It would be easy just to say that all you have to do is plug the values into a formula for determining angular velocity and linear velocity, but each question will have its own challenges.....the most direct path to the answer will be to determine what units you are asked to have your answer in and set up your question accordingly. With that said, there are some general formulas that may assist you.
Linear Velocity....as the name implies....deals with speed in a straight line, the units are often km/hr or m/s or mph (miles per hour).
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Angular Velocity....as the name implies...deals with speed through an angle, or in a circular motion, the units are often radians per second or degrees per second.
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To relate the two types of velocity to each other, we can use the following relationship:
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where r = radius
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Example 1
Linear Velocity
Driving to Moose Jaw took Bob 40 minutes to travel the 70 kms. Determine his speed in km / hr.
Example 2
Angular Velocity
A merry-go-round makes one revolution every four seconds. Determine it's angular velocity in radians /second.
Example 3
a) A car's tire revolves 400 times per minute. Determine the angular velocity in rads /minute.
b) Determine the angular velocity in degrees /second.
Example 4
A ferris wheel with a radius of 6m rotates once every 20 seconds.Determine the linear speed of a rider in meters/second.
