Question 1

The average distance between the Earth and the Sun is 1.5 $\times$ 1011 m. The tangential speed of the Earth in its orbit about the Sun is

Accepted Answer

A)  45 km/s. 
B)  60 km/s. 
C)  15 km/s. 
D)  30 km/s. 
A)  45 km/s. 
B)  60 km/s. 
C)  15 km/s. 
D)  30 km/s.

Question 2

A uniform solid sphere with a mass of 0.15 kg rolls without slipping with a tangential velocity of 1.0 m/s. The kinetic energy of rotation of the sphere is

Accepted Answer

A)  30 mJ. 
B)  15 mJ. 
C)  60 mJ. 
D)  45 mJ. 
A)  30 mJ. 
B)  15 mJ. 
C)  60 mJ. 
D)  45 mJ.

Question 3

A particle moves with constant velocity. At instant t = 0, the particle is at the position of minimum separation from fixed point P. Its angular momentum about P is L ( $\not \neq$ 0). Subsequently its angular momentum about point P

Accepted Answer

A)  increases with time. 
B)  decreases with time. 
C)  does not change with time. 
D)  Hold it! A particle moving with constant velocity has no angular momentum. 
A)  increases with time. 
B)  decreases with time. 
C)  does not change with time. 
D)  Hold it! A particle moving with constant velocity has no angular momentum.

Question 4

An object is rotating with an angular acceleration given by $\alpha = c + d t ^ { 2 }$ , where $\surd$ is in radians/s2, t is in seconds, c = -3.0 rad/s2, and d = 0.40 rad/s4. At t = 2.0 s the angular acceleration of the object is

Accepted Answer

A)  -2.2 rad/s2. 
B)  -1.4 rad/s2. 
C)  3.8 rad/s2. 
D)  4.6 rad/s2. 
A)  -2.2 rad/s2. 
B)  -1.4 rad/s2. 
C)  3.8 rad/s2. 
D)  4.6 rad/s2.

Question 5

A car's engine redlines (reaches its maximum rotational frequency) at 8000 rpm. The time taken for one revolution is

Accepted Answer

A)  2.5 ms. 
B)  5.0 ms. 
C)  7.5 ms. 
D)  10. ms. 
A)  2.5 ms. 
B)  5.0 ms. 
C)  7.5 ms. 
D)  10. ms.

Question 6

Two point masses of 5.0 kg and 15.0 kg, separated by 2.0 m, are spinning about their center of mass. The moment of inertia of the system is

Accepted Answer

A)  5.0 kg.m2. 
B)  10 kg.m2. 
C)  16 kg.m2. 
D)  20 kg.m2. 
A)  5.0 kg.m2. 
B)  10 kg.m2. 
C)  16 kg.m2. 
D)  20 kg.m2.

Question 7

The dimensions of the moment of inertia, I, are the same as those of

Accepted Answer

A)  [mass]. 
B)  [mass]·[distance]. 
C)  [mass]·[distance]2. 
D)  [mass]/[distance]2. 
A)  [mass]. 
B)  [mass]·[distance]. 
C)  [mass]·[distance]2. 
D)  [mass]/[distance]2.

Question 8

An object rotates with a constant angular acceleration of 5.0 rad/s2, an initial angular speed of -10 rad/s, and a total time of rotation of 4.0 seconds. The average angular velocity has a magnitude of

Accepted Answer

A)  +10 rad/s. 
B)  +20 rad/s. 
C)  -10 rad/s. 
D)  zero. 
A)  +10 rad/s. 
B)  +20 rad/s. 
C)  -10 rad/s. 
D)  zero.

Question 9

A billiard ball of mass 0.16 kg, radius 2.86 cm, and moment of inertia about its diameter of 5.23 $\times$ 10-5 kg·m2 moves on a table at 1.5 m/s. The total kinetic energy of the ball is

Accepted Answer

A)  0.072 J. 
B)  0.14 J. 
C)  0.25 J. 
D)  0.32 J. 
A)  0.072 J. 
B)  0.14 J. 
C)  0.25 J. 
D)  0.32 J.

