Question

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

Answer 1

The speed must change by
`(1)/(√(2))` factor in order to have the same radial acceleration.

Step-by-step explanation:

The radial or centripetal acceleration is given by:

`a_(c) = (v^(2))/(r)`

Where:

v: is the speed = v₀

r: is the radius = r₀

`a_(c) = (v_(0)^(2))/(r_(0))` (1)

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

`a_(c) = (v^(2))/(r_(0)/2)` (2)

By equating equation (1) and (2):

`(v_(0)^(2))/(r_(0)) = (v^(2))/(r_(0)/2)`

`v^(2) = (v_(0)^(2))/(2)`

`v = (v_(0))/(√(2))`

Therefore, the speed must change by
`(1)/(√(2))` factor in order to have the same radial acceleration.

I hope it helps you!