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- Jun 21, 2007
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So a question asked what would happen to the the centripetal acceleration if a boy got off his horse in a merry go round and moved towards the center of the thing.
Now I know that centripetal acceleration = v^2/r = w^2 r
So I thought that since radius was decreasing acceleration would increase but I was wrong because as he moved towards the center his angular velocity (w) remained the same but his tangential/linear velocity (v) decreased.
I get it now.
But just to make sure I have it right, v is dependent upon how much of the "displacement" you cover as you go around the circle? and w is how much "angle-age" you cover as you go around the circle? But unlike v, it does not change as radius increases or decreases. v increases if your radius increases since you cover more distance, but it decreases as you move closer to the center since you're basically not covering any distance at all?
Is that right? thanks.
Now I know that centripetal acceleration = v^2/r = w^2 r
So I thought that since radius was decreasing acceleration would increase but I was wrong because as he moved towards the center his angular velocity (w) remained the same but his tangential/linear velocity (v) decreased.
I get it now.
But just to make sure I have it right, v is dependent upon how much of the "displacement" you cover as you go around the circle? and w is how much "angle-age" you cover as you go around the circle? But unlike v, it does not change as radius increases or decreases. v increases if your radius increases since you cover more distance, but it decreases as you move closer to the center since you're basically not covering any distance at all?
Is that right? thanks.