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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1) In an amusement park ride, passengers stand inside an 8 m radius cylinder. Initially, the cylinder
rotates with its axis oriented along the vertical. After the cylinder has acquired sufficient speed, it
tilts into a vertical plane, that is, the axis tilts into the horizontal, as shown in the figure. Suppose
that, once the axis has tilted into the horizontal, the ring rotates once every 4.5 s. If a riderʹs mass is
40 kg, with how much force does the ring push on her at the top of the ride?
A) 230 N
B) 390 N
C) 1000 N
1)
D) 620 N
2) In the figure, a given force F is applied to a rod in several different ways. In which case is the
torque due to F about the pivot P greatest?
A) 1
B) 2
C) 3
D) 4
E) 5
2)
3) A croquet mallet balances when suspended from its center of mass, as shown in the figure (left). If
you cut the mallet in two at its center of mass, as shown, how do the masses of the two pieces
compare?
3)
A) It is impossible to tell.
B) The piece with the head of the mallet has the smaller mass.
C) The piece with the head of the mallet has the greater mass.
D) The masses are equal.
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4) Calculate the angular speed, in rad/s, of a flywheel turning at 520.0 rpm.
A) 8.656 rad/s
B) 54.44 rad/s
C) 60.97 rad/s
4)
D) 40.83 rad/s
5) An ice skater doing a spin pulls in her arms, decreasing her moment of inertia by a factor of two.
How does her angular speed changes?
A) It increases by a factor of two.
B) It is reduced by a factor of four.
C) It is reduced by a factor of two.
D) It increases by a factor of four.
5)
6) A merry-go-round is spinning at a fixed rate. As a person is walking toward the edge,
A) the force of static friction must decrease in order for the person not to slide off.
B) the force of static friction must increase in order for the person not to slide off.
C) the force of static friction such that the person does not slide off remains the same.
6)
Figure 11-2
7) A storeʹs sign, with a mass of 20.0 kg and 3.00 m long, has its center of gravity at the center of the
sign. It is supported by a loose bolt attached to the wall at one end and by a wire at the other end,
as shown in Figure 11-2. The wire makes an angle of 25.0° with the horizontal. What is the tension
in the wire?
A) 196 N
B) 464 N
C) 232 N
D) 297 N
7)
8) If an astronaut were exactly half way between Earth and the Moon, the net gravitational force
exerted on the astronaut by these two objects would be
A) directed toward Earth.
B) directed toward the Moon.
C) zero.
8)
9) Find the orbital speed of an ice cube in the rings of Saturn, if the mass of Saturn is 5.67 × 1026 kg
and the rings have an average radius of 100,000 km.
A) 1.95 km/s
B) 19.5 km/s
C) 27.5 km/s
D) 13.8 km/s
9)
10) A cylinder is rolling without slipping. What fraction of its kinetic energy is rotational?
A) 1/2
B) 3/4
C) 1/3
D) 2/3
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10)
11) A disk and a sphere are released simultaneously at the top of an inclined plane. They roll down
without slipping. Which will reach the bottom first?
A) the one of greatest mass
B) the one of smallest diameter
C) the sphere
D) the disk
E) They will reach the bottom at the same time.
11)
12) A ball is released from rest on a no-slip surface, as shown. After reaching its lowest point, the ball
begins to rise again, this time on a frictionless surface.
12)
When the ball reaches its maximum height on the frictionless surface, it is
A) at a lesser height as when it was released.
B) at a greater height as when it was released.
C) at the same height as when it was released.
D) impossible to tell without knowing the mass of the ball.
13) In the figure, a mass of 35.30 kg is attached to a light string that is wrapped around a cylindrical
spool of radius 10 cm and moment of inertia 4.00 kg · m2 . The spool is suspended from the ceiling,
13)
and the mass is then released from rest a distance 3.50 m above the floor. How long does it take to
reach the floor?
A) 2.97 s
B) 5.89 s
C) 2.85 s
D) 4.18 s
E) 0.892 s
14) A potterʹs wheel is rotating at 1.00 rpm. What centripetal force is required to hold a 1.00 g lump of
clay in place, 10.0 cm from the axis of rotation?
