Question:

A child sitting 1.20 m from the center of a merry-go-round moves with a speed of 1.10 m/s. Calculate

- the centripetal acceleration of the child and
- the net horizontal force exerted on the child (mass = 22.5 kg).

Source: Giancoli, Douglas C., Physics: Principles with Applications, 7th Edition, 2014.

Quick Answer:

- $1.01\textrm{ m/s}^2$
- $22.7\textrm{ N}$

### Transcript for this Giancoli solution

This is Giancoli Answers with Mr. Dychko. This child sitting on the merry go round at a point that’s 1.2 meters from the center, traveling with a tangental velocity of 1.1 meters per second, will experience a centripetal acceleration of*v squared*over

*r*which is 1.1 meters per second squared divided by 1.2 meters which is 1.01 meters per second squared. So that’s the acceleration radially or towards the center of the circle. The centripetal force that is responsible for that acceleration is gonna be the child’s mass of 22.5 kilograms times the centripetal acceleration 1.0083; we use the unrounded number in our calculations and we round only our final answers up here. And we get 22.7 Newtons with 3 significant figures.