A 35 kg child moves with uniform circular motion while riding a horse on a carousel. The horse is 3.2 m from the carousel's axis of rotation and has a tangential speed of 2.6 m/s. what is the child's centripetal acceleration?

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Answer 1 · 2017-11-29T17:41:54

The child's centripetal acceleration is $2.1125m \/s^2$ .

Newton's second law relates force $F$ , mass $m$ and acceleration $a$ .

$F=ma$

The centripetal force required to keep an object of mass $m$ with tangential velocity $v$ at a radius $r$ is:

$F=(mv^2)/r$

Combining these two equations gives:

$ma=(mv^2)/r$

Mass $m$ is a factor of both sides and cancels out.

$a=v^2/r$

In the case of the child $v=2.6$ and $r=3.2$ . So the centripetal acceleration $a$ is:

$a=2.6^2/3.2=2.1125$