True-false questions are worth 2 points each, three-choice multiple
choice questions are worth 3 points each, five-choice multiple choice
questions are worth 6 points each. The maximum possible score is 113.
The exam period was 90 minutes. The mean score was75.2; the median was
75. Click here to see page1
page2 of the formula sheet that came
with the exam.
Unless told otherwise, you should assume that the acceleration of
gravity near the surface of the earth is 9.8 m/s2 downward
and ignore any effects due to air resistance.
A solid spherical ball with mass M = 7 kg, radius R = 0.3 m, and
initial velocity vi = 5 m/s rolls without slipping up
a ramp and reaches the top. (Recall I = 2/5 M R2 for a solid
Calculate Li, the initial angular momentum of the
ball around its rotation axis before it goes up the ramp.
(a) Li = 3.57 kg m2/s
(b) Li = 4.20 kg m2/s
(c) Li = 8.62 kg m2/s
(d) Li = 13.3 kg m2/s
(e) Li = 35 kg m2/s
(a) Li < Lf
(b) Li = Lf
(c) Li > Lf
(a) E = 67.5 J
(b) E = 84.3 J
(c) E = 98.1 J
(d) E = 123 J
(e) E = 152 J
(a) vf = 1.49 m/s
(b) vf = 3.15 m/s
(c) vf = 3.82 m/s
(d) vf = 4.10 m/s
(e) vf = 5.00 m/s
You have your bicycle upside down for repair. The front wheel is
free to rotate about its axis and is perfectly balanced except for the
0.025 kg valve stem 0.3 m from the rotation axis. The location of the
stem is at an angle θ with respect to the horizontal, as shown in
the figure. Gravity points downward in the figure.
For which of the following values of θ is the torque about the
wheel’s axis due to the weight of the stem the smallest?
(a) 0.176 Nm
(b) 0.363 Nm
(c) 0.014 Nm
(d) 0.067 Nm
(e) 0.214 Nm
A uniform board of length L and weight W is supported in two places:
one on the extreme left end and the other 2L/3 from the left end. What
is the force exerted by the right support on the board?
Which force results in the largest torque about an axis perpendicular to
the plane of plane of the board and passing through its center?
(a) object A
(b) object B
(c) Both objects have the same moment of inertia about the x axis.
A star is a uniform sphere of mass M and radius R. It rotates about
its center with angular velocity ω. The star then collapses to
radius R/10 (with the mass still M). What is the angular velocity of the
star after its collapse? Note that there are no external torque on the
star during the collapse.
(a) ω / 100
(b) ω / 10
(d) 10 ω
(e) 100 ω
(a) It increases.
(b) It decreases.
(c) It stays the same.
A 0.125 kg ball is dropped from a height h above the ground
and is observed to be traveling downward with a speed of 7 m/s just
before hitting the ground. It bounces back up to a height of 2 meters.
Neglect any energy losses due to the friction with the air.
From what height h was the ball dropped?
(a) h = 1.5 m
(b) h = 2.1 m
(c) h = 2.5 m
(a) F = 13 N
(b) F = 18 N
(c) F = 24 N
(d) F = 28 N
(e) F = 37 N
An 85 kg bobsled starts from rest at the top of a frictionless course
with a net 80 meter vertical drop. The bobsledder starts by running and
pushing the sled with a constant force F over the first 15 meter
flat section. The bobsled is observed to be traveling 45 m/s when it
reaches the bottom of the run (before applying the brakes to stop).
What is the minimum average force F the bobsledders must have
applied over those 15 meters to accelerate the bobsled at the start of
(a) 1300 N
(b) 1800 N
(c) 4300 N
(a) 71 m
(b) 90 m
(c) 116 m
(d) 138 m
(e) 156 m
Two blocks are sliding to the right on a frictionless surface and
collide as shown below. Before the collision, the block M on the
left has a speed of 4 m/s, and block 3M has a speed of 1 m/s. After the
collision the right block (3M) is observed to travel to the right with
speed 3 m/s.
What is the velocity of the 1M-block after the collision?
(a) 2 m/s to the left
(b) 5 m/s to the left
(c) 0 m/s
(d) 2 m/s to the right
(e) 5 m/s to the right
A 75 kg student (represented by the solid black circle) standing at
R=0.8 m from the center of a merry-go-round that is rotating with
angular velocity ω = 2.5 radians/second. The merry-go-round alone
has a moment of inertia of 599 kg-m2.
What is the speed of the student as he goes around standing on the
rim of the merry-go-round?
(a) 2.0 m/s
(b) 3.5 m/s
(c) 4.3 m/s
(a) 0.124 radians/s2
(b) 0.750 radians/s2
(c) 1.23 radians/s2
An external torque t is applied to the disk and the student standing
on it. The torque slows down the rotation
a constant angular acceleration of α = -65
rad/s2. What is the magnitude of the applied torque? That
is, what is the absolute value of the average torque on the
merry-go-round while it is slowing down?
(a) τ = 21 N-m
(b) τ = 119 N-m
(c) τ = 3710 N-m
(d) τ = 40070 N-m
(e) τ = 42060 N-m
(a) Wf = -34 J
(b) Wf = -15 J
(c) Wf = -7.5 J
(d) Wf = -0.8 J
(e) Wf = 0 J
Two disks are traveling on a frictionless surface and collide.
Before the collision, the 1M disk is traveling 3 m/s in the positive x
direction, and the 2M disk is traveling 2 m/s in the positive y
direction as shown below. The two disks collide and stick together.
(Gravity is perpendicular to the plane of the frictionless surface, i.e.
perpendicular to the x-y plane)
Calculate the x component of the velocity of the two disks after the
(a) vx = 1 m/s
(b) vx = 2 m/s
(c) vx = 3 m/s
(a) vy = 1 m/s
(b) vy = 1.3 m/s
(c) vy = 2 m/s