Question 10

A point on a rotating object at a distance $R$ from the axis of rotation has associated with it several angular kinematic variables: namely $\theta , \omega$, and $\alpha$. To obtain the corresponding linear variables, one can multiply the respective angular variable by the factor

Accepted Answer

A)  1/R2. 
B)  1/R. 
C)  R. 
D)  R2. 
A)  1/R2. 
B)  1/R. 
C)  R. 
D)  R2.

Question 11

An object, starting from rest at the origin, rotates with an angular acceleration given by $\alpha = c + d t ^ { 2 }$ , where $\surd$is in radians/s2, t is in seconds, c = -3.0 rad/s2, and d = 0.40 rad/s4. At time t = 2.0 s, the rotation (in radians) the object has made is

Accepted Answer

A)  -1.1 rad. 
B)  1.1 rad. 
C)  -4.9 rad. 
D)  -5.5 rad. 
A)  -1.1 rad. 
B)  1.1 rad. 
C)  -4.9 rad. 
D)  -5.5 rad.

Question 12

A uniform, flat, square plate has a mass of 3.0 kg and a side 2.0 m in length. The moment of inertia about an axis that passes through its center and is parallel to one edge is 1.0 kg·m2. The moment of inertia of the plate about an axis perpendicular to the plane through its center is

Accepted Answer

A)  2.0 kg·m2. 
B)  4.0 kg·m2. 
C)  12 kg·m2. 
D)  13 kg·m2. 
A)  2.0 kg·m2. 
B)  4.0 kg·m2. 
C)  12 kg·m2. 
D)  13 kg·m2.

Question 13

The average Earth-Sun distance is approximately 1.5 x 1011 m, and the Sun's radius is approximately 7.0 x 108 m. The approximate angle (in degrees) that the Sun subtends when viewed from Earth is

Accepted Answer

A)  1/4°. 
B)  1/2°. 
C)  1°. 
D)  2°. 
A)  1/4°. 
B)  1/2°. 
C)  1°. 
D)  2°.

Question 14

A uniform, flat, square plate has a mass of 3.0 kg and a side 2.0 m in length. The moment of inertia about an axis that passes through its center and is parallel to one edge is 1.0 kg·m2. The moment of inertia of the plate about one edge is

Accepted Answer

A)  2.0 kg·m2. 
B)  4.0 kg·m2. 
C)  12 kg·m2. 
D)  13 kg·m2. 
A)  2.0 kg·m2. 
B)  4.0 kg·m2. 
C)  12 kg·m2. 
D)  13 kg·m2.

Question 15

A wheel undergoes rotational motion according to the equation $\phi ( \mathrm { rad } ) = c t + d t ^ { 3 }$ , where $\surd$is in radians, c = 1.0 rad/s, and d = -0.50 rad/s3. At t = 2.0 s the magnitude of the tangential acceleration of an object placed 10.0 cm from the center of the wheel is

Accepted Answer

A)  -0.60 m/s2. 
B)  -0.30 m/s2. 
C)  0 m/s2. 
D)  0.30 m/s2. 
A)  -0.60 m/s2. 
B)  -0.30 m/s2. 
C)  0 m/s2. 
D)  0.30 m/s2.

Question 16

A billiard ball of mass 0.16 kg, radius 2.86 cm, and moment of inertia about its diameter of 5.23 $\times$ 10-5 kg·m2 moves on a table at 1.5 m/s. The rotational kinetic energy of the ball is

Accepted Answer

A)  0 J. 
B)  0.072 J. 
C)  0.14 J. 
D)  0.25 J. 
A)  0 J. 
B)  0.072 J. 
C)  0.14 J. 
D)  0.25 J.

Question 17

An object rotates with a constant angular acceleration of 5.0 rad/s2, an initial angular speed of -10. rad/s, and a total time of rotation of 4.0 s. The instant at which the object has a zero instantaneous angular speed is

Accepted Answer

A)  1.0 s. 
B)  2.0 s. 
C)  3.0 s. 
D)  4.0 s. 
A)  1.0 s. 
B)  2.0 s. 
C)  3.0 s. 
D)  4.0 s.

