Question

The centripetal acceleration of an object moving uniformly in a circle varies inversely with the radius of the circle. If the object feels acceleration of 20 m/s2 when the radius is 4 m, find the acceleration when the radius is 5 m.

Answer 1

`a_c=16m/s^2`

Explanation:

the centripetal acceleration is defined by the following formula:

`a=v^2/r`

where v is the tangential velocity, and r is the radius.

if we have an acceleration of
`20m/s^2` and a radius of 4m the equation becomes:

`20m/s^2=v^2/(4m)`

and from here we can find the tangential velocity of the object:

`v^2=(20m/s^2)(4m)\\v^2=80m^2/s^2`

we can use this quantity to find the centripetal acceleration when the radius is 5m.

Again using the centripetal acceleration formula:

`a=v^2/r`

we substitute
`v^2` and
`r=5m`:

`a_c=(80m^2/s^2)/(5m)\\a_c=16m/s^2`

the centripetal acceleration is 16
`m/s^2`