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 114. The exam period was 90 minutes. The mean score was 73.1; the median was 74. Click here to see page1 page2 of the formula sheet that came with the exam.

Unless told otherwise, you should assume that the acceleration of gravity near the surface of the earth is 9.8 m/s^{2} downward and ignore any effects due to air resistance.

In the figure below, A is a circular cylinder of radius R with moment of inertia I (> 0). B is an identical cylinder except that a point mass of mass m_{p} (> 0) is attached at the center.

We release the cylinders gently at the top of the slope in the figure without motion.

Suppose the slope is frictionless. After sliding down the slope for 1 m (see the figure), which has a faster translational motion??

(a) A (b) B (c) A and B have the same speed.

(a) 5.85 N (b) 8.90 N (c) 11.7 N (d) 15.8 N (e) 21.3 N

Consider a pulley made of two connected cylinders of radius R and R/2 as shown in the figure. The moment of inertia of the pulley is I. Two blocks with the same mass M are hung with weightless strings that do not slip against the pulley.

The masses start to move and the pulley starts to rotate from the initial stationary condition. M = 1.2 kg and R = 1.5 m. When the right mass goes down by 1 m, what is the total kinetic energy of the system? Notice that the distance the left mass moves is just half of the right mass.

(a) 3.7 J (b) 4.8 J (c) 5.9 J (d) 7.0 J (e) 8.1 J

(a) 0.5 v_{0} (b) 1.0 v_{0} (c) 1.1 v_{0} (d) 1.4 v_{0} (e) none of the above

There is a weightless bar of length 1 m. At one end A is a mass M = 30 kg and at the other end B is a mass m = 5 kg. The bar is at rest on the pivot P. (Note: Assume + is for counterclockwise rotation.)

What is the torque around B due to mass M?

(a) +294 Nm (b) +187 Nm (c) 0 (d) -187 Nm (e) -294 Nm

(a) +98 Nm (b) +49 Nm (c) 0 (d) -49 Nm (e) -98 Nm

There is a table whose top surface is frictionless and horizontal. A massive pulley is attached to its edge and two masses M_{1} and M_{2} are connected with a weightless string passing though the pulley as illustrated below. The block M_{1} has mass 1.3 kg and M_{2} = 5 kg. The string does not slip against the pulley whose radius R is 30 cm and whose moment of inertia is I= 1.2 kgm^{2}.

The tension T_{1} is 11.9 N. Find the angular acceleration of the pulley.

(a) 1.1 rad/s^{2} (b) 2.2 rad/s^{2} (c) 3.3 rad/s^{2} (d) 4.4 rad/s^{2} (e) 5.5 rad/s^{2}

(a) larger (b) smaller (c) not enough information

A round horizontal table is turning freely. It has a moment of inertia I = 60 kgm^{2} with a radius R = 2 m. On the table stands a child of mass 15 kg. In the following you may ignore the size (cross section) of the child (i.e., you may regard her as a point mass).

From the initial position at the edge of the table the child moves to the center. What happens to the angular speed of the table?

(a) It speeds up. (b) It slows down. (c) It stays the same speed.

(a) 170 kg m^{2}/s (b) 245 kg m^{2}/s (c) 420 kg m^{2}/s (d) 560 kg m^{2}/s (e) 720 kg m^{2}/s

Two blocks moving in a straight line, along the x-axis, on a frictionless, horizontal surface collide in a completely elastic collision (no energy is lost in the collision).

Block 1 has m_{1} = 2 kg, v_{1} = 3.3 m/s, Block 2 has m_{2} = 0.1 kg, v_{2} = -3.3 m/s.

What is the magnitude of the total momentum of the blocks after the collision?

(a) less than it was before the collision (b) the same as it was before the collision (c) more than it was before the collision

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

(a) yes (b) no (c) It is impossible to tell from the information given.

(a) v_{x} = +16 m/s, v_{y} = -2 m/s (b) v_{x} = -17 m/s, v_{y} = +1.3 m/s (c) v_{x} = -24 m/s, v_{y} = -4 m/s (d) v_{x} = -17 m/s, v_{y} = -1.3 m/s (e) v_{x} = -25 m/s, v_{y} = +2 m/s

A car of mass M = 1000 kg is moving in a straight line on level ground at 70 m/s. It applies its brakes and slides (skids) to a halt. Which one of the following forces does nonzero work?

(a) normal force (b) gravitational force (c) kinetic friction (d) static friction (e) centripetal force

(a) M g h (b) 0 (c) (1/2) M v^{2}

(a) 300,000 J (b) 2,940,000 J (c) 4,400,000 J (d) 10,100,000 J (e) 39,000,000 J

A box sits on the floor. A force F = 200 N is then applied to the right but slightly upward at an angle of 30° from the horizontal (see diagram) such that the box moves 5 meters horizontally to the right. How much work is done by the force?

(a) 50 J (b) 866 J (c) 1900 J (d) 2430 J (e) 3230 J

(a) less than when the force was applied at an angle (b) the same as when the force was applied at an angle (c) more than when the force was applied at an angle

(a) 10 W (b) 18 W (c) 30 W (d) 40 W (e) 44 W

(a) 0 (b) 0.01 J (c) It is impossible to tell from the information given.

(a) 0.98 kg m/s (b) 1.2 kg m/s (c) 1.9 kg m/s (d) 2.0 kg m/s (e) 4.7 kg m/s

(a) 0 (b) 2 (c) 3 (d) 3.5 (e) 4