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

Answer:

$a_c=16m/s^2$

Step-by-step 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 $m/s^2$