Question

What are the period and (constant) speed of a person on a carousel if the person has an acceleration magnitude of 0.80 m/s2 (direction is toward the center) when she is standing 4.0 m from the axis? (b) what are her acceleration magnitude, and speed if she then moves in to a distance of 2.0 m from the carousel center and the carousel keeps rotating with the same period?

Answer 1

part a)

Centripetal acceleration is given as

`a_c = \omega^2 R`

`0.80 = \omega^2 * 4`

`\omega = 0.45 rad/s`

Now time period is given as

`T = (2\pi)/(\omega)`

`T = (2\pi)/(0.45)`

`T = 14.04 s`

constant speed is given as

`v = R \omega`

`v = 4* 0.45 = 1.8 m/s`

part b)

now when she is at radius r = 2 m

centripetal acceleration is given as

`a_c = \omega^2 R`

`a_c = 0.45^2 * 2 = 0.405 m/s^2`

now the linear speed is given as

`v = r\omega`

`v = 2 * 0.45 = 0.9 m/s`