Question 1

The rotational inertia of a disk about its axis is 0.70 kg . m2. When a 2.0 kg weight is added to its rim, 0.40 m from the axis, the rotational inertia becomes:

Accepted Answer

A)  0.38 kg . m2 
B)  0.54 kg . m2 
C)  0.70 kg . m2 
D)  0.86 kg . m2 
E)  1.0 kg . m2 
A)  0.38 kg . m2 
B)  0.54 kg . m2 
C)  0.70 kg . m2 
D)  0.86 kg . m2 
E)  1.0 kg . m2

Question 2

A wheel starts from rest and has an angular acceleration of 4.0 rad/s2. When it has made 10 rev its angular velocity is:

Accepted Answer

A)  16 rad/s 
B)  22 rad/s 
C)  32 rad/s 
D)  250 rad/s 
E)  500 rad/s 
A)  16 rad/s 
B)  22 rad/s 
C)  32 rad/s 
D)  250 rad/s 
E)  500 rad/s

Question 3

Wrapping paper is being from a 5.0-cm radius tube, free to rotate on its axis. If it is pulled at the constant rate of 10 cm/s and does not slip on the tube, the angular velocity of the tube is:

Accepted Answer

A)  2.0 rad/s 
B)  5.0 rad/s 
C)  10 rad/s 
D)  25 rad/s 
E)  50 rad/s 
A)  2.0 rad/s 
B)  5.0 rad/s 
C)  10 rad/s 
D)  25 rad/s 
E)  50 rad/s

Question 4

A thin circular hoop of mass 1.0 kg and radius 2.0 m is rotating about an axis through its center and perpendicular to its plane. It is slowing down at the rate of 7.0 rad/s2. The net torque acting on it is:

Accepted Answer

A)  7.0 N . m 
B)  14.0 N .m 
C)  28.0 N . m 
D)  44.0 N . m 
E)  none of these 
A)  7.0 N . m 
B)  14.0 N .m 
C)  28.0 N . m 
D)  44.0 N . m 
E)  none of these

Question 5

The rotational inertia of a solid uniform sphere about a diameter is (2/5)MR2, where M is its mass and R is its radius. If the sphere is pivoted about an axis that is tangent to its surface, its rotational inertia is:

Accepted Answer

A)  MR2 
B)  (2/5)MR2 
C)  (3/5)MR2 
D)  (5/2)MR2 
E)  (7/5)MR2 
A)  MR2 
B)  (2/5)MR2 
C)  (3/5)MR2 
D)  (5/2)MR2 
E)  (7/5)MR2

Question 6

One revolution is the same as:

Accepted Answer

A)  1 rad 
B)  57 rad 
C)   $\pi$/2 rad 
D)   $\pi$ rad 
E)  2 $\pi$ rad 
A)  1 rad 
B)  57 rad 
C)   $\pi$/2 rad 
D)   $\pi$ rad 
E)  2 $\pi$ rad

Question 7

A disk is free to rotate on a fixed axis. A force of given magnitude F, in the plane of the disk, is to be applied. Of the following alternatives the greatest angular acceleration is obtained if the force is:

Accepted Answer

A)  applied tangentially halfway between the axis and the rim 
B)  applied tangentially at the rim 
C)  applied radially halfway between the axis and the rim 
D)  applied radially at the rim 
E)  applied at the rim but neither radially nor tangentially 
A)  applied tangentially halfway between the axis and the rim 
B)  applied tangentially at the rim 
C)  applied radially halfway between the axis and the rim 
D)  applied radially at the rim 
E)  applied at the rim but neither radially nor tangentially

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

Two uniform circular disks having the same mass and the same thickness are made from different materials. The disk with the smaller rotational inertia is:

Accepted Answer

A)  the one made from the more dense material 
B)  the one made from the less dense material 
C)  neither - both rotational inertias are the same 
D)  the disk with the larger angular velocity 
E)  the disk with the larger torque 
A)  the one made from the more dense material 
B)  the one made from the less dense material 
C)  neither - both rotational inertias are the same 
D)  the disk with the larger angular velocity 
E)  the disk with the larger torque

Question 10

When a thin uniform stick of mass M and length L is pivoted about its midpoint, its rotational inertia is ML2/12. When pivoted about a parallel axis through one end, its rotational inertia is:

Accepted Answer

A)  ML2/12 
B)  ML2/6 
C)  ML2/3 
D)  7ML2/12 
E)  13ML2/12 
A)  ML2/12 
B)  ML2/6 
C)  ML2/3 
D)  7ML2/12 
E)  13ML2/12

Question 11

A disk starts from rest and rotates around a fixed axis, subject to a constant net torque. The work done by the torque during the second 5 s is ______ as the work done during the first 5 s.

Accepted Answer

A)  the same 
B)  twice as much 
C)  half as much 
D)  four times as much 
E)  one fourth as much 
A)  the same 
B)  twice as much 
C)  half as much 
D)  four times as much 
E)  one fourth as much

Question 12

A wheel starts from rest and has an angular acceleration that is given by $\alpha$(t) = (6.0 rad/s4)t2.  After it has turned through 10 rev its angular velocity is:

Accepted Answer

A)  63 rad/s 
B)  75 rad/s 
C)  89 rad/s 
D)  130 rad/s 
E)  210 rad/s 
A)  63 rad/s 
B)  75 rad/s 
C)  89 rad/s 
D)  130 rad/s 
E)  210 rad/s

Question 13

The fan shown has been turned on and is slowing as it rotates clockwise. The direction of the acceleration of the acceleratrion point X on the fan tip could be:

