15. A length of rope is wrapped around a spool of weight W with inner radius r and outer radius R as shown above. The rope is pulled with a tension 7 at an angle 0. Which of the following conditions must be satisfied for the spool to slide uniformly without rolling? (A) cose = r/R (B) sine = r/R (C) T = W (D) T = W sine (E) T= W cose F = 20 N r= 1 m R = 2 m 6. Two wheels with fixed hubs, each having a mass of 10 kg and forces applied as shown. The forces rotate the wheels from rest at a constant rate. The moment of inertia of each wheel is MR2. In order to impart equal angular accelerations about their hubs, how large must F' be? (A) 10 N (B) 20 N (C) 30 N (D) 40 N (E) 50 N 7. A uniform disk, a thin hoop and a uniform sphere all with the same mass and outer radius, are simultaneously released from the top of an incl of an inclined plane. Rank objects according to the velocities at the bottom of the incline, from least to greatest. (A) Disk, hoop, sphere (B) Sphere, disk, hoop (C) Hoop, sphere, disk (D) Disk, sphere hoop (E) Hoop, disk, sphere 0.2 m 6 k9 / 9. A 2.0 kg mass is attached to a string that is wrapped around a uniform pulley of mass 8.0 kg. The moment of inertia of the pulley is 1 = 1/2 MR. The string doesn't slip. What is the acceleration of the suspended mass when it is released from rest? 8. A 6.0 kg rock is suspended by a string from one end of a uniform meter stick. What is the mass of the stick if it is balanced by a support at the 0.2 m mark? (A) 5.0 m/s2 (B) 4.0 m/s2 (C) 3.0 m/s2 (D) 2.0 m/s? (E) 1.0 m/s? ( A) 0.5 ka (B) 1.0 kg (C) 2.5 kg (D) 3.0 kg (E) 4.0 kg 13. A thin ring of mass m and radius / rolls across the floor with a velocity v. Which of the following would be the best estimate of the ring's total kinetic energy as it rolls across the floor? I = mR2 (A) mv2 (B) 1/2 my2 (C) 14 mvz (D) muz+ moz ( E ) = muz + mx 2 4F 2F 4. A light rigid rod with two masses attached to its ends is pivoted about a horizontal axis into the of the system? page. The system rotates with a constant angular velocity w. What is the angular momentum (A) 20ML ZW (B) 18MLZW (C) 16ML2W (D) 12MLZW (E) 8MLZW 5. A turntable that is initially at rest is set in motion with a constant angular acceleration a. What is the angular velocity of the turntable after it has made five complete revolutions (A) V5na (B) 3V7na (C) 2V5na (D) V3na (E) Vina 17. A particle is moving in a circle of radius 2 m according to the relation 0 = 612 + 4t. The speed of the particle at t = 4 s is: B (A) 52 m/s (B) 104 m/s (C) 226m/s (D) 352 m/ s (E) 438 m/ s