This exam consists of 24 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 108. The exam period was 90 minutes; the average score was 92.9; the median score was 96. Click here to see the formula sheet that came with the exam.

A solid cylinder of mass 2 kg and radius 10 cm rotates with a constant angular velocity of 2 rad/s about a fixed axis passing through its center. What is the rotational kinetic energy of the cylinder?

(a) 0.005 J (b) 0.01 J (c) 0.02 J (d) 0.05 J (e) 0.1 J

(a) Cylinder 1. (b) Cylinder 2. (c) Both get to the bottom at the same time.

A ramp is 2 m long and makes an angle of 30° with respect to horizontal. A hollow cylinder is released from rest at the top of the ramp, and rolls to the bottom without slipping. As the cylinder rolls, compare the magnitude of its translational kinetic energy, KE_{TRANS}, to the magnitude of its rotational kinetic energy, KE_{ROT}.

(a) KE_{TRANS} > KE_{ROT} (b) KE_{TRANS} < KE_{ROT} (c) KE_{TRANS} = KE_{ROT}

(a) 0.7 m/s (b) 1.3 m/s (c) 2.4 m/s (d) 3.1 m/s (e) 4.9 m/s

A circular merry-go-round of mass 200 kg and 2 m radius rotates freely with an initial angular velocity of 0.5 rad/s about a vertical axis passing through its center. A 50 kg student is initially standing on the rim of the merry-go-round. Treat the merry-go-round as a solid disk and the student as a point particle.

What is the magnitude of the angular momentum of the student plus merry-go-round?

(a) 100 kg-m^{2}/s (b) 200 kg-m^{2}/s (c) 300 kg-m^{2}/s (d) 400 kg-m^{2}/s (e) 500 kg-m^{2}/s

(a) 0.50 rad/s (b) 0.75 rad/s (c) 1.25 rad/s (d) 1.50 rad/s (e) 1.75 rad/s

(a) Only the angular momentum of the system is conserved. (b) Only the kinetic energy of the system is conserved. (c) Both the angular momentum and the kinetic energy is conserved.

A block of mass 2.0 kg is resting on a horizontal frictionless surface and is attached to a spring with force constant k = 150 N/m. The other end of the spring is fixed to a wall. The block is located at x = 0 when the spring is relaxed.

A force of 200 N is applied to the block in the x-direction, 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.

What is the amplitude of the oscillation?

(a) 0.5 m (b) 0.7 m (c) 1.0 m (d) 1.3 m (e) 2.0 m

(a) 14 (b) 52 (c) 67 (d) 95 (e) 110

(a) x(t) = A sin(ωt) (b) x(t) = A cos(ωt) (c) x(t) = A tan(ωt)

(a) T_{new} = T_{0} (b) T_{new} = 2 T_{0} (c) T_{new} = T_{0} / 2

A pendulum is made by hanging a 0.5 kg mass from a massless string. The pendulum oscillates with simple harmonic motion with an angular velocity of ω_{0} = 1 rad/s. How long is the string?

(a) 2.75 m (b) 4.14 m (c) 6.54 m (d) 8.91 m (e) 9.81 m

(a) 0.5 rad/s (b) 2.0 rad/s (c) 4.0 rad/s

A 2.4 kg object is attached to one end of a spring with force constant k = 9000 N/m, and the other end of the spring is fixed. You pull the mass so that the spring is stretched 0.1 m from equilibrium, and then let go so that the mass starts oscillating back and forth. You can ignore gravity and friction.

What is the total mechanical energy of the system after you let go of the mass?

(a) 22.5 J (b) 9 J (c) 5 J (d) 90 J (e) 45 J

(a) E_{new} = 2 E_{tot} (b) E_{new} = E_{tot} / 2 (c) E_{new} = E_{tot}

A block of wood has a mass of 25 kg and a volume of 0.04 m^{3}. This block of wood (which would normally float on the surface) is held under water by a string tied to the bottom of the pool. The density of the water in the pool is 1000 kg/m^{3}.

What is the magnitude of the buoyant force acting on the block?

(a) 98 N (b) 147 N (c) 245 N (d) 392 N (e) 517 N

(a) equal to the weight of the block. (b) greater than the weight of the block. (c) less than the weight of the block.

Hose A has an inner radius of 2 cm and water flows through it with a speed of 50 m/s. Hose A is attached hose B, which has a larger inner radius. The speed of the water in hose B is measured to be 2 m/s.

What is the inner radius of hose B?

(a) 1 cm (b) 4 cm (c) 6 cm (d) 8 cm (e) 10 cm

(a) P_{A} < P_{B} (b) P_{A} = P_{B} (c) P_{A} > P_{B}

(a) Exactly half of the ball in bucket B is under water. (b) More than half of the ball in bucket B is under water. (c) Less than half of the ball in bucket B is under water.

(a) increases. (b) decreases. (c) stays the same.

(a) 1.2 × 10^{6} J (b) 1.7 × 10^{6} J (c) 2.2 × 10^{6} J (d) 2.7 × 10^{6} J (e) 3.2 × 10^{6} J