Question 1

The figure shows forces acting on a meter stick, which is constrained to rotate around the axis indicated by the dot    Which force(s)create a positive torque around that axis?

Accepted Answer

A)    only 
B)    and
  
C)    only 
D)    ,
  and
  
E)    only 
A)    only 
B)    and
  
C)    only 
D)    ,
  and
  
E)    only B

Question 2

Instantaneous angular speed is:

Accepted Answer

A) total angular displacement divided by time 
B) the integral of the displacement over time 
C) the rate at which the angular acceleration is changing 
D) the magnitude of the instantaneous angular velocity 
E) a vector directed along the axis of rotation 
A) total angular displacement divided by time 
B) the integral of the displacement over time 
C) the rate at which the angular acceleration is changing 
D) the magnitude of the instantaneous angular velocity 
E) a vector directed along the axis of rotation D

Question 3

A wheel initially has an angular velocity of 18 rad/s.It has a constant angular acceleration of 2.0 rad/s2 and is slowing at first.What time elapses before its angular velocity is18 rad/s in the direction opposite to its initial angular velocity?

Accepted Answer

A) 3.0 s 
B) 6.0 s 
C) 9.0 s 
D) 18 s 
E) 36 s 
A) 3.0 s 
B) 6.0 s 
C) 9.0 s 
D) 18 s 
E) 36 s D

Question 4

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) 0.32 kg.m2 
B) 0.54 kg.m2 
C) 0.70 kg.m2 
D) 0.86 kg.m2 
E) 1.0 kg.m2 
A) 0.32 kg.m2 
B) 0.54 kg.m2 
C) 0.70 kg.m2 
D) 0.86 kg.m2 
E) 1.0 kg.m2

Question 5

A radian is about:

Accepted Answer

A) 25 $\degree$ 
B) 37 $\degree$ 
C) 45 $\degree$ 
D) 57 $\degree$ 
E) 90 $\degree$ 
A) 25 $\degree$ 
B) 37 $\degree$ 
C) 45 $\degree$ 
D) 57 $\degree$ 
E) 90 $\degree$

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 ° 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 ° to the tangent

Question 7

A wheel initially has an angular velocity of -36 rad/s but after 6.0 s its angular velocity is -24 rad/s.If its angular acceleration is constant the value is:

Accepted Answer

A) 2.0 rad/s2 
B) -2.0 rad/s2 
C) 3.0 rad/s2 
D) -3.0 rad/s2 
E) -6.0 rad/s2 
A) 2.0 rad/s2 
B) -2.0 rad/s2 
C) 3.0 rad/s2 
D) -3.0 rad/s2 
E) -6.0 rad/s2

Question 8

A uniform disk, a thin hoop, and a uniform solid sphere, all with the same mass and same outer radius, are each free to rotate about a fixed axis through its center.Assume the hoop is connected to the rotation axis by light spokes.With the objects starting from rest, identical forces are simultaneously applied to the rims, as shown.Rank the objects according to their angular velocities after a given time t, least to greatest.

Accepted Answer

A) disk, hoop, sphere 
B) disk, sphere, hoop 
C) hoop, sphere, disk 
D) hoop, disk, sphere 
E) sphere, disk, hoop 
A) disk, hoop, sphere 
B) disk, sphere, hoop 
C) hoop, sphere, disk 
D) hoop, disk, sphere 
E) sphere, disk, hoop

Question 9

A constant torque of 260 N∙m acts on a flywheel.If the flywheel makes 25 complete revolutions, how much work has been done by the torque on the flywheel?

Accepted Answer

A) 1.7 J 
B) 41 J 
C) 600 J 
D) 6.5 x 103 J 
E) 4.1 x 104 J 
A) 1.7 J 
B) 41 J 
C) 600 J 
D) 6.5 x 103 J 
E) 4.1 x 104 J

Question 10

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 11

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

Accepted Answer

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

Question 12

A and B are two solid cylinders made of aluminum.Their dimensions are shown.The ratio of the rotational inertia of B to that of A about the common axis X─X' is:

Accepted Answer

A) 2 
B) 4 
C) 8 
D) 16 
E) 32 
A) 2 
B) 4 
C) 8 
D) 16 
E) 32

Question 13

If the angular velocity vector of a spinning body points out of the page then, when viewed from above the page, the body is spinning:

Accepted Answer

A) clockwise about an axis that is perpendicular to the page 
B) counterclockwise about an axis that is perpendicular to the page 
C) about an axis that is parallel to the page 
D) about an axis that is changing orientation 
E) about an axis that is getting longer 
A) clockwise about an axis that is perpendicular to the page 
B) counterclockwise about an axis that is perpendicular to the page 
C) about an axis that is parallel to the page 
D) about an axis that is changing orientation 
E) about an axis that is getting longer