Question 18

A wheel undergoes rotational motion according to the equation $\phi ( \mathrm { rad } ) = c t + d t ^ { 3 }$ , where $\surd$ is in radians, c = 1.0 rad/s, and d = -0.50 rad/s3. At t = 2.0 s the magnitude of the tangential speed of an object placed 10.0 cm from the center of the wheel is

Accepted Answer

A)  1.0 m/s. 
B)  0.50 m/s. 
C)  0.0 m/s. 
D)  1.5 m/s. 
E)  2.0 m/s. 
A)  1.0 m/s. 
B)  0.50 m/s. 
C)  0.0 m/s. 
D)  1.5 m/s. 
E)  2.0 m/s.

Question 19

Two masses, MA = 1.0 kg and MB = 2.5 kg, are attached at the opposite ends of a rod 1.0 m in length. The mass of the rod is 1.5 kg. The moment of inertia of the system about an axis perpendicular to the rod passing through its center is

Accepted Answer

A)  1.0 kg.m2. 
B)  1.5 kg.m2. 
C)  2.0 kg.m2. 
D)  2.5 kg.m2. 
A)  1.0 kg.m2. 
B)  1.5 kg.m2. 
C)  2.0 kg.m2. 
D)  2.5 kg.m2.

Question 20

Two uniform solid spheres have masses M0 and (1/2)M0 and radii R0 and (1/2)R0 respectively. The ratio of their moments of inertia about their own diameters is

Accepted Answer

A)  8:1. 
B)  4:1. 
C)  2:1. 
D)  1:1. 
A)  8:1. 
B)  4:1. 
C)  2:1. 
D)  1:1.

Exam 12: Rotation of a Rigid Body

The average distance between the Earth and the Sun is 1.5 ×\times× 1011 m. The tangential speed of the Earth in its orbit about the Sun is

A uniform solid sphere with a mass of 0.15 kg rolls without slipping with a tangential velocity of 1.0 m/s. The kinetic energy of rotation of the sphere is

A particle moves with constant velocity. At instant t = 0, the particle is at the position of minimum separation from fixed point P. Its angular momentum about P is L ( ≠̸\not \neq= 0). Subsequently its angular momentum about point P

An object is rotating with an angular acceleration given by α=c+dt2\alpha = c + d t ^ { 2 }α=c+dt2 , where √\surd√ is in radians/s2, t is in seconds, c = -3.0 rad/s2, and d = 0.40 rad/s4. At t = 2.0 s the angular acceleration of the object is

A car's engine redlines (reaches its maximum rotational frequency) at 8000 rpm. The time taken for one revolution is

Two point masses of 5.0 kg and 15.0 kg, separated by 2.0 m, are spinning about their center of mass. The moment of inertia of the system is

The dimensions of the moment of inertia, I, are the same as those of

An object rotates with a constant angular acceleration of 5.0 rad/s2, an initial angular speed of -10 rad/s, and a total time of rotation of 4.0 seconds. The average angular velocity has a magnitude of

A billiard ball of mass 0.16 kg, radius 2.86 cm, and moment of inertia about its diameter of 5.23 ×\times× 10-5 kg·m2 moves on a table at 1.5 m/s. The total kinetic energy of the ball is

A point on a rotating object at a distance RRR from the axis of rotation has associated with it several angular kinematic variables: namely θ,ω\theta , \omegaθ,ω , and α\alphaα . To obtain the corresponding linear variables, one can multiply the respective angular variable by the factor

An object, starting from rest at the origin, rotates with an angular acceleration given by α=c+dt2\alpha = c + d t ^ { 2 }α=c+dt2 , where √\surd√ is in radians/s2, t is in seconds, c = -3.0 rad/s2, and d = 0.40 rad/s4. At time t = 2.0 s, the rotation (in radians) the object has made is

A uniform, flat, square plate has a mass of 3.0 kg and a side 2.0 m in length. The moment of inertia about an axis that passes through its center and is parallel to one edge is 1.0 kg·m2. The moment of inertia of the plate about an axis perpendicular to the plane through its center is

The average Earth-Sun distance is approximately 1.5 x 1011 m, and the Sun's radius is approximately 7.0 x 108 m. The approximate angle (in degrees) that the Sun subtends when viewed from Earth is

A uniform, flat, square plate has a mass of 3.0 kg and a side 2.0 m in length. The moment of inertia about an axis that passes through its center and is parallel to one edge is 1.0 kg·m2. The moment of inertia of the plate about one edge is