Accepted Answer

A)    
B)    
C)  $\downarrow$ 
D)  $\leftarrow$ 
E)  $\rightarrow$ 
A)    
B)    
C)  $\downarrow$ 
D)  $\leftarrow$ 
E)  $\rightarrow$

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

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 16

Two wheels are identical but wheel B is spinning with twice the angular speed of wheel A. The ratio of the magnitued of the radical acceleration of a point on the rim of B to the magnitude of the radial acceleration of a point on the rim of A is:

Accepted Answer

A)  1 
B)  2 
C)  1/2 
D)  4 
E)  1/4 
A)  1 
B)  2 
C)  1/2 
D)  4 
E)  1/4

Question 17

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 18

A car travels north at constant velocity. It goes over a piece of mud which sticks to the tire. The initial acceleration of the mud, as it leaves the ground, is:

Accepted Answer

A)  vertically upward 
B)  horizontally to the north 
C)  horizontally to the south 
D)  zero 
E)  upward and forward at 45$\degree$ to the horizontal 
A)  vertically upward 
B)  horizontally to the north 
C)  horizontally to the south 
D)  zero 
E)  upward and forward at 45$\degree$ to the horizontal

Question 19

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 20

A wheel rotates with a constant angular acceleration of  $\pi$ rad/s2. During a certain time interval its angular displacement is  $\pi$ rad. At the end of the interval its angular velocity is 2 $\pi$ rad/s. Its angular velocity at the beginning of the interval is:

Accepted Answer

A)  zero 
B)  1 ras/s 
C)   $\pi$ras/s 
D)    ras/s 
E)  2 $\pi$ ras/s 
A)  zero 
B)  1 ras/s 
C)   $\pi$ras/s 
D)    ras/s 
E)  2 $\pi$ ras/s

Exam 10: Rotation

The rotational inertia of a disk about its axis is 0.70 kg . m2. When a 2.0 kg weight is added to its rim, 0.40 m from the axis, the rotational inertia becomes:

A wheel starts from rest and has an angular acceleration of 4.0 rad/s2. When it has made 10 rev its angular velocity is:

Wrapping paper is being from a 5.0-cm radius tube, free to rotate on its axis. If it is pulled at the constant rate of 10 cm/s and does not slip on the tube, the angular velocity of the tube is:

A thin circular hoop of mass 1.0 kg and radius 2.0 m is rotating about an axis through its center and perpendicular to its plane. It is slowing down at the rate of 7.0 rad/s2. The net torque acting on it is:

The rotational inertia of a solid uniform sphere about a diameter is (2/5)MR2, where M is its mass and R is its radius. If the sphere is pivoted about an axis that is tangent to its surface, its rotational inertia is:

One revolution is the same as:

A disk is free to rotate on a fixed axis. A force of given magnitude F, in the plane of the disk, is to be applied. Of the following alternatives the greatest angular acceleration is obtained if the force 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:

Two uniform circular disks having the same mass and the same thickness are made from different materials. The disk with the smaller rotational inertia is:

When a thin uniform stick of mass M and length L is pivoted about its midpoint, its rotational inertia is ML2/12. When pivoted about a parallel axis through one end, its rotational inertia is:

A disk starts from rest and rotates around a fixed axis, subject to a constant net torque. The work done by the torque during the second 5 s is ______ as the work done during the first 5 s.

A wheel starts from rest and has an angular acceleration that is given by α\alphaα (t) = (6.0 rad/s4)t2. After it has turned through 10 rev its angular velocity is:

The fan shown has been turned on and is slowing as it rotates clockwise. The direction of the acceleration of the acceleratrion point X on the fan tip could be:

One revolution per minute is about:

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:

Two wheels are identical but wheel B is spinning with twice the angular speed of wheel A. The ratio of the magnitued of the radical acceleration of a point on the rim of B to the magnitude of the radial acceleration of a point on the rim of A is:

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

A car travels north at constant velocity. It goes over a piece of mud which sticks to the tire. The initial acceleration of the mud, as it leaves the ground, is:

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

A wheel rotates with a constant angular acceleration of π\piπ rad/s2. During a certain time interval its angular displacement is π\piπ rad. At the end of the interval its angular velocity is 2 π\piπ rad/s. Its angular velocity at the beginning of the interval is:

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The rotational inertia of a disk about its axis is 0.70 kg . m². When a 2.0 kg weight is added to its rim, 0.40 m from the axis, the rotational inertia becomes:

A wheel starts from rest and has an angular acceleration of 4.0 rad/s². When it has made 10 rev its angular velocity is:

A thin circular hoop of mass 1.0 kg and radius 2.0 m is rotating about an axis through its center and perpendicular to its plane. It is slowing down at the rate of 7.0 rad/s². The net torque acting on it is:

The rotational inertia of a solid uniform sphere about a diameter is (2/5)MR², where M is its mass and R is its radius. If the sphere is pivoted about an axis that is tangent to its surface, its rotational inertia 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:

When a thin uniform stick of mass M and length L is pivoted about its midpoint, its rotational inertia is ML²/12. When pivoted about a parallel axis through one end, its rotational inertia is:

A wheel starts from rest and has an angular acceleration that is given by $\alpha$ (t) = (6.0 rad/s⁴)t^2. After it has turned through 10 rev its angular velocity 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:

A wheel rotates with a constant angular acceleration of $\pi$ rad/s². During a certain time intervalits angular displacement is $\pi$ rad. At the end of the interval its angular velocity is 2 $\pi$ rad/s. Its angular velocity at the beginning of the interval is: