12. Rotational Kinematics

A tiny object spins with 5 rad/s around a circular path of radius 10 m. The object then accelerates at 3 rad/s². Calculate its angular speed 8 s after starting to accelerate.

BONUS:Calculate its linear displacement in the 8 s.

The turntable of a DJ set is spinning at a constant rate just before it is turned off. If the turntable decelerates at 3 rad/s² and goes through an additional 30 rotations before stopping, how fast (in RPM) was the turntable initially spinning? 

BONUS:How long (in seconds) does the turntable take to stop?

(I) 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.

(a) What was its angular acceleration (assumed constant)?

(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

(a) the angular acceleration of the arm, and

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(I) The blades in a blender rotate at a rate of 8500 rpm (rpm = revolutions per minute = rev/min) . When the motor is turned off during operation, the blades slow to rest in 4.0 s. What is the angular acceleration as the blades slow down?

(I) 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.

(b) what was its final angular speed in rpm?

(II) A cooling fan is turned off when it is running at 780 rev/min . It turns 1250 revolutions before it comes to a stop.

(b) How long did it take the fan to come to a complete stop?

(II) Calculate the average angular velocity of a clock’s second hand, its minute hand, and its hour hand. State in rad/s .

(d) What is the average angular acceleration in each case?

(II) Calculate the angular velocity of the Earth (a) in its orbit around the Sun, and (b) about its axis.

A bicycle wheel has an initial angular velocity of 1.50 rad/s. (a) If its angular acceleration is constant and equal to 0.200 rad/s^2, what is its angular velocity at t = 2.50 s? (b) Through what angle has the wheel turned between t = 0 and t = 2.50 s?