Question 1

A wheel starts from rest and has an angular acceleration of 4.0 rad/s2. The time it takes to make 10 revolutions is:

Accepted Answer

A)  0.50 s 
B)  0.71 s 
C)  2.2 s 
D)  2.8 s 
E)  5.6 s 
A)  0.50 s 
B)  0.71 s 
C)  2.2 s 
D)  2.8 s 
E)  5.6 s

Question 2

The rotational inertia of a wheel about its axle does not depend upon its:

Accepted Answer

A)  diameter 
B)  mass 
C)  distribution of mass 
D)  speed of rotation 
E)  material composition 
A)  diameter 
B)  mass 
C)  distribution of mass 
D)  speed of rotation 
E)  material composition

Question 3

A phonograph turntable, initially rotating at 0.75 rev/s, slows down and stops in 30 s. The magnitude of its average angular acceleration in rad/s2 for this process is:

Accepted Answer

A)  1.5 
B)  1.5 $\pi$ 
C)    $\pi$ /40 
D)   $\pi$ /20 
E)  0.75 
A)  1.5 
B)  1.5 $\pi$ 
C)    $\pi$ /40 
D)   $\pi$ /20 
E)  0.75

Question 4

A particle moves in a circular path of radius 0.10 m with a constant angular speed of 5 rev/s. The acceleration of the particle is:

Accepted Answer

A)  0.10  $\pi$  m/s2 
B)  0.50 m/s2 
C)  500  $\pi$  m/s2 
D)  1000  $\pi$ 2 m/s2 
E)  10 $\pi$ 2 m/s2 
A)  0.10  $\pi$  m/s2 
B)  0.50 m/s2 
C)  500  $\pi$  m/s2 
D)  1000  $\pi$ 2 m/s2 
E)  10 $\pi$ 2 m/s2

Question 5

A flywheel of diameter 1.2 m has a constant angular acceleration of 5.0 rad/s2. The tangential acceleration of a point on its rim is:

Accepted Answer

A)  5.0 rad/s2 
B)  3.0 m/s2 
C)  5.0 m/s2 
D)  6.0 m/s2 
E)  12 m/s2 
A)  5.0 rad/s2 
B)  3.0 m/s2 
C)  5.0 m/s2 
D)  6.0 m/s2 
E)  12 m/s2

Question 6

A force with a given magnitude is to be applied to a wheel. The torque can be maximized by:

Accepted Answer

A)  applying the force near the axle, radially outward from the axle 
B)  applying the force near the rim, radially outward from the axle 
C)  applying the force near the axle, parallel to a tangent to the wheel 
D)  applying the force at the rim, tangent to the rim 
E)  applying the force at the rim, at 45 $\degree$ to the tangent 
A)  applying the force near the axle, radially outward from the axle 
B)  applying the force near the rim, radially outward from the axle 
C)  applying the force near the axle, parallel to a tangent to the wheel 
D)  applying the force at the rim, tangent to the rim 
E)  applying the force at the rim, at 45 $\degree$ to the tangent

Question 7

String is wrapped around the periphery of a 5.0-cm radius cylinder, free to rotate on its axis. The string is pulled straight out at a constant rate of 10 cm/s and does not slip on the cylinder. As each small segment of string leaves the cylinder, its acceleration changes by:

Accepted Answer

A)  0 
B)  0.010 m/s2 
C)  0.020 m/s2 
D)  0.10 m/s2 
E)  0.20 m/s2 
A)  0 
B)  0.010 m/s2 
C)  0.020 m/s2 
D)  0.10 m/s2 
E)  0.20 m/s2

Question 8

A solid uniform sphere of radius R and mass M has a rotational inertia about a diameter that is given by (2/5)MR2. A light string of length 3R is attached to the surface and used to suspend the sphere from the ceiling. Its rotational inertia about the point of attachment at the ceiling is:

Accepted Answer

A)  (2/5)MR2 
B)  9MR2 
C)  16MR2 
D)  47/5MR2 
E)  (82/5)MR2 
A)  (2/5)MR2 
B)  9MR2 
C)  16MR2 
D)  47/5MR2 
E)  (82/5)MR2

Question 9

A flywheel is initially roatating at 20 rad/s and has a constant angular acceleration. After 9.0 s it has rotated through 450 rad. Its angular acceleration is:

Accepted Answer

A)  3.3 rad/s 
B)  4.4 rad/s 
C)  5.6 rad/s 
D)  6.7 rad/s 
E)  11 rad/s 
A)  3.3 rad/s 
B)  4.4 rad/s 
C)  5.6 rad/s 
D)  6.7 rad/s 
E)  11 rad/s

Question 10

A wheel is spinning at 27 rad/s but is slowing with an angular acceleration that has a magnitude given by (3.0 rad/s4)t2. It stops in a time of:

