Question

An object is traveling in a circular motion at constant speed. If the speed is doubled, the centripetal acceleration is changed by a factor of

Answer 1

Answer: the centripetal acceleration is changed by a factor of four

Explanation:  An object moving in a circular motion at constant speed has zero tangential acceleration but the direction of the tangential velocity vector changes as the object rotates. This change in direction of the tangential velocity vector results in centripetal acceleration ($a_c$) given by

$a_c=\frac{v^{2}}{r}$

where v=speed of object , r= radius of circular path

Thus if $v_2=2v_1$ then

$a_2=\frac{v_2^{2}}{r_2}=\frac{(2v_1)^{2}}{r_1}=4\times \frac{v_1^{2}}{r_1}=4a_1$

Thus If the speed is doubled, the centripetal acceleration is changed by a factor of four .