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84 Torque 25. (II) Calculate the net torque about the axle ofthe wheel shown in Fig. 842. Assume that a friction torque of 0.60 m - N opposes the motion. 27. (II) Two blocks, each of mass m, are attached to the ends of a massless rod which pivots as shown in Fig. 843. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system when it is first released. 29. (II) Determine the net torque on the 2.0-m-long uniform beam shown in Fig. 845. All forces are shown. Calculate about (a) point C, the CM, and (b) point P at one end. \f9. A bicycle wheel has an outside diameter of 66 cm. Through what distance does a point on the rim move as the wheel rotates through an angle of 70? B i U Font Family AAA DE E E. 10. A bowling ball of mass 7.5 kg and diameter 18 cm rolls without slipping down a 10-m bowling lane with a constant speed 4.3 m/s. (a) Through what angle does the bowling ball turn as it travels the length of the lane? (b) What is the angular speed of the bowling ball? (c) Calculate the maximum radial acceleration that a point on the surface of the bowling ball could have. (d) Calculate the tangential acceleration of a point on the surface of the bowling ball. B i U Font Family AAA DEE12. A bicycle wheel has an initial angular speed of 7.2 rad/s. After turning through one-half of a revolution, the angular speed is reduced to 2.2 rad/s. If the angular acceleration of the wheel was constant during the motion, how long will it take the wheel to make the one-half revolution? B U Font Family 13. A turntable 45 cm in diameter starts from rest and makes its first complete revolution in 3.4 s with constant angular acceleration. If it maintains the same acceleration, how long will it take the turntable to make its second complete revolution? B i U Font Family 14. In the figure, a weightlifter's barbell consists of two identical small but dense spherical weights, each of mass 50 kg. These weights are connected by a thin 0.96-m rod with a mass of 24 kg. Find the moment of inertia of the barbell through the axis perpendicular to the rod at its center, assuming the two weights are small enough to be treated as point masses. 1 0.96 m- B i U Font Family19. A solid uniform ball of mass 1.0 kg and radius 1.0 cm starts from rest and rolls down a 1.0-m high ramp. There is enough friction on the ramp to prevent the ball from slipping as it rolls down. (a) What is the forward speed of the ball when it reaches the bottom of the ramp? (b) What would be the forward speed of the ball if there were no friction on the ramp? (c) Since the ball starts from the same height in both cases, why is the speed different? B i U Font Family21. The drive chain in a bicycle is applying a torque of 0.850 N . m to the wheel of the bicycle. The wheel has a moment of inertia of 0.100 kg . m . What is the angular acceleration of the wheel? B U Font Family AVA DE E . E .GO25. A 1.53-kg bucket hangs on a rope wrapped around a pulley of mass 7.07 kg and radius 66 cm. This pulley is frictionless in its axle, and has the shape of a solid uniform disk. After the bucket has been released, (a) what is the angular acceleration of the pulley, and (b) what is the acceleration of the bucket? B i U Font Family28. A 24.5-kg child is standing on the outer edge of a horizontal merry-go-round that has a moment of inertia of 989 kg .m about a vertical axis through its center and a radius of 2.40 m. The entire system (including the child) is initially rotating at 0.180 rev/s. Find the angular velocity if the child moves to a new position 1.10 m from the center of the merry-go-round. B i U Font Family 29. NASA puts a satellite into space that consists of two small 32-kg balls connected by a 12-m long light cable, as shown in the figure. The entire system is initially rotating at 4.0 rpm about an axis perpendicular to the cable at the center of mass. Motors in each mass reel out more cable so that the masses double their separation to 24 m. (a) What is the final rotational speed (in rpm) of the balls? (b) If the initial rotational kinetic energy of the system was K, what is the final rotational kinetic energy in terms of K ? 32 kg 12 m 32 kg 3 i U Font Family