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angular velocity and angular acceleratoin

Could you please provide the answers and workings out to the following physics problems.

1. A wheel with a 0.10-m radius is rotating at 35 rev/s. It then slows uniformly to 15 rev/s over 3.0-s interval. What is the angular acceleration of a point on the wheel?
2. During the spin-dry cycle of a washing machine, the motor slows form 95 rad/s to 30 rad/s while the turning the drum through an angle of 402 radians. What is the magnitude of the angular acceleration of the motor?
3. An airplane engine starts from rest; and 2 seconds later, it is rotating with an angular speed of 300 rev/min. If the angular acceleration is constant, how many revolutions does the propeller undergo during this time?
A grindstone of radius 4.0 m is initially spinning with an angular speed of 8.0 rad/s. The angular speed is then increased to 10 rad/s over the next 4.0 seconds. Assume that the angular acceleration is constant.
4. What is the average angular speed of the grindstone?
5. What is the magnitude of the angular acceleration of the grindstone?
6. Through how many revolutions does the grindstone turn during the 4.0-second interval?

7. A wheel turns through an angle of 188 radians in 8.0s and its angular speed at the end of the period is 40 rad/s. If the angular acceleration is constant, what was the angular speed of the wheel at the beginning of the 8.0 s interval?

8. What is the tangential speed of a lug nut on a wheel of a car if the lug nut is located 0.114 m from the axis of rotation and the wheel is rotating at 6.53 rev/s?

9. A circular disk of radius 0.010 m rotates with a constant angular speed of 5.0 rev/s. What is the acceleration of a point on the angle of the disk?

10. A bicycle with wheels of radius 0.4 m travels on a level road at a speed of 8 m/s. What is the angular speed of the wheels?

11. A bicycle wheel of radius 0.70 m is turning at an angular speed of 6.3 rad/s as it rolls on a horizontal surface without slipping. What is the linear speed of the wheel?

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Solution Summary

It shows how to compute the angular velocity and angular acceleratoin of the rotation. The solution is detailed and well presented.

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