12. Rotational Kinematics

Equations of Rotational Motion

12. Rotational Kinematics

# Equations of Rotational Motion - Video Tutorials & Practice Problems

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## Equations of Rotational Motion

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## Rotational velocity of disc

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Problem

ProblemA tiny object spins with 5 rad/s around a circular path of radius 10 m. The object then accelerates at 3 rad/s^{2}. Calculate its angular speed 8 s after starting to accelerate.

BONUS:Calculate its linear displacement in the 8 s.

A

19 rad/s

B

29 rad/s

C

43 rad/s

D

53 rad/s

4

Problem

ProblemThe turntable of a DJ set is spinning at a constant rate just before it is turned off. If the turntable decelerates at 3 rad/s^{2} 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

33.6 RPM

B

321 RPM

C

2,016 RPM

D

3,167 RPM

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PRACTICE PROBLEMS AND ACTIVITIES (20)

- A high-speed flywheel in a motor is spinning at 500 rpm when a power failure suddenly occurs. The flywheel has...
- An electric fan is turned off, and its angular velocity decreases uniformly from 500 rev/min to 200 rev/min in...
- An electric fan is turned off, and its angular velocity decreases uniformly from 500 rev/min to 200 rev/min in...
- 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...
- 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...
- An electric turntable 0.750 m in diameter is rotating about a fixed axis with an initial angular velocity of 0...
- 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...
- A wheel of diameter 40.0 cm starts from rest and rotates with a constant angular acceleration of 3.00 rad/s^2....
- (I) Pilots can be tested for the stresses of flying high-speed jets in a whirling “human centrifuge,” which ta...
- (II) Assume that a 1.00-kg ball is thrown solely by the action of the forearm, which rotates about the elbow j...
- (I) The blades in a blender rotate at a rate of 8500 rpm (rpm = revolutions per minute = rev/min) . When the m...
- An 18-cm-long bicycle crank arm, with a pedal at one end, is attached to a 20-cm-diameter sprocket, the toothe...
- A ceiling fan with 80-cm-diameter blades is turning at 60 rpm. Suppose the fan coasts to a stop 25 s after bei...
- A ceiling fan with 80-cm-diameter blades is turning at 60 rpm. Suppose the fan coasts to a stop 25 s after bei...
- A high-speed drill reaches 2000 rpm in 0.50 s. (a) What is the magnitude of the drill's angular acceleration?
- The 2.0 kg, 30-cm-diameter disk in FIGURE P12.65 is spinning at 300 rpm. How much friction force must the brak...
- (I) Pilots can be tested for the stresses of flying high-speed jets in a whirling “human centrifuge,” which ta...
- (II) A cooling fan is turned off when it is running at 780 rev/min . It turns 1250 revolutions before it comes...
- (II) Calculate the average angular velocity of a clock’s second hand, its minute hand, and its hour hand. St...
- (II) Calculate the angular velocity of the Earth (a) in its orbit around the Sun, and (b) about its axis.