Accepted Answer

A)  1.7 s 
B)  2.6 s 
C)  3.0 s 
D)  4.4 s 
E)  7.3 s 
A)  1.7 s 
B)  2.6 s 
C)  3.0 s 
D)  4.4 s 
E)  7.3 s

Question 11

The magnitude of the acceleration of a point on a spinning wheel is increased by a factor of 4 if:

Accepted Answer

A)  the magnitues of the angular velocity and the angular acceleration are each multiplied by a factor of 4 
B)  the magnitues of the angular velocity is multuplied by a factor of 4 and the angular acceleration is not changed 
C)  the magnitues of the angular velocity and the angular acceleration are each multiplied by a factor of 2 
D)  the magnitues of the angular velocity is multiplied by a factor of 2 and the angular acceleration is not changed 
E)  the magnitues of the angular velocity is multiplied by a factor of 2 and the magnitudeof the angular acceleration is multiplied by a factor of 4 
A)  the magnitues of the angular velocity and the angular acceleration are each multiplied by a factor of 4 
B)  the magnitues of the angular velocity is multuplied by a factor of 4 and the angular acceleration is not changed 
C)  the magnitues of the angular velocity and the angular acceleration are each multiplied by a factor of 2 
D)  the magnitues of the angular velocity is multiplied by a factor of 2 and the angular acceleration is not changed 
E)  the magnitues of the angular velocity is multiplied by a factor of 2 and the magnitudeof the angular acceleration is multiplied by a factor of 4

Question 12

A block is attached to each end of a rope that passes over a pulley suspended from the ceiling. The blocks do not have the same mass. If the rope does not slip on the pulley, then at any instant after the blocks start moving, the rope:

Accepted Answer

A)  pulls on both blocks, but exerts a greater force on the heavier block 
B)  pulls on both blocks, but exerts a greater force on the lighter block 
C)  pulls on both blocks and exerts the same magnitude force on both blocks 
D)  does not pull on either block 
E)  pulls only on the lighter block 
A)  pulls on both blocks, but exerts a greater force on the heavier block 
B)  pulls on both blocks, but exerts a greater force on the lighter block 
C)  pulls on both blocks and exerts the same magnitude force on both blocks 
D)  does not pull on either block 
E)  pulls only on the lighter block

Question 13

A uniform solid cylinder made of lead has the same mass and the same length as a uniform solid cylinder made of wood. The rotational inertia of the lead cylinder compared to the wooden one is:

Accepted Answer

A)  greater 
B)  less 
C)  same 
D)  unknown unless the radii are given 
E)  unknown unless both the masses and the radii are given 
A)  greater 
B)  less 
C)  same 
D)  unknown unless the radii are given 
E)  unknown unless both the masses and the radii are given

Question 14

One revolution per minute is about:

Accepted Answer

A)  0.0524 rad/s 
B)  0.105 rad/s 
C)  0.95 rad/s 
D)  1.57 rad/s 
E)  6.28 rad/s 
A)  0.0524 rad/s 
B)  0.105 rad/s 
C)  0.95 rad/s 
D)  1.57 rad/s 
E)  6.28 rad/s

Question 15

Three identical balls, with masses of M, 2M, and 3M are fastened to a massless rod of length L as shown. The rotational inertia about the left end of the rod is:

Accepted Answer

A)  ML2/2 
B)  ML2 
C)  3ML2/2 
D)  6ML2 
E)  3ML2/4 
A)  ML2/2 
B)  ML2 
C)  3ML2/2 
D)  6ML2 
E)  3ML2/4

Question 16

A meter stick on a horizontal frictionless table top is pivoted at the 80-cm mark. A horizontal force   is applied perpendicularly to the end of the stick at 0 cm, as shown. A second horizontal force   (not shown) is applied at the 100-cm end of the stick. If the stick does not rotate:

Accepted Answer

A)    for all orientations of   
B)    for all orientations of   
C)    for all orientations of   
D)    for some orientations of   for others 
E)    for some orientations of   for others 
A)    for all orientations of   
B)    for all orientations of   
C)    for all orientations of   
D)    for some orientations of   for others 
E)    for some orientations of   for others

Question 17

The angular velocity vector of a spinning body points out of the page. If the angular acceleration vector points into the page then:

Accepted Answer

A)  the body is slowing down 
B)  the body is speeding up 
C)  the body is starting to turn in the opposite direction 
D)  the axis of rotation is changing orientation 
E)  none of the above 
A)  the body is slowing down 
B)  the body is speeding up 
C)  the body is starting to turn in the opposite direction 
D)  the axis of rotation is changing orientation 
E)  none of the above

Question 18

A radian is about:

