BackAn 18-cm-long bicycle crank arm, with a pedal at one end, is attached to a 20-cm-diameter sprocket, the toothed disk around which the chain moves. A cyclist riding this bike increases her pedaling rate from 60 rpm to 90 rpm in 10 s. What is the tangential acceleration of a tooth on the sprocket?
(II) Calculate the angular velocity of the Earth (a) in its orbit around the Sun, and (b) about its axis.
Pilots can be tested for the stresses of flying high-speed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 26 complete revolutions before reaching its final speed. What was its final angular speed in rpm?
(II) Assume that a 1.00-kg ball is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 10–57. The ball is accelerated uniformly from rest to 8.5 m/s in 0.38 s, at which point it is released. Calculate the angular acceleration of the arm.
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A wheel of diameter 40.0 cm starts from rest and rotates with a constant angular acceleration of 3.00 rad/s2. Compute the radial acceleration of a point on the rim for the instant the wheel completes its second revolution from the relationship arad = ω2r.
A high-speed flywheel in a motor is spinning at 500 rpm when a power failure suddenly occurs. The flywheel has mass 40.0 kg and diameter 75.0 cm. The power is off for 30.0 s, and during this time the flywheel slows due to friction in its axle bearings. During the time the power is off, the flywheel makes 200 complete revolutions. At what rate is the flywheel spinning when the power comes back on?
Pilots can be tested for the stresses of flying high-speed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 26 complete revolutions before reaching its final speed. What was its angular acceleration (assumed constant)?
An electric fan is turned off, and its angular velocity decreases uniformly from 500 rev/min to 200 rev/min in 4.00 s. How many more seconds are required for the fan to come to rest if the angular acceleration remains constant at the value calculated in part (a)?