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 101. The exam period was 90 minutes; the average score was 79.4; the median score was 84. Click here to see the formula sheet that came with the exam.

A solid puck with radius R_{1} = 1 m and mass M = 1.5 kg is sitting on a frictionless table. A top view of the puck is shown in the figure. Three constant forces are applied to the puck as shown: F_{1} = 3 N and F_{2} = 5 N are applied at radius R_{1}, while F_{3} = 4 N is applied at radius R_{2} = 0.4 m. The moment of inertia for the puck is I = MR^{2}/2.

What is the angular acceleration of the puck?

(a) 0.5 rad/s^{2} (b) 1.9 rad/s^{2} (c) 2.1 rad/s^{2} (d) 2.8 rad/s^{2} (e) 6.0 rad/s^{2}

(T) True (F) False

(a) 1 s (b) 2 s (c) 3 s (d) 4 s (e) 5 s

A block of mass m_{1} = 1 kg sits atop a frictionless plane and is connected to mass m_{2} = 2 kg through a string that goes over a pulley of mass M_{pulley} = 4 kg and radius R_{pulley} = 0.2 m. The pulley rotates about its axis without friction and the string moves over the pulley without slipping. The system starts at rest and mass m_{2} falls through a height H = 2 m. The moment of inertia of the pulley is I = MR^{2}/2.

What is the velocity (v) of mass m_{2} immediately before it hits the ground?

(a) v = 2.4 m/s (b) v = 2.8 m/s (c) v = 3.1 m/s (d) v = 4.0 m/s (e) v = 5.1 m/s

(a) increase. (b) stay the same. (c) decrease.

A girl sits fixed on a merry-go-round of mass M = 500 kg and radius R = 2 m. The merry-go-round is initially at rest and is free to rotate without friction. The girl shoots a gun in a horizontal direction tangent to the outer edge of the merry-go-round as shown in the figure. The bullet has mass m = 0.025 kg and a speed v = 700 m/s relative to the ground. The moment of inertia of the merry-go-round is I = MR^{2}/2.

If you ignore the mass of the girl, what is the angular velocity ω of the girl and merry-go-round after the gun has been shot?

(a) ω = 0.009 rad/s (b) ω = 0.035 rad/s (c) ω = 0.11 rad/s (d) ω = 0.21 rad/s (e) ω = 0.47 rad/s

(a) ω' < ω (b) ω' = ω (c) ω' > ω

A plank of length L = 2 m and mass M = 3 kg sits atop two scales that are fixed to the ground. Scale 1 is at the left end of the plank and scale 2 is a distance D = 1.25 m from scale 1. A block having the same mass as the plank (3 kg) is placed 0.5 m from the left end of the plank as shown in the picture.

What does scale 2 read?

(a) 10.9 N (b) 22.6 N (c) 27.0 N (d) 35.3 N (e) 43.1 N

(a) directly over scale 2 (b) directly over the center of mass of the plank (c) a distance on 0.25 m to the right of scale 2

A cylinder of mass M sits on a rough incline, as shown. The cylinder is attached at its outer radius to a wall by a string that is parallel to the inclined surface. Friction between the cylinder and the incline keeps the bottom from moving. Compare the magnitude of the frictional force f acting on the cylinder to the tension in the string T.

(a) f = T (b) f < T (c) f > T

(a) Mg (b) Mg / 2 (c) Mg / 4 (d) Mg / 6 (e) Mg / 16

(a) B (b) A and C (c) B and D

A uniform, massless pole 6 m long is attached to a wall by a pivot at one end. The pole is held at an angle of 30° above the horizontal by a horizontal wire attached to the pole 4.0 m from the end pivot. A load of 60 kg hangs from the upper end of the pole.

What is the tension in the wire connecting the pole to the wall?

(a) 1190 N (b) 1270 N (c) 1340 N (d) 1480 N (e) 1530 N

(a) points up. (b) points down. (c) is zero.

A turntable has a mass of 1.14 kg and a radius of 0.17 m and is initially rotating freely at 78 rpm (ω_{i,t} = 8.168 rad/s). There are no external forces acting on the system. The moment of inertia of the turntable can be approximated by that of a disk (I_{disk} = MR^{2}/2).

A point particle, initially at rest, is dropped onto the turntable and sticks to it at a distance d = 0.10 m from its center as shown in the figure. The final angular velocity of the system is 72.7 rpm (7.613 rad/s). What is the mass of the particle?

(a) 0.038 kg (b) 0.070 kg (c) 0.102 kg (d) 0.116 kg (e) 0.120 kg

(a) Kf > Ki (b) Kf = Ki (c) Kf < Ki

A plank having length L = 2 m and mass M = 3 kg is suspended from the ceiling by a wire that is attached a distance d = 0.5 m from its left end. The right end is initially held up so that the plank is horizontal, but is then released.

What is the magnitude of the acceleration of the center of mass of the plank just after the right end is released?

(a) A_{cm} = 2.9 m/s^{2} (b) A_{cm} = 3.5 m/s^{2} (c) A_{cm} = 4.2 m/s^{2} (d) A_{cm} = 6.6 m/s^{2} (e) A_{cm} = 11.0 m/s^{2}

(a) = Mg (b) > Mg (c) < Mg

A grindstone of mass 17 kg and radius 0.6 m is initially rotating freely at 18π radians/s. An axe is brought into contact with the grindstone, which brings it to a stop in 7.3 seconds.

Assuming that the angular acceleration of the grindstone was constant as it slowed down, through what angle did the stone rotate during the 7.3 seconds it took to stop it?

(a) 180 radians (b) 206 radians (c) 211 radians (d) 223 radians (e) 278 radians

(a) 4893 J (b) 5129 J (c) 9753 J (d) 10234 J (e) 12345 J

(a) = W_{1} (b) > W_{1} (c) < W_{1}