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Question :
41. A solid cylinder (I = MR2/2) has a string : 2102158

41. A solid cylinder (*I* = *MR*^{2}/2) has a string wrapped around it many times. When I release the cylinder, holding on to the string, the cylinder falls and spins as the string unwinds. What is the downward acceleration of the cylinder as it falls?

A. 0

B. 4.9 m/s^{2}

C. 6.5 m/s^{2}

D. 9.8 m/s^{2}

42. A 40-kg boy is standing on the edge of a stationary 30-kg platform that is free to rotate. The boy tries to walk around the platform in a counterclockwise direction. As he does:

A. the platform doesn't rotate.

B. the platform rotates in a clockwise direction just fast enough so that the boy remains stationary relative to the ground.

C. the platform rotates in a clockwise direction while the boy goes around in a counterclockwise direction relative to the ground.

D. both go around with equal angular velocities but in opposite directions.

43. A rod of length *L* is hinged at one end. The moment of inertia as the rod rotates around that hinge is *ML*^{2}/3. Suppose a 2.00-m rod with a mass of 3.00 kg is hinged at one end and is held in a horizontal position. The rod is released as the free end is allowed to fall. What is the angular acceleration as it is released?

A. 3.70 rad/s^{2}

B. 7.35 rad/s^{2}

C. 2.45 rad/s^{2}

D. 4.90 rad/s^{2}

44. Two hoops or rings (*I* = *MR*^{2}) are centered, lying on a turntable. The smaller ring has radius = 0.050 m; the larger has radius = 0.10 m. Both have a mass of 3.0 kg. What is the total moment of inertia as the turntable spins? Ignore the mass of the turntable.

A. 0.030 kg?m^{2}

B. 0.007 5 kg?m^{2}

C. 0.038 kg?m^{2}

D. 0.075 kg?m^{2}

45. An automobile accelerates from zero to 30 m/s in 6.0 s. The wheels have a diameter of 0.40 m. What is the average angular acceleration of each wheel?

A. 5.0 rad/s^{2}

B. 15 rad/s^{2}

C. 25 rad/s^{2}

D. 35 rad/s^{2}