Practice Test, Rotation & Angular Momentum, Fall 2007
Start in class and finish for homework: feel free to discuss the problems BUT do not copy any answers. To earn a homework grade of 100% you must show work to all the problems and answer at least half of them correctly.
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1.
If a wheel turns with constant angular speed then:
A.
each point on its rim moves with constant velocity
B.
each point on its rim moves with constant acceleration
C.
the wheel turns through equal angles in equal times
D.
the angle through which the wheel turns in each second increases as time goes on
E.
the angle through which the wheel turns in each second decreases as time goes on


2.
The angular speed of the minute hand of a watch is:
A.
(60/π) m/s
B.
(1800/π) m/s
C.
(π) m/s
D.
(π/1800) m/s
E.
(π/60) m/s


3.
A flywheel rotating at 12 rev/s is brought to rest in 6 s. The magnitude of the average angular acceleration in rad/s2 of the wheel during this process is:
A.
1/π
B.
2
C.
4
D.
4π
E.
72


4.
A wheel initially has an angular velocity of 36 rad/s but after 6.0s its angular velocity is 24 rad/s. If its angular acceleration is constant the value is:
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


5.
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.
0.50 s
B.
0.71 s
C.
2.2 s
D.
2.8 s
E.
5.6 s


6.
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:
A.
1.7 s
B.
2.6 s
C.
3.0 s
D.
4.4 s
E.
7.3 s


7.
The figure shows a cylinder of radius 0.7 m rotating about its axis at 10 rad/s. The speed of the point P is:
A.
7.0 m/s
B.
14π rad/s
C.
7π rad/s
D.
0.70 m/s
E.
none of these


8.
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.
vertically upward
B.
horizontally to the north
C.
horizontally to the south
D.
zero
E.
upward and forward at 45° to the horizontal


9.
For a wheel spinning with constant angular acceleration on an axis through its center, the ratio of the speed of a point on the rim to the speed of a point halfway between the center and the rim is:
A.
1
B.
2
C.
1/2
D.
4
E.
1/4


10.
A wheel starts from rest and spins with a constant angular acceleration. As time goes on the acceleration vector for a point on the rim:
A.
decreases in magnitude and becomes more nearly tangent to the rim
B.
decreases in magnitude and becomes more nearly radial
C.
increases in magnitude and becomes more nearly tangent to the rim
D.
increases in magnitude and becomes more nearly radial
E.
increases in magnitude but retains the same angle with the tangent to the rim


11.
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.
ML2/2
B.
ML2
C.
3ML2/2
D.
6ML2
E.
3ML2/4


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:
A.
2
B.
4
C.
8
D.
16
E.
32


13.
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.
0.38 kg ⋅ m2
B.
0.54 kg ⋅ m2
C.
0.70 kg ⋅ m2
D.
0.86 kg ⋅ m2
E.
1.0 kg ⋅ m2


14.
A force with a given magnitude is to be applied to a wheel. The torque can be maximized by:
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


15.
A meter stick on a horizontal frictionless table top is pivoted at the 80-cm mark. A horizontal force ¢1 is applied perpendicularly to the end of the stick at 0 cm, as shown. A second horizontal force ¢2 (not shown) is applied at the 100-cm end of the stick. If the stick does not rotate:
A.
¢2 > ¢1 for all orientations of ¢2
B.
¢2 < ¢1 for all orientations of ¢2
C.
¢2 = ¢1 for all orientations of ¢2
D.
¢2 > ¢1 for some orientations of ¢2 and ¢2 < ¢1 for others
E.
¢2 > ¢1 for some orientations of ¢2 and ¢2 = ¢1 for others


16.
A disk with a rotational inertia of 2.0 kg ⋅ m2 and a radius of 0.40 m rotates on a frictionless fixed axis perpendicular to the disk faces and through its center. A force of 5.0 N is applied tangentially to the rim. The angular acceleration of the disk is:
A.
0.40 rad/s2
B.
0.60 rad/s2
C.
1.0 rad/s2
D.
2.5 rad/s2
E.
10 rad/s2


