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An airplane propellor turns at a constant rate of *3000* revolutions per minute. Find
its angular velocity in radians per second.

Angle turned through in one minute

= *(3000*rev*)= (3000)(2*rad*) = 6000*rad
* = (6000*rad*)/(60*s*) = 100*rad/s

*= 314*rad/s

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An airplane propellor spins up from zero to *3000*rpm (*314*rad/s) in ten seconds. What is its
angular acceleration in rad/s?

* = (314*rad/s *- 0)/(10*s*) = 31.4*rad/s.

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A model airplane flys in a circle with a radius of 10 meters. It circles once every ten
seconds. Find its speed relative to the ground.

First calculate the angular velocity in rad/s.

= (*2*rad*)/(10*s*) = 0.628*rad/s.

Next, use the relationship between angular and linear velocity:

*v = (10*m*)(0.628*rad/s*) = 6.28*m/s.

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A diver is suspended at the end of a long rope which is wound around a drum of radius 0.5m.
The drum is turned by a motor which spins up from zero to 6rad/s (about one rev/s) in one second.
Calculate the initial upward acceleration of the diver.

The acceleration of the rope in its direction of motion is the same all along its length. Calculate the
acceleration where the rope is on the drum by using the formula:

= (0.5m)(6rad/s) = 3m/s.

A yo-yo is supported by a string which is wound around its central post. The string unwinds
as the yo-yo descends. If the radius of the central post is half a centimeter (*0.005*m) and the
yo-yo is accelerating downward at *1*m/s, what is the
angular acceleration of the yo-yo around its central post?

Use the relation

and solve it for .
* = (1*m/s*)/(0.005*m*) = 200*rad/s.
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