A) 1.30 × 10 -6 N
B) 1.10 × 10 -6 N
C) 1.40 × 10 -6 N
D) 1.20 × 10 -6 N
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14)
15) The rotating systems shown in the figure differ only in that the two identical movable masses are
positioned a distance r from the axis of rotation (left), or a distance r/2 from the axis of rotation
(right). If you release the hanging blocks simultaneously from rest,
15)
A) it is impossible to tell which block reaches the bottom first.
B) the block at right lands first.
C) both blocks land at the same time.
D) the block at left lands first.
16) A soccer ball whose radius is 11 cm rolls a distance of 10 m in 3.50 s. What is the angular speed of
the ball?
A) 13 m/s
B) 26 m/s
C) 52 m/s
D) 39 m/s
16)
17) When you ride a bicycle, in what direction is the angular velocity of the wheels?
A) forwards
B) to your right
C) to your left
D) backwards
17)
18) How long does it take a wheel that is rotating at 33.3 rpm to speed up to 78.0 rpm if it has an
angular acceleration of 2.15 rad/s2 ?
18)
A) 10.4 s
B) 5.20 s
C) 2.18 s
D) 20.8 s
19) What is the correct expression for torque, in terms of the magnitude of the force, F, the radial
distance from the axis of rotation, r, and the angle between the force and the radial line, θ?
A) τ = F r cosθ
B) τ = F r tanθ
C) τ = F r sinθ
D) τ = F r θ
19)
20) A torque of 12 N · m is applied to a solid, uniform disk of radius 0.50 m. If the disk accelerates at
5.7 rad/s 2 , what is the mass of the disk?
20)
A) 13 kg
B) 8.5 kg
C) 4.3 kg
D) 17 kg
Figure 11-1
21) An 82.0 kg-diver stands at the edge of a light 5.00-m diving board, which is supported by two
pillars 1.60 m apart, as shown in Figure 11-1. Find the force exerted by pillar A.
A) 2.51 kN downwards
B) 2.51 kN upwards
C) 1.71 kN downwards
D) 1.71 kN upwards
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21)
22) A person ties a rock to a string and whirls it around in a vertical circle such that sometimes the
rock is going straight upward and sometimes the rock is going straight down. She whirls the rock
at the minimum speed (constant in time) such that the string is always taut (no sag). When is the
tension the highest?
A) It is highest when the rock is at the highest elevation.
B) The tension is constant as the rock moves around in a circle.
C) It is highest when the rock is at the lowest elevation.
22)
23) Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of
rotation than child B. Which child has the larger centripetal acceleration?
A) Child A
B) Child B
C) They have the same centripetal acceleration.
D) There is not enough information given to answer the question.
23)
24) A child is sitting on the outer edge of a merry-go-round that is 18 m in diameter. If the
merry-go-round makes 4.9 rev/min, what is the velocity of the child in m/s?
A) 4.6 m/s
B) 3.2 m/s
C) 9.2 m/s
D) 0.7 m/s
24)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
25) How is it possible for someone to remain in her seat (without any straps) while upside
down on a loop-the-loop roller coaster?
25)
26) If there is no such thing as a centrifugal force, why does someone in a car making a turn
feel as if he or she is being pulled toward the outside of the curve?
26)
27) When a car decelerates, its front end goes down. Explain.
27)
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Answer Key
Testname: UNTITLED1
1) A
2) A
3) C
4) B
5) A
6) B
7) C
8) A
9) B
10) C
11) C
12) A
13) A
14) B
15) B
16) B
17) C
18) C
19) C
20) D
21) C
22) C
23) A
24) A
25) If the velocity of the roller coaster car is sufficiently large at the top of the loop, the person (and car) will remain on the
track. For lower speeds, the normal force on the person goes to 0 before she reaches the top, meaning that she comes
out of the seat.
mV2
(This follows from N = r - mg.)
26) The car is making a turn, but the person in the car is not part of the car. According to Newtonʹs First Law, you will
move in a straight line until acted on by an outside force - thus, you move in a straight line while the car turns (at
least until you run into the door. At this time, the car exerts a force on you, causing your direction of motion to
change.).
27) The frictional force between the road and the tires required to decelerate the car acts below the center of mass of the
car. For a car traveling to the left, this translates into a counterclockwise torque. The normal forces on the front and
back tires are redistributed to produce a clockwise torque. This requires an increase in the normal force at the front
and a decrease in the normal force at the back. As a result, the car dips down at the front.
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