17.
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.
0.016 N ⋅ m
B.
0.18 N ⋅ m
C.
0.57 N ⋅ m
D.
2.1 N ⋅ m
E.
3.6 N ⋅ m


18.
A small disk of radius R1 is mounted coaxially with a larger disk of radius R2. The disks are securely fastened to each other and the combination is free to rotate on a fixed axle that is perpendicular to a horizontal frictionless table top,as shown in the overhead veiw below. The rotational inertia of the combination is I. A string is wrapped around the larger disk and attached to a block of mass m, on the table. Another string is wrapped around the smaller disk and is pulled with a force ¢ as shown. The acceleration of the block is:
A.
R1F/mR2
B.
R1R2F/(I – mR2 2)
C.
R1R2F/(I + mR2 2)
D.
R1R2F/(I – mR1R 2)
E.
R1R2F/(I + mR1R 2)


19.
A circular saw is powered by a motor. When the saw is used to cut wood, the wood exerts a torque of 0.80 N · m on the saw blade. If the blade rotates with a constant angular velocity of 20 rad/s the work done on the blade by the motor in 1.0 min is:
A.
0
B.
480 J
C.
960 J
D.
1400 J
E.
1800 J


20.
Two wheels roll side-by-side without sliding, at the same speed. The radius of wheel 2 is twice the radius of wheel 1. The angular velocity of wheel 2 is:
A.
twice the angular velocity of wheel 1
B.
the same as the angular velocity of wheel 1
C.
half the angular velocity of wheel 1
D.
more than twice the angular velocity of wheel 1
E.
less than half the angular velocity of wheel 1


21.
A solid wheel with mass M, radius R, and rotational inertia MR2/2, rolls without sliding on a horizontial surface. A horizontal force F is applied to the axle and the center of mass has an acceleration a. The magnitudes of the applied force F and the frictional force f of the surface, respectively, are:
A.
F = Ma, f = 0
B.
F = Ma, f = Ma/2
C.
F = 2Ma, f = Ma
D.
F = 2Ma, f = Ma/2
E.
F = 3Ma/2, f = Ma/2


22.
A sphere and a cylinder of equal mass and radius are simultaneously released from rest on the same inclined plane sliding down the incline. Then:
A.
the sphere reaches the bottom first because it has the greater inertia
B.
the cylinder reaches the bottom first because it picks up more rotational energy
C.
the sphere reaches the bottom first because it picks up more rotational energy
D.
they reach the bottom together
E.
none of the above is true


23.
Two identical disks, with rotational inertia I (= 1/2 MR2), roll without slipping across a horizontal floor and then up inclines. Disk A rolls up its incline without sliding. On the other hand, disk B rolls up a frictionless incline. Otherwise the inclines are identical. Disk A reaches a height 12 cm above the floor before rolling down again. Disk B reaches a height above the floor of:
A.
24 cm
B.
18 cm
C.
12 cm
D.
8 cm
E.
6 cm


24.
Two uniform cylinders have different masses and different rotational inertias. They simultaneously start from rest at the top of an inclined plane and roll without sliding down the plane. The cylinder that gets to the bottom first is:
A.
the one with the larger mass
B.
the one with the smaller mass
C.
the one with the larger rotational inertia
D.
the one with the smaller rotational inertia
E.
neither (they arrive together)


25.
The fundamental dimensions of angular momentum are:
A.
mass·length·time–1
B.
mass·length–2·time–2
C.
mass·2·time–1
D.
mass·length2·time–2
E.
none of these


