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Chapter 10: Q9P (page 287)
A drum rotates around its central axis at an angular velocity of . If the drum then slows at a constant rate of .
(a) how much time does it take and
(b) through what angle does it rotate in coming to rest?
a. The time required to slow down is
b. The angle of the rotation when it coming to rest is
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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?
A uniform spherical shell of mass and radius can r otate about a vertical axis on frictionless bearings (Fig.). A massless cord passes around the equator of the shell, over a pulley of rotational inertia and radius,and is attached to a small object of mass .There is no friction on the pulley鈥檚 axle; the cord does not slip on the pulley. What is the speed of the object when it has fallen after being released from rest? Use energy considerations.
A pulsar is a rapidly rotating neutron star that emits a radio beam the way a lighthouse emits a light beam. We receive a radio pulse for each rotation of the star. The period T of rotation is found by measuring the time between pulses. The pulsar in the Crab nebula has a period of rotation of that is increasing at the rate of .
(a) What is the pulsar鈥檚 angular acceleration ?
(b) If is constant, how many years from now will the pulsar stop rotating?
(c) The pulsar originated in a supernova explosion seen in the year .Assuming constant a, find the initial T.
The angular acceleration of a wheel is , with is in radians per second-squared and in seconds. At time , the wheel has an angular velocity of and an angular position of .
Write expressions for (a) the angular velocity (rad/s) and (b) the angular position (rad) as functions of time (s).
In the overhead view of Fig. 10 - 24, five forces of the same magnitude act on a strange merry-go-round; it is a square that can rotate about point P, at mid-length along one of the edges. Rank the forces according to the magnitude of the torque they create about point P, greatest first.
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