A boy on a bicycle rides in a circle of radius ro at speed vo. If the boy now rides at a radius equal to half the initial radius ro, by what approximate factor must he change his speed in order to have the same radial acceleration

The speed must change by factor in order to have the same radial acceleration.

Explanation:

The radial or centripetal acceleration is given by:

Where:

v: is the speed = v₀

r: is the radius = r₀

   (1)

If the radius is now equal to half the initial radius the speed must be:

   (2)

By equating equation (1) and (2):

Therefore, the speed must change by factor in order to have the same radial acceleration.      

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