A billiard ball of mass 0.16 kg, radius 2.86 cm, and moment of inertia about its diameter of 5.23 ×\times× 10-5 kg·m2 moves on a table at 1.5 m/s. The rotational kinetic energy of the ball is

An object rotates with a constant angular acceleration of 5.0 rad/s2, an initial angular speed of -10. rad/s, and a total time of rotation of 4.0 s. The instant at which the object has a zero instantaneous angular speed is

Two masses, MA = 1.0 kg and MB = 2.5 kg, are attached at the opposite ends of a rod 1.0 m in length. The mass of the rod is 1.5 kg. The moment of inertia of the system about an axis perpendicular to the rod passing through its center is

Two uniform solid spheres have masses M0 and (1/2)M0 and radii R0 and (1/2)R0 respectively. The ratio of their moments of inertia about their own diameters is

Space, Time, and Mass

Motion Along a Straight Line

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Newtons Laws of Motion

Further Applications of Newtons Laws

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Filters

The average distance between the Earth and the Sun is 1.5 $\times$ 10¹¹ m. The tangential speed of the Earth in its orbit about the Sun is

A particle moves with constant velocity. At instant t = 0, the particle is at the position of minimum separation from fixed point P. Its angular momentum about P is L ( $\not \neq$ 0). Subsequently its angular momentum about point P

An object is rotating with an angular acceleration given by $\alpha = c + d t ^ { 2 }$ , where $\surd$ is in radians/s², t is in seconds, c = -3.0 rad/s², and d = 0.40 rad/s⁴. At t = 2.0 s the angular acceleration of the object is

An object rotates with a constant angular acceleration of 5.0 rad/s², an initial angular speed of -10 rad/s, and a total time of rotation of 4.0 seconds. The average angular velocity has a magnitude of

A billiard ball of mass 0.16 kg, radius 2.86 cm, and moment of inertia about its diameter of 5.23 $\times$ 10^-5 kg·m² moves on a table at 1.5 m/s. The total kinetic energy of the ball is

A point on a rotating object at a distance $R$ from the axis of rotation has associated with it several angular kinematic variables: namely $\theta , \omega$ , and $\alpha$ . To obtain the corresponding linear variables, one can multiply the respective angular variable by the factor

An object, starting from rest at the origin, rotates with an angular acceleration given by $\alpha = c + d t ^ { 2 }$ , where $\surd$ is in radians/s², t is in seconds, c = -3.0 rad/s², and d = 0.40 rad/s⁴. At time t = 2.0 s, the rotation (in radians) the object has made is

A uniform, flat, square plate has a mass of 3.0 kg and a side 2.0 m in length. The moment of inertia about an axis that passes through its center and is parallel to one edge is 1.0 kg·m². The moment of inertia of the plate about an axis perpendicular to the plane through its center is

The average Earth-Sun distance is approximately 1.5 x 10¹¹ m, and the Sun's radius is approximately 7.0 x 10⁸ m. The approximate angle (in degrees) that the Sun subtends when viewed from Earth is

A uniform, flat, square plate has a mass of 3.0 kg and a side 2.0 m in length. The moment of inertia about an axis that passes through its center and is parallel to one edge is 1.0 kg·m². The moment of inertia of the plate about one edge is

A billiard ball of mass 0.16 kg, radius 2.86 cm, and moment of inertia about its diameter of 5.23 $\times$ 10^-5 kg·m² moves on a table at 1.5 m/s. The rotational kinetic energy of the ball is

An object rotates with a constant angular acceleration of 5.0 rad/s², an initial angular speed of -10. rad/s, and a total time of rotation of 4.0 s. The instant at which the object has a zero instantaneous angular speed is

Two masses, M_A = 1.0 kg and M_B = 2.5 kg, are attached at the opposite ends of a rod 1.0 m in length. The mass of the rod is 1.5 kg. The moment of inertia of the system about an axis perpendicular to the rod passing through its center is

Two uniform solid spheres have masses M₀ and (1/2)M₀ and radii R₀ and (1/2)R₀ respectively. The ratio of their moments of inertia about their own diameters is