This exam consists of 25 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. When the exam was given, the mean was 85.3; the median was 87. The maximum possible score is 113. Click here to see the formula sheet that came with the exam.

A bowling ball is a sphere of mass M = 2.0 kg and radius R = 0.10 m. It rolls without slipping on a horizontal surface with a center-of-mass speed V_{CM} = 3 m/s. What is the rotational speed of the ball in units of revolutions per minute (rpm)?

(a) 490 (b) 160 (c) 120 (d) 290 (e) 330

(a) 0.64 (b) 0.85 (c) 1.17 (d) 1.43 (e) 1.85

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

A solid cylinder has mass M = 1.5 kg and radius R = 0.25 m. A torque of magnitude t = 0.3 N-m is applied about the rotation axis. What is the angular acceleration of the cylinder?

(a) 0.4 rad/s^{2} (b) 6.4 rad/s^{2} (c) 3.4 rad/s^{2} (d) 1.5 rad/s^{2} (e) 2.3 rad/s^{2}

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

A star is a uniform sphere of mass M and radius R. It rotates about its center with angular velocity w . The star then collapses to radius R/10 (with the mass still M). What is the angular velocity of the star after its collapse?

(a) w / 100 (b) w / 10 (c) w (d) 10 w (e) 100 w

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

(a) shift his center of mass. (b) increase his moment of inertia about a horizontal axis. (c) reduce the torque due to gravity.

A big man (mass 100 kg) is riding his bicycle south at 4 m/s. A little man (mass 50 kg) rides his bicycle north at 10 m/s. You may neglect the mass of each bicycle.

Whose momentum is larger in magnitude?

(a) big man (b) little man (c) both are the same

(a) 4.0 m/s south (b) 3.3 m/s south (c) 0.33 m/s north (d) 0.67 m/s north (e) 3.3 m/s north

(a) 0 J (b) 1280 J (c) 3300 J (d) 4990 J (e) 6670 J

Two hockey players, each having an identical mass of 50 kg, are gliding across the ice toward the puck. Player A is moving at 3 m/s in the +x direction. Player B is moving at 4 m/s in the +y direction.

What is the magnitude of their total momentum?

(a) 5 kg m/s (b) 200 kg m/s (c) 250 kg m/s (d) 300 kg m/s (e) 460 kg m/s

(a) along the x axis (b) 27° (c) 53° (d) 109° (e) 220°

(a) The direction would be the same. (b) The direction would be closer to the x axis. (c) The direction would be closer to the y axis.

(a) 0.85 m/s (b) 1.25 m/s (c) 1.65 m/s (d) 2.00 m/s (e) 2.45 m/s

(T) True (F) False

(a) 0.15 m/s (b) 0.20 m/s (c) 0.24 m/s (d) 0.29 m/s (e) 0.33 m/s

A wheel of radius R rolls without slipping on a horizontal surface at a nonzero speed V. The instantaneous speed of the dot at the top of the wheel (see drawing) is:

(a) V (b) 2V (c) 0

(a) the dot (b) the diamond (c) they both have the same angular velocity

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

You have your bicycle upside down for repair. The front wheel is free to rotate about its axis and is perfectly balanced except for the 0.025 kg valve stem 0.3 m from the rotation axis. The location of the stem is at an angle q with respect to the horizontal, as shown in the figure. Gravity points downward in the figure.

For which of the following values of q is the torque about the wheel’s due to weight of the stem the smallest?

(a) 0° (b) 45° (c) 90°

(a) 0.176 Nm (b) 0.363 Nm (c) 0.014 Nm (d) 0.067 Nm (e) 0.214 Nm

A 5 m long uniform beam has a mass of 100 kg and is hanging vertically, supported by a cable which is 2 m from the right end of the beam. How far from the right end of the beam must a 50 kg box be placed in order that the beam be in static equilibrium?

(a) 0.5 m (b) 1.0 m (c) 1.5 m (d) 2.0 m (e) 3.0 m

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

(a) 150 (b) 300 (c) 450 (d) 600 (e) 750