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2 Name: 4. Two people are on a ride where the inside cars rotate at constant angular velocity three times the constant angular velocity of the outer cars. If the two cars are in line at t = 0, and moving at 3ω and ω respectively, at what time will they next pass each other? a. t = 0. π b. t = 2ω. c. t = π ω. d. t = 2π ω. e. t = 3π ω. 5. A small sphere attached to a light rigid rod rotates about an axis perpendicular to and fixed to the other end of the rod. Relative to the positive direction of the axis of rotation, the angular positions of the sphere are positive, its angular velocity is positive, and its angular acceleration is negative. The sphere is a. rotating clockwise and slowing down. b. rotating counterclockwise and slowing down. c. rotating clockwise and speeding up. d. rotating counterclockwise and speeding up. e. first rotating clockwise and then counterclockwise. 6. A particle whose mass is 2 kg moves in the xy plane with a constant speed of 3 m/s along the direction r8 = i 8 + j 8. What is its angular momentum (in kg m 2 /s) relative to the origin? a. 0k 8 b. 6 2 k 8 c. 6 2 k 8 d. 6k 8 e. 6k 8 2

3 Name: 7. A massless rope is wrapped around a uniform cylinder that has radius R and mass M, as shown in the figure. Initially, the unwrapped portion of the rope is vertical and the cylinder is horizontal. The linear acceleration of the cylinder is a. (2/3)g b. (1/2)g c. (1/3)g d. (1/6)g e. (5/6)g 8. A solid cylinder rolls without slipping down an incline as shown in the figure. The linear acceleration of its center of mass is a. (5/7)g sin θ b. (1/2)g sin θ c. (2/3)g sin θ d. (3/5)g sin θ e. (4/5)g sin θ 3

4 Name: 9. A force F ä is applied to a cylindrical roll of paper of radius R and mass M by pulling on the paper as shown. The acceleration of the center of mass of the roll of paper (when it rolls without slipping) is a. b. c. d. e. 1 F 2 M. F M. 3 F 2 M. 4 F 3 M. 2F M. 10. A hockey puck traveling at speed v on essentially frictionless ice collides with one end of a straight stick lying flat on the ice and sticks to that end. In this collision a. momentum is conserved. b. angular momentum is conserved. c. energy is conserved. d. all of the above are conserved. e. only momentum and angular momentum are conserved. 11. A uniform beam having a mass of 60 kg and a length of 2.8 m is held in place at its lower end by a pin. Its upper end leans against a vertical frictionless wall as shown in the figure. What is the magnitude of the force the pin exerts on the beam? a kn b kn c kn d kn e kn 4

5 Name: 12. Aluminum Rod#1 has a length L and a diameter d. Aluminum Rod#2 has a length 2L and a diameter 2d. If Rod#1 is under tension T and Rod#2 is under tension 2T, how do the changes in length of the two rods compare? a. They are the same. b. Rod#1 has double the change in length that Rod#2 has. c. Rod#2 has double the change in length that Rod#1 has. d. Rod#1 has quadruple the change in length that Rod#2 has. e. Rod#2 has quadruple the change in length that Rod#1 has. 13. Which one of the following cannot be a definition of an elastic modulus? ΔP a. V i ΔV Fh b. AΔx FL i c. AΔL ΔV d. V i ΔP stress e. strain 14. A 50-kg satellite circles planet Cruton every 5.6 h in an orbit with a radius of m. What is the magnitude of the gravitational force on the satellite by planet Cruton? a. 63 N b. 58 N c. 68 N d. 73 N e. 50 N 15. A satellite of mass m circles a planet of mass M and radius R in an orbit at a height 2R above the surface of the planet. What minimum energy is required to change the orbit to one for which the height of the satellite is 3R above the surface of the planet? a. GmM 24R b. GmM 15R c. GmM 12R d. 2GmM 21R e. 3GmM 5R 5

6 Name: 16. Two identical planets orbit a star in concentric circular orbits in the star's equatorial plane. Of the two, the planet that is farther from the star must have a. the smaller period. b. the greater period. c. the smaller gravitational mass. d. the larger gravitational mass. e. the larger universal gravitational constant. 6

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