 
E)  36 rad, CCW.

Question 18

The graphs below show angular velocity as a function of time. In which one is the magnitude of the angular acceleration constantly decreasing?

Accepted Answer

A) 
 
B) 
 
C) 
 
D) 
 
E)

Question 19

A uniform meter stick is pivoted to rotate about a horizontal axis through the 25-cm mark on the stick. The stick is released from rest in a horizontal position. The moment of inertia of a uniform rod about an axis perpendicular to the rod and through the center of mass of the rod is given by (1/12)ML2. Determine the magnitude of the initial angular acceleration of the stick.

Accepted Answer

A)  17 rad/s2 
B)  13 rad/s2 
C)  15 rad/s2 
D)  19 rad/s2 
E)  23 rad/s2

Question 20

A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s. During a 5.0-s interval the angular velocity decreases to 10 rad/s. Assume that the angular acceleration is constant during the 5.0-s interval. How many radians does the wheel turn through during the 5.0-s interval?

Accepted Answer

A)  95 rad 
B)  85 rad 
C)  65 rad 
D)  75 rad 
E)  125 rad

Exam 10: Rotation of a Rigid Object About a Fixed Axis

You throw a Frisbee of mass m and radius r so that it is spinning about a horizontal axis perpendicular to the plane of the Frisbee. Ignoring air resistance, the torque exerted about its center of mass by gravity is

The figure below shows a graph of angular velocity as a function of time for a car driving around a circular track. Through how many radians does the car travel in the first 10 minutes?

Exhibit 10-2 The figure below shows a graph of angular velocity versus time for a man bicycling around a circular track. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-2. What is his average angular acceleration, in rad/s², in the first 10 minutes?

A uniform solid sphere rolls without slipping along a horizontal surface. What fraction of its total kinetic energy is in the form of rotational kinetic energy about the CM?

A wheel starts from rest and rotates with a constant angular acceleration about a fixed axis. It completes the first revolution 6.0 s after it started. How long after it started will the wheel complete the second revolution?

When a wheel is rolling without slipping, the magnitude of its velocity relative to the ground is greatest at

A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s² starts from rest at t = 0. The wheel has a diameter of 20 cm. What is the magnitude of the total linear acceleration of a point on the outer edge of the wheel at t = 0.60 s?

A uniform rod is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at the horizontal position. What is the angular acceleration of the rod at the instant the rod makes an angle of 70° with the horizontal?

The angular speed of the hour hand of a clock, in rad/s, is

Exhibit 10-3 The graph below shows a plot of angular velocity in rad/s versus time in s from t = 0 s to t = 7 s. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-3. The change in angular position, Δθ, during the 7-second period is

Exhibit 10-3 The graph below shows a plot of angular velocity in rad/s versus time in s from t = 0 s to t = 7 s. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-3. The angular position, θ, at t = 0 s is 3.0 rad, clockwise. The angular position, θ, at t = 7 s is

The graphs below show angular velocity as a function of time. In which one is the magnitude of the angular acceleration constantly decreasing?

A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s. During a 5.0-s interval the angular velocity decreases to 10 rad/s. Assume that the angular acceleration is constant during the 5.0-s interval. How many radians does the wheel turn through during the 5.0-s interval?

Exam 10: Rotation of a Rigid Object About a Fixed Axis

You throw a Frisbee of mass m and radius r so that it is spinning about a horizontal axis perpendicular to the plane of the Frisbee. Ignoring air resistance, the torque exerted about its center of mass by gravity is

The figure below shows a graph of angular velocity as a function of time for a car driving around a circular track. Through how many radians does the car travel in the first 10 minutes?

Exhibit 10-2 The figure below shows a graph of angular velocity versus time for a man bicycling around a circular track. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-2. What is his average angular acceleration, in rad/s2, in the first 10 minutes?

A uniform solid sphere rolls without slipping along a horizontal surface. What fraction of its total kinetic energy is in the form of rotational kinetic energy about the CM?

A wheel starts from rest and rotates with a constant angular acceleration about a fixed axis. It completes the first revolution 6.0 s after it started. How long after it started will the wheel complete the second revolution?

When a wheel is rolling without slipping, the magnitude of its velocity relative to the ground is greatest at

A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s2 starts from rest at t = 0. The wheel has a diameter of 20 cm. What is the magnitude of the total linear acceleration of a point on the outer edge of the wheel at t = 0.60 s?

A uniform rod is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at the horizontal position. What is the angular acceleration of the rod at the instant the rod makes an angle of 70° with the horizontal?

The angular speed of the hour hand of a clock, in rad/s, is

Exhibit 10-3 The graph below shows a plot of angular velocity in rad/s versus time in s from t = 0 s to t = 7 s. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-3. The change in angular position, Δθ, during the 7-second period is

Exhibit 10-3 The graph below shows a plot of angular velocity in rad/s versus time in s from t = 0 s to t = 7 s. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-3. The angular position, θ, at t = 0 s is 3.0 rad, clockwise. The angular position, θ, at t = 7 s is

The graphs below show angular velocity as a function of time. In which one is the magnitude of the angular acceleration constantly decreasing?

A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s. During a 5.0-s interval the angular velocity decreases to 10 rad/s. Assume that the angular acceleration is constant during the 5.0-s interval. How many radians does the wheel turn through during the 5.0-s interval?

Exhibit 10-2 The figure below shows a graph of angular velocity versus time for a man bicycling around a circular track. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-2. What is his average angular acceleration, in rad/s², in the first 10 minutes?

A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s² starts from rest at t = 0. The wheel has a diameter of 20 cm. What is the magnitude of the total linear acceleration of a point on the outer edge of the wheel at t = 0.60 s?