Accepted Answer

A)  25 ° 
B)  37 ° 
C)  45 ° 
D)  57 ° 
E)  90 ° 
A)  25 ° 
B)  37 ° 
C)  45 ° 
D)  57 ° 
E)  90 °

Question 19

A pulley with a radius of 3.0 cm and a rotational inertia of 4.5 * 10-3 kg . m2 is suspended from the ceiling. A rope passes over it with a 2.0-kg block attached to one end and a 4.0-kg block attached to the other. The rope does not slip on the pulley. At any instant after the blocks start moving the object with the greatest kinetic energy is:

Accepted Answer

A)  the heavier block 
B)  the lighter block 
C)  the pulley 
D)  either block (the two blocks have the same kinetic energy) 
E)  none (all three objects have the same kinetic energy) 
A)  the heavier block 
B)  the lighter block 
C)  the pulley 
D)  either block (the two blocks have the same kinetic energy) 
E)  none (all three objects have the same kinetic energy)

Question 20

The angular velocity of a rotating wheel increases 2 rev/s every minute. The angular acceleration, in rad/s2 of this wheel is:

Accepted Answer

A)  4  $\pi$ 2 
B)  2  $\pi$ 
C)  1/30 
D)  2  $\pi$ /30 
E)  4 $\pi$ 
A)  4  $\pi$ 2 
B)  2  $\pi$ 
C)  1/30 
D)  2  $\pi$ /30 
E)  4 $\pi$

Exam 10: Rotation

A wheel starts from rest and has an angular acceleration of 4.0 rad/s2. The time it takes to make 10 revolutions is:

The rotational inertia of a wheel about its axle does not depend upon its:

A phonograph turntable, initially rotating at 0.75 rev/s, slows down and stops in 30 s. The magnitude of its average angular acceleration in rad/s2 for this process is:

A particle moves in a circular path of radius 0.10 m with a constant angular speed of 5 rev/s. The acceleration of the particle is:

A flywheel of diameter 1.2 m has a constant angular acceleration of 5.0 rad/s2. The tangential acceleration of a point on its rim is:

A force with a given magnitude is to be applied to a wheel. The torque can be maximized by:

String is wrapped around the periphery of a 5.0-cm radius cylinder, free to rotate on its axis. The string is pulled straight out at a constant rate of 10 cm/s and does not slip on the cylinder. As each small segment of string leaves the cylinder, its acceleration changes by:

A solid uniform sphere of radius R and mass M has a rotational inertia about a diameter that is given by (2/5)MR2. A light string of length 3R is attached to the surface and used to suspend the sphere from the ceiling. Its rotational inertia about the point of attachment at the ceiling is:

A flywheel is initially roatating at 20 rad/s and has a constant angular acceleration. After 9.0 s it has rotated through 450 rad. Its angular acceleration is:

A wheel is spinning at 27 rad/s but is slowing with an angular acceleration that has a magnitude given by (3.0 rad/s4)t2. It stops in a time of:

The magnitude of the acceleration of a point on a spinning wheel is increased by a factor of 4 if:

A block is attached to each end of a rope that passes over a pulley suspended from the ceiling. The blocks do not have the same mass. If the rope does not slip on the pulley, then at any instant after the blocks start moving, the rope:

A uniform solid cylinder made of lead has the same mass and the same length as a uniform solid cylinder made of wood. The rotational inertia of the lead cylinder compared to the wooden one is:

One revolution per minute is about:

Three identical balls, with masses of M, 2M, and 3M are fastened to a massless rod of length L as shown. The rotational inertia about the left end of the rod is:

A meter stick on a horizontal frictionless table top is pivoted at the 80-cm mark. A horizontal force is applied perpendicularly to the end of the stick at 0 cm, as shown. A second horizontal force (not shown) is applied at the 100-cm end of the stick. If the stick does not rotate:

The angular velocity vector of a spinning body points out of the page. If the angular acceleration vector points into the page then:

A radian is about:

The angular velocity of a rotating wheel increases 2 rev/s every minute. The angular acceleration, in rad/s2 of this wheel is:

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A wheel starts from rest and has an angular acceleration of 4.0 rad/s². The time it takes to make 10 revolutions is:

A phonograph turntable, initially rotating at 0.75 rev/s, slows down and stops in 30 s. The magnitude of its average angular acceleration in rad/s² for this process is:

A flywheel of diameter 1.2 m has a constant angular acceleration of 5.0 rad/s². The tangential acceleration of a point on its rim is:

A solid uniform sphere of radius R and mass M has a rotational inertia about a diameter that is given by (2/5)MR². A light string of length 3R is attached to the surface and used to suspend the sphere from the ceiling. Its rotational inertia about the point of attachment at the ceiling is:

A wheel is spinning at 27 rad/s but is slowing with an angular acceleration that has a magnitude given by (3.0 rad/s⁴)t^2. It stops in a time of:

The angular velocity of a rotating wheel increases 2 rev/s every minute. The angular acceleration, in rad/s² of this wheel is: