12. Rotational Kinematics

A cooling fan is turned off when it is running at 780 rev/min. It turns 1250 revolutions before it comes to a stop. How long did it take the fan to come to a complete stop?

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.

A wheel is rotating about an axis that is in the z-direction. The angular velocity ω_z is -6.00 rad/s at t = 0, increases linearly with time, and is +4.00 rad/s at t = 7.00 s. We have taken counterclockwise rotation to be positive. What is the angular displacement of the wheel at t = 7.00 s?

A ceiling fan with 80-cm-diameter blades is turning at 60 rpm. Suppose the fan coasts to a stop 25 s after being turned off. What is the speed of the tip of a blade 10 s after the fan is turned off?

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

A ceiling fan with 80-cm-diameter blades is turning at 60 rpm. Suppose the fan coasts to a stop 25 s after being turned off. Through how many revolutions does the fan turn while stopping?

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?

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/s², 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?

A high-speed drill reaches 2000 rpm in 0.50 s. What is the magnitude of the drill's angular acceleration?

A wheel is rotating about an axis that is in the z-direction. The angular velocity ω_z is -6.00 rad/s at t = 0, increases linearly with time, and is +4.00 rad/s at t = 7.00 s. We have taken counterclockwise rotation to be positive. Is the angular acceleration during this time interval positive or negative?

(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?

An electric turntable 0.750 m in diameter is rotating about a fixed axis with an initial angular velocity of 0.250 rev/s and a constant angular acceleration of 0.900 rev/s².

(a) Compute the angular velocity of the turntable after 0.200 s.

(b) Through how many revolutions has the turntable spun in this time interval?

The 2.0 kg, 30-cm-diameter disk in FIGURE P12.65 is spinning at 300 rpm. How much friction force must the brake apply to the rim to bring the disk to a halt in 3.0 s?

A wheel is rotating about an axis that is in the z-direction. The angular velocity ω_z is -6.00 rad/s at t = 0, increases linearly with time, and is +4.00 rad/s at t = 7.00 s. We have taken counterclockwise rotation to be positive. During what time interval is the speed of the wheel increasing? Decreasing?

An electric fan is turned off, and its angular velocity decreases uniformly from 500 rev/min to 200 rev/min in 4.00 s. Find the angular acceleration in rev/s² and the number of revolutions made by the motor in the 4.00-s interval.