9-10. A wall clock on Planet X has two hands that are aligned at midnight and turn in the same direction at uniform rates, one at 0.0435 rad/s and the other at 0.0163 rad/s. At how many seconds after midnight are these hands (a) first aligned and (b) next aligned?
9-19. Emilie’s potter’s wheel rotates with a constant 2.25 rad/s2 angular acceleration. After 4.00 s, the wheel has rotated through an angle of 60.0 rad. What was the angular velocity of the wheel at the beginning of the 4.00 s interval?
9-26. A flywheel with a radius of 0.300 m starts from rest and accelerates with a constant angular acceleration of 0.600 rad/s2. Compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim (a) at the start, (b) after it has turned through 60.00, (c) and after it has turned through 120.00.
9-28. Electric toothbrushes can be effective in removing dental plague. One model consists of a head 1.1 cm in diameter that rotates back and forth through a 70.00 angle 7600 times per minute. The rim of the head contains a thin row of bristles. (a) What is the average linear speed in each direction of the rotating head, in rad/s? (b) What is the average linear speed in each direction of the bristles against the teeth? (c) Using your own observations, what is the approximate speed of the bristles against your teeth when you brash by hand with an ordinary toothbrush?
9-43. A solid uniform 3.25 cylinder, 65.0 cm in diameter and 12.4 cm long weight over two massless frictionless pulleys as shown in Figure. The cylinder is free to rotate about an axel through its center perpendicular to its circular faces, and the system is released from rest. (a) How far must the 1.50 kg weight fall before it reaches a speed of 2.50m/s? (b) How fast is the cylinder turning at this instant?
9-58. Speedometer. Your car’s speedometer works in much the same way as its odometer, except that it converts the angular speed of the wheels to a linear speed of the car, assuming standard-size tires and no slipping on the pavement. (a) If your car has standard 24-inch-diameter tires, how fast are your wheels turning when you are driving at a free way speed of 55 mph? (b) How fast are you going when your wheels are turning at 500 rpm? (c) If you put on undersize 20-inch-diameter tires, what will the speedometer read when you are actually traveling at 50 mph?