Question

A ladybug initially sits at the outer edge of a merry-go-round and completes one revolution every second. Bored with life on the outer edge the ladybug heads to a new position halfway between the axis of rotation and her initial position. The centripetal acceleration of the ladybug in her new position is _________ of her original centripetal acceleration. Select the answer that correctly completes the previous sentence.

Answer 1

Half of her original centripetal acceleration

Step-by-step explanation:

Centripetal force Fc = mrw^2

Where m is mass, w is angular speed and r is the radius.

Recall that force F = ma

Where a is acceleration.

Comparing the two force, one can see that centripetal acceleration Ac is equal to rw^2.

For initial position, radius is equal to r, therefore Ac = rw^2

For second position, radius = r/2, therefore Ac = (rw^2)/2

Comparing the two acceleration, one can see that the acceleration for the final position is half the acceleration of the original position.