Centripetal acceleration confusion (TBR question)

[angldrps]

This is example 2.8a from TBR physics book on page 85.

A child riding on a merry go round jumps off a horse and starts walking towards center of the ride. As he moves, the acceleration he feels:
A. Increases, because tangential speed decreases
B/ Increases, because radius from center decreases
C. decreases, becasue tangential speed increases
D. decreases, because his radius from center decreases

I chose B. My reasoning was: formula Centripetal Acceleration= v^2/radius tells us that as the child moves towards the center, his radius decreases hence increasing his acceleration

TBR says that correct answer is D. The explanation says the tangential speed (i am assuming this is the 'v' in the above formula) decreases as child moves closer to center hence it is not ok to use Centripetal Acceleration= v^2/radius to solve this question . I remember learning that for circular motion, the magnitude of tangential velocity ,which is the speed, remains constant as its direction changes. So , how can tangential speed decrease?!?!

Can someone please help!

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[Pisiform]

yes you are right about the tangential speed remaining constant - but this happens only when radius is constant. However, when radius changes tangential velocity changes (v = 2 pi r /t = 2 pi f r = omega r). So as radius changes tangential velocity changes. The only thing that doesn't change when changing the radius is the angular frequency because the time taken to go around a circle would remain the same. So you would use a = omega^2 r. So as r decreases, acc decreases and omega is constant.

However, if there was a question in which a bike was going around a circular track and its speed was increasing, then you would have used a = v^2/r since radius is constant.

 

[Ssina]

It's like a disk that is rotating and you put two stickers one on the edge and one on the inside along a straight line through the center.... When you rotate the disk one revolution they are both at the same spot again, but the spot that is furthest from the center traveled a longer distance, essentially a bigger circumference in the same time, so it had to be traveling faster!

That's how I think about these questions any ways!

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[MedPR]

yes you are right about the tangential speed remaining constant - but this happens only when radius is constant. However, when radius changes tangential velocity changes (v = 2 pi r /t = 2 pi f r = omega r). So as radius changes tangential velocity changes. The only thing that doesn't change when changing the radius is the angular frequency because the time taken to go around a circle would remain the same. So you would use a = omega^2 r. So as r decreases, acc decreases and omega is constant.

However, if there was a question in which a bike was going around a circular track and its speed was increasing, then you would have used a = v^2/r since radius is constant.

This. The key to this problem is recognizing that you need to use a=w^2r and not a=v^2/r