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 page1 page2 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 θ_{1} and θ_{2}.

The relationship between θ_{1} and θ_{2} is:

(a) θ_{1} = 4 θ_{2} (b) θ_{1} = 2 θ_{2} (c) θ_{1} = θ_{2}

A cube (mass 2.50 kg, volume 0.0026 m^{3}) and a cylinder (mass 1.25 kg, volume 0.0026 m^{3}) 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 kg/m^{3}.

Let the buoyant force acting on the cube be F_{B,cube} and that acting on the cylinder F_{B,cylinder}. These buoyant forces are related by:

(a) F_{B,cube} > F_{B,cylinder} (b) F_{B,cube} = F_{B,cylinder} (c) F_{B,cube} < F_{B,cylinder}

(a) T_{cube} > T_{cylinder} (b) T_{cube} = T_{cylinder} (c) T_{cube} < T_{cylinder}

(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 = ½MR^{2}. 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 merry-go-round.

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

(T) True (F) False

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

Two discs of identical size, but different masses (M_{A} = 0.45 kg, M_{B} = 0.25 kg) are shown below. Initially, disc A is suspended directly over disc B and is rotating with constant angular speed ω_{A} = 12 rad/sec. Disc B is at rest on a frictionless surface. Viewed from above, A is rotating counterclockwise.

Then, A’s suspension breaks and it falls onto B. Later both disks move with the same angular velocity ω_{f}.

(a) ω_{f} = 12 rad/s (b) ω_{f} = 7.7 rad/s (c) ω_{f} = 6.0 rad/s

(a) KE_{after} / KE_{before} = 0.37 (b) KE_{after} / KE_{before} = 0.50 (c) KE_{after} / KE_{before} = 0.64 (d) KE_{after} / KE_{before} = 1.0 (e) KE_{after} / KE_{before} = 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) = -v_{max} sin(ωt) (b) v(t) = -v_{max} cos(ωt) (c) v(t) = +v_{max} cos(ωt)

(a) 2.5 m/s (b) 5.3 m/s (c) 7.8 m/s

(a) double. (b) quadruple. (c) be unchanged.

A section of pipe carries water (ρ = 1000 kg/m^{3}). In section a, the pipe has a diameter 0.04m, and the water is flowing to the right with velocity v_{a} = 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 v_{a}, the speed of the fluid in the pipe marked a with v_{b}, the speed of the fluid in section b of the pipe.

(a) v_{a} > v_{b} (b) v_{a} = v_{b} (c) v_{a} < v_{b}

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

(a) v_{a} > v_{c} (b) v_{a} = v_{c} (c) v_{a} < v_{c}

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

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

(a) slower. (b) at the same rate. (c) faster.

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 (c) same

(a) 1.5 m/s (b) 2.1 m/s (c) 2.8 m/s

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