This exam consists of 26 questions; 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 92. The exam period was 90 minutes; the
average score was 70.2; the median score was 71. Click here to see
of the formula sheet that came with the exam.
The first has mass M and is acted on by a torque T. The second
has a mass 2M and is acted on by a torque T/2. Both cylinders start
from rest and after a certain amount of time have rotated through angles
θ1 and θ2.
The relationship between θ1 and θ2
(a) θ1 = 4 θ2
(b) θ1 = 2 θ2
(c) θ1 = θ2
A cube (mass 2.50 kg, volume 0.0026 m3) and a cylinder
(mass 1.25 kg, volume 0.0026 m3) are attached by strings to
the bottom of a fish tank. Without the strings, both objects would
float at the surface. The water in the fish tank has a density of 1000
Let the buoyant force acting on the cube be FB,cube and
that acting on the cylinder FB,cylinder. These buoyant
forces are related by:
(a) FB,cube > FB,cylinder
(b) FB,cube = FB,cylinder
(c) FB,cube < FB,cylinder
(a) Tcube > Tcylinder
(b) Tcube = Tcylinder
(c) Tcube < Tcylinder
(a) 8.71 N
(b) 9.26 N
(c) 12.5 N
(d) 13.2 N
(e) 21.9 N
(a) 1 km
(b) 2 km
(c) 3 km
(d) 4 km
(e) 5 km
A solid cylinder (mass M = 0.50 kg, radius R = 2.5 cm) rolls without
slipping down a plane inclined at 15° to the horizontal.
If the cylinder is released from rest, what is its speed after it
travels 1.2 m down the plane?
(a) 1.4 m/s
(b) 2.0 m/s
(c) 2.5 m/s
(d) 2.9 m/s
(e) 3.4 m/s
(a) the cylinder would reach the bottom first.
(b) the sphere would reach the bottom first.
(c) they would tie.
A physics grad student is playing in a park. He runs toward a
stationary merry-go-round (mass M = 200 kg and radius R =
3.0 m) with a velocity of 5.0 m/s. The merry-go-round is initially at
rest and is free to rotate without friction. He leaps aboard and
remains at the outer edge of the merry-go-round. The moment of inertia
of the merry-go-round is I = ½MR2. The student can be
treated as a point mass of 75 kg. At the moment he leaps onto the
merry-go-round, his velocity is exactly tangential to the
What is the angular velocity (ω) of the merry-go-round after the
student has jumped on?
(a) ω = 0.044 rad/s
(b) ω = 0.60 rad/s
(c) ω = 0.71 rad/s
(d) ω = 0.82 rad/s
(e) ω = 0.13 rad/s
(a) It decreases.
(b) It stays the same.
(c) It increases.
Two discs of identical size, but different masses (MA =
0.45 kg, MB = 0.25 kg) are shown below. Initially, disc A is
suspended directly over disc B and is rotating with constant angular
speed ωA = 12 rad/sec. Disc B is at rest on a
frictionless surface. Viewed from above, A is rotating
Then, A’s suspension breaks and it falls onto B. Later both disks
move with the same angular velocity ωf.
(a) ωf = 12 rad/s
(b) ωf = 7.7 rad/s
(c) ωf = 6.0 rad/s
(a) KEafter / KEbefore = 0.37
(b) KEafter / KEbefore = 0.50
(c) KEafter / KEbefore = 0.64
(d) KEafter / KEbefore = 1.0
(e) KEafter / KEbefore = 1.3
A block of mass 2.0 kg resting on a horizontal frictionless surface
is attached to a spring with force constant k = 250 N/m. The other end
of the spring is fixed to a wall. A force of unknown magnitude is
applied to the block in the x-direction, thereby stretching the spring
(see picture). The block is initially at rest. At time t = 0, the
force is removed and the block starts to oscillate back and forth along
the x-axis with amplitude 0.7 m.
What was the magnitude of the initial applied force?
(a) 150 N
(b) 175 N
(c) 250 N
(a) 0.56 s
(b) 0.78 s
(c) 1.32 s
(a) v(t) = -vmax sin(ωt)
(b) v(t) = -vmax cos(ωt)
(c) v(t) = +vmax cos(ωt)
(a) 2.5 m/s
(b) 5.3 m/s
(c) 7.8 m/s
(c) be unchanged.
A section of pipe carries water (ρ = 1000 kg/m3). In
section a, the pipe has a diameter 0.04m, and the water is
flowing to the right with velocity va = 2 m/s. In region
b, the pipe has a diameter 0.04 m. Region c has a
slight constriction reducing the diameter to 0.03 m.
Compare va, the speed of the fluid in the pipe marked
a with vb, the speed of the fluid in section b
of the pipe.
(a) va > vb
(b) va = vb
(c) va < vb
(a) Pa > Pb
(b) Pa = Pb
(c) Pa < Pb
(a) va > vc
(b) va = vc
(c) va < vc
(a) Pb > Pc
(b) Pb = Pc
(c) Pb < Pc
A grandfather clock keeps time with a simple pendulum. The pendulum
is made with a 4.0 kg mass suspended at the end of a thin rod. The
period of the small amplitude simple harmonic motion is 1.0 sec.
What is the length of the thin rod?
(a) 24.8 cm
(b) 29.7 cm
(c) 31.4 cm
(b) at the same rate.
A 0.5 m cylinder is filled to the top with water. Two identical
holes are placed in the side of the cylinder. The first hole is placed
in the middle of the cylinder, the second hole is 0.1 m from the bottom
Through which hole will the water flow the fastest?
(a) hole 1
(b) hole 2
(a) 1.5 m/s
(b) 2.1 m/s
(c) 2.8 m/s
(c) remains the same.