About angular velocity and tangential/linear velocity in rotational motion

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bonoz

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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.

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"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?"

--- Under the same frequency, that's basically it. However, it doesn't hold truth with diff. frequencies.
 
"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?"

--- Under the same frequency, that's basically it. However, it doesn't hold truth with diff. frequencies.

By frequency you mean the complete cycles per second? how would that change things? isn't frequency dependent on how fast the circle is completing a complete cycle?
 
By frequency you mean the complete cycles per second? how would that change things?
uhm ... How about in a sitution that you want to keep a constant speed as an object approaches the center? You would increase its frequency right?

In your scenario, the frequency must be held constant in order for the object to slow down as it moves toward the center.

isn't frequency dependent on how fast the circle is completing a complete cycle?
You might be thinking 'bout Period (T) I supposed.
 
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