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 105; the average score was 78.6; the median score was 84. The exam period was 90 minutes. Click here to see page1 page2 of the formula sheet that came with the exam.

A small solid cylinder of mass M and radius R is released from rest at the top of a hill. The height of the hill is H . The cylinder rolls without slipping down the hill. Assume no energy is lost to friction.

When the cylinder is part of the way down the hill, the magnitude of its acceleration is a. What is the magnitude of the torque about an axis through the center of the cylinder due to the static friction between the cylinder and the surface?

(a) MR^{2}a (b) MRa/2 (c) MRa (d) MR^{2}a (e) MRa/4

(a) greater than MgH. (b) equal to MgH. (c) less than MgH.

(a) 12.4 m/s (b) 18.1 m/s (c) 16.2 m/s (d) 24.3 m/s (e) 32.5 m/s

(a) greater than V. (b) equal to V. (c) less than V.

A student of mass 60 kg stands at the edge of the platform of a merry-go-round, which is a uniform circular disk of radius 2 m and mass 200 kg. Assume that the student can be treated as a point mass.

If the merry-go-round rotates at an angular velocity of 2 rad/s around its axis, what is the angular momentum of the system consisting of student plus merry-go-round around the axis of rotation of the platform?

(a) 60 kg-m^{2}/s (b) 100 kg-m^{2}/s (c) 200 kg-m^{2}/s (d) 520 kg-m^{2}/s (e) 1280 kg-m^{2}/s

(a) 2.8 rad/s (b) 2.0 rad/s (c) 4.6 rad/s (d) 4.0 rad/s (e) 0.5 rad/s

(a) smaller (b) equal (c) larger

Disk A has moment of inertia 10 kg-m^{2} and initial angular velocity ω = 20 rad/s about its axis. Disk B has moment of inertia 30 kg-m^{2} and is initially at rest. Disk A is then dropped onto Disk B so that they stick together and their axes line up. What is the angular velocity of the combined disks about their mutual axis?

(a) 5 rad/s (b) 10 rad/s (c) 15 rad/s (d) 20 rad/s (e) 25 rad/s

(a) K_{before} < K_{after} (b) K_{before} = K_{after} (c) K_{before} > K_{after}

Calculate the density of fluid B.

(a) ρ_{B} = 500 kg/m^{3} (b) ρ_{B} = 666 kg/m^{3} (c) ρ_{B} = 1000 kg/m^{3} (d) ρ_{B} = 1500 kg/m^{3} (e) ρ_{B} = 2000 kg/m^{3}

While waiting to get into the elevator that goes to the observation floor in the Sears Tower in Chicago, you suspend your keys from a thread and set the resulting pendulum oscillating. It completes exactly 90 cycles in 1 minute. Assume that the angle through which the pendulum swings is small.

What is the length of the thread?

(a) 7 cm (b) 11 cm (c) 15 cm (d) 19 cm (e) 23 cm

(a) more than 90 cycles in 1 minute. (b) exactly 90 cycles in 1 minute. (c) less than 90 cycles in 1 minute.

(a) 33000 N (b) 38000 N (c) 42000 N

A block of mass 1.5 kg is suspended from the ceiling by a spring with spring constant k= 15 N/m. A force of 20 N is applied to the block in the +y-direction, thereby compressing the spring (see picture). The block is initially at rest. At time t = 0, the force is removed and the block starts to oscillate down and up.

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) 2 (b) 5 (c) 8

(a) a(t) = -A ω^{2} sin(ωt) (b) a(t) = -A ω^{2} cos(ωt) (c) a(t) = -A ω^{2} tan(ωt)

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

A funnel of water is connected to pipes as shown in the figure. The top of the funnel is sufficiently large that the speed downwards of the water (ρ = 1000 kg/m^{3}) at the top of the funnel is nearly zero. The water is observed to be moving at 2.0 m/s through the pipe at point B and the water is observed to exit pipe C at a speed of 2.8 m/s. Note that the pressure at point C is the atmospheric pressure.

Compare the pressure at point A in the funnel with the pressure at point C in the horizontal pipe. Assume that the speed at point A is 0.5 m/s.

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

(a) P_{B} - P_{Atm} = 1.6 × 10^{4} N/m^{2} (b) P_{B} - P_{Atm} = 1.8 × 10^{4} N/m^{2} (c) P_{B} - P_{Atm} = 2.0 × 10^{4} N/m^{2} (d) P_{B} - P_{Atm} = 2.2 × 10^{4} N/m^{2} (e) P_{B} - P_{Atm} = 2.4 × 10^{4} N/m^{2}

(a) r_{c} = 0.110 m (b) r_{c} = 0.127 m (c) r_{c} = 0.178 m

(a) 1.2 m (b) 1.4 m (c) 1.6 m

A plastic cube with length 0.3 m on each side is floating in a pool of water (ρ = 1000 kg/m^{3}). A cylinder with volume 0.005 m^{3 }is supported by a string attached to the upper cube. The tension T in the string attaching the two objects is 24.5 N. The system is at equilibrium with the cube submerged a distance h = 0.2 m.

Calculate the mass of the submerged cylinder.

(a) 2.5 kg (b) 5.0 kg (c) 7.5 kg (d) 10.0 kg (e) 15.0 kg

(a) 13.0 kg (b) 15.5 kg (c) 18 kg (d) 20.5 kg (e) 23.0 kg

(a) sink lower in the water (h increases). (b) stay at the same level (h remains the same). (c) float higher in the water (h decreases).