Angular speed - Math Central

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Question from Julie, a student:

If the angular speed of a circle is 360 degrees divided by the time it took to rotate,
how do I calculate ones that have greater rotations than the amount of time?
I mean, you calculate the angular speed of a merry-go-around that spins once every 5 seconds
by doing 360degrees/5 sec, but how do you calculate a merry-go-around that has 16 rotations every 4 seconds?

Hi Julie,

If you want the angular speed in degrees per second then you divide the number of degrees of rotation by the time it took in seconds. That's what you did for the merry-go-round that rotated once (360 degrees) in 5 seconds to get 360/5 = 72 degrees per second. When the merry-go-round increased its speed to 16 rotations every 5 seconds that's 16 × 360 = 5760 degrees every 5 seconds or 5760/5 = 1152 degrees per second.

Penny

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