Question

Which of the following changes to the system would result in a larger centripetal acceleration? The length of the sling is increased and the linear velocity of the stone stays the same. A decrease in the angular velocity of the stone . A decrease in the linear velocity of the stone. The length of the sling is increased and the angular velocity of the stone stays the same. None of the choices. All of the the choices.

Answer 1

Answer:

The length of the sling is increased and the linear velocity of the stone stays the same.

Explanation:

Centripetal acceleration is given by

$a_C = \dfrac{v^2}{r}$

where v is the linear velocity and r is the radius of motion.

In terms of the angular velocity, ω

$a_C = \omega^2r$,   since $v=\omega r$

From the relation, $a_C$ is directly proportional to the square of the velocity and inversely proportional to the radius.

Hence, an increase in linear velocity results in an increase in the centripetal acceleration if the radius is kept constant. A decrease in the radius also causes an increase of the centripetal acceleration.