An object is moving at a constant speed around a circle. (a) In which of these c

Question

An object is moving at a constant speed around a circle.
(a) In which of these cases does the magnitude of the centripetal acceleration of the object increase? (Assume all other factors are kept the same.)
- The object's speed doubles
- The object's speed is halved
- The radius of the circle doubles
- The radius of the circle is halved
(b) In which case does the centripetal acceleration increase the most?
- The object's speed doubles
- The object's speed is halved
- The radius of the circle doubles
- The radius of the circle is halved

Explanation / Answer

You know that centripetal acceleration is, by definition,

a = v2 / r Think about the math. (a) For a to increase, the object speed must increase, or the radius r must decrease. (b) Because v is squared, any increase in speed results in a much larger increase in a. eg. doubling v, makes a 4x bigger because of the exponential "power of 2" factor. Halving the radius only doubles a. --> This means the greatest a is caused by doubling the speed.

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