26.
The newton⋅second is a unit of:
A.
work
B.
angular momentum
C.
power
D.
linear momentum
E.
none of these


27.
A 6.0-kg particle moves to the right at 4.0 m/s as shown. The magnitude of its angular momentum about the point O is:
A.
zero
B.
288 kg ⋅ m2/s
C.
144 kg ⋅ m2/s
D.
24 kg ⋅ m2/s
E.
249 kg ⋅ m2/s


28.
A 15-g paper clip is attached to the rim of a phonograph record with a radius of 30 cm, spinning at 3.5 rad/s. The magnitude of its angular momentum is:
A.
1.4 × 10–3 kg ⋅ m2/s
B.
4.7 × 10–3 kg ⋅ m2/s
C.
1.6 × 10–-2 kg ⋅ m2/s
D.
3.2 × 10–1 kg ⋅ m2/s
E.
1.1 kg ⋅ m2/s


29.
As a 2.0-kg block travels around a 0.50-m radius circle with an angular speed of 12 rad/s. The circle is parallel to the xy plane and is centered on the z axis, 0.75 m from the origin. The component in the xy plane of the angular momentum around the origin has magnitude:
A.
0
B.
6.0 kg ⋅ m2/s
C.
9.0 kg ⋅ m2/s
D.
11 kg ⋅ m2/s
E.
14 kg ⋅ m2/s


30.
A single force acts on a particle situated on the positive x axis. The torque about the origin is in the negative z direction. The force might be:
A.
in the positive y direction
B.
in the negative y direction
C.
in the positive x direction
D.
in the negative x direction
E.
in the positive z direction


31.
A 2.0-kg stone is tied to a 0.50 m string and swung around a circle at a constant angular velocity of 12 rad/s. The circle is parallel to the xy plane and is centered on the z axis, 0.75 m from the origin. The magnitude of the torque about the origin is:
A.
0
B.
6.0 N ⋅ m
C.
14 N ⋅ m
D.
72 N ⋅ m
E.
108 N ⋅ m


32.
A single force acts on a particle P. Rank each of the orientations of the force shown below according to the magnitude of the time rate of change of the particle's angular momentum about the point O, least to greatest.
A.
1, 2, 3, 4
B.
1 and 2 tie, then 3, 4
C.
1 and 2 tie, then 4, 3
D.
1 and 2 tie, then 3 and 4 tie
E.
All are the same


33.
A man, with his arms at his sides, is spinning on a light frictionless turntable. When he extends his arms:
A.
his angular velocity increases
B.
his angular velocity remains the same
C.
his rotational inertia decreases
D.
his rotational kinetic energy increases
E.
his angular momentum remains the same


34.
When a man on a frictionless rotating stool extends his arms horizontally, his rotational kinetic energy:
A.
must increase
B.
must decrease
C.
must remain the same
D.
may increase or decrease depending on his initial angular velocity
E.
may increase or decrease depending on his angualar acceleration


35.
A wheel,with rotational inertia I, mounted on a vertical shaft with negligible ratational inertia, is rotating with angular speed ω 0. A nonrotation wheel with rotational inertia 2I is suddenly dropped onto the same shaft as shown.. The resultant combination of the two wheels and shaft will rotate at:
A.
ω 0 /2
B.
2ω 0
C.
ω 0 /3
D.
3ω 0
E.
ω 0 /4


36.
A playground merry-go-round has a radius of 3.0 m and a rotational inertia of 600 kg ⋅ m2. It is initially spinning at 0.80 rad/s when a 20-kg child crawls from the center to the rim. When the child reaches the rim the angular velocity of the merry-go-round is:
A.
0.61 rad/s
B.
0.73 rad/s
C.
0.80 rad/s
D.
0.89 rad/s
E.
1.1 rad/s


37.
A block with mass M, on the end of a string, moves in a circle on a horizontal frictionless table as shown. As the string is slowly pulled through a small hole in the table:
A.
the angular momentum of M remains constant
B.
the angular momentum of M decreases
C.
the kinetic energy of M remains constant
D.
the kinetic energy of M decreases
E.
none of the above


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