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Chapter 10: Q89P (page 293)
A bicyclist of mass puts all his mass on each downward moving pedal as he pedals up a steep road. Take the diameter of the circle in which the pedals rotate to be , and determine the magnitude of the maximum torque he exerts about the rotation axis of the pedals.
Magnitude of maximum torque is
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Betweenand, the top of the leaning bell tower at Pisa, Italy, moved toward the south at an average rate of. The tower is tall. In radians per second, what is the average angular speed of the tower’s top about its base?
A small ball with massis mounted on one end of a rod long and of negligible mass. The system rotates in a horizontal circle about the other end of the rod at .
(a) Calculate the rotational inertia of the system about the axis of rotation.
(b) There is an air drag of on the ball, directed opposite its motion. What torque must be applied to the system to keep it rotating at constant speed?
Attached to each end of a thin steel rod of length and mass is a small ball of mass . The rod is constrained to rotate in a horizontal plane about a vertical axis through its midpoint. At a certain instant, it is rotating at . Because of friction, it slows to a stop in .Assuming a constant retarding torque due to friction, compute
(a) the angular acceleration,
(b) the retarding torque,
(c) the total energy transferred from mechanical energy to thermal energy by friction, and
(d) the number of revolutions rotated during the .
(e) Now suppose that the retarding torque is known not to be constant. If any of the quantities (a), (b), (c), and (d) can still be computed without additional information, give its value.
When a slice of buttered toast is accidentally pushed over the edge of a counter, it rotates as it falls. If the distance to the floor isand for rotation less than, what are the (a) smallest and (b) largest angular speeds that cause the toast to hit and then topple to be butter-side down?
A pulley, with a rotational inertia of about its axle and a radius of ,is acted on by a force applied tangentially at its rim. Theforce magnitude varies in time as ,with F in newtons and t in seconds. Thepulley is initially at rest. At what are its (a) angular acceleration and (b) angular speed?
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