Question 14

A wheel starts from rest and has an angular acceleration that is given by  $\alpha$ (t)= (6.0 rad/s4)t2.The time it takes to make 10 rev is:

Accepted Answer

A) 1.3 s 
B) 2.1 s 
C) 2.8 s 
D) 3.3 s 
E) 4.0 s 
A) 1.3 s 
B) 2.1 s 
C) 2.8 s 
D) 3.3 s 
E) 4.0 s

Question 15

A certain wheel has a rotational inertia of 12 kg∙m2.As it turns through 5.0 rev its angular velocity increases from 5.0 rad/s to 6.0 rad/s.If the net torque is constant its value is:

Accepted Answer

A) 0.015 N∙m 
B) 0.18 N∙m 
C) 0.57 N∙m 
D) 2.1 N∙m 
E) 13 N∙m 
A) 0.015 N∙m 
B) 0.18 N∙m 
C) 0.57 N∙m 
D) 2.1 N∙m 
E) 13 N∙m

Question 16

a hoop in the x,y plane The order of increasing rotational inertia about an axis through the center of mass and parallel to the z axis is:

Accepted Answer

A) 1, 2, 3, 4 
B) 4, 3, 2, 1 
C) 1, 3, 2, 4 
D) 4, 2, 3, 1 
E) 3, 1, 2, 4 
A) 1, 2, 3, 4 
B) 4, 3, 2, 1 
C) 1, 3, 2, 4 
D) 4, 2, 3, 1 
E) 3, 1, 2, 4

Question 17

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) "0 rad/s" 
B) "1 rad/s" 
C) "$\pi$ rad/s" 
D)  "  rad/s" 
E) "2$\pi$ rad/s" 
A) "0 rad/s" 
B) "1 rad/s" 
C) "$\pi$ rad/s" 
D)  "  rad/s" 
E) "2$\pi$ rad/s"

Question 18

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 19

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

Question 20

One-dimensional linear position is measured along a line, from a point designated x = 0.One-dimensional angular position:

Accepted Answer

A) is measured along a line, from a point designated θ = 0. 
B) is measured along the axis of rotation. 
C) is the angle that an internal reference line makes with a fixed external reference line. 
D) is measured relative to the positive y axis. 
E) is meaningless, as rotations take place in two dimensions. 
A) is measured along a line, from a point designated θ = 0. 
B) is measured along the axis of rotation. 
C) is the angle that an internal reference line makes with a fixed external reference line. 
D) is measured relative to the positive y axis. 
E) is meaningless, as rotations take place in two dimensions.

Exam 10: Rotation

The figure shows forces acting on a meter stick, which is constrained to rotate around the axis indicated by the dot Which force(s)create a positive torque around that axis?

Instantaneous angular speed is:

A wheel initially has an angular velocity of 18 rad/s.It has a constant angular acceleration of 2.0 rad/s2 and is slowing at first.What time elapses before its angular velocity is18 rad/s in the direction opposite to its initial angular velocity?

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 radian is about:

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

A wheel initially has an angular velocity of -36 rad/s but after 6.0 s its angular velocity is -24 rad/s.If its angular acceleration is constant the value is:

A constant torque of 260 N∙m acts on a flywheel.If the flywheel makes 25 complete revolutions, how much work has been done by the torque on the flywheel?

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:

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

A and B are two solid cylinders made of aluminum.Their dimensions are shown.The ratio of the rotational inertia of B to that of A about the common axis X─X' is:

If the angular velocity vector of a spinning body points out of the page then, when viewed from above the page, the body is spinning:

A wheel starts from rest and has an angular acceleration that is given by α\alphaα (t)= (6.0 rad/s4)t2.The time it takes to make 10 rev is:

A certain wheel has a rotational inertia of 12 kg∙m2.As it turns through 5.0 rev its angular velocity increases from 5.0 rad/s to 6.0 rad/s.If the net torque is constant its value is:

a hoop in the x,y plane The order of increasing rotational inertia about an axis through the center of mass and parallel to the z axis is:

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:

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

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.

One-dimensional linear position is measured along a line, from a point designated x = 0.One-dimensional angular position:

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A wheel initially has an angular velocity of 18 rad/s.It has a constant angular acceleration of 2.0 rad/s²and is slowing at first.What time elapses before its angular velocity is18 rad/s in the direction opposite to its initial angular velocity?

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 that is given by $\alpha$ (t)= (6.0 rad/s⁴)t².The time it takes to make 10 rev is:

A certain wheel has a rotational inertia of 12 kg∙m².As it turns through 5.0 rev its angular velocity increases from 5.0 rad/s to 6.0 rad/s.If the net torque is constant its value is:

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: