PHY $203$ Homework #$8$ NAME:

$1.$ A child is sitting on the outer edge of a merry$-$go$-$round, at a distance $12$ m from the center.

a$)$ If the merry$-$go$-$round makes $5$ revolutions in $1$ minute, what is the child$$s speed, in m$/$s$?$

$($Hint: in one revolution, the distance the child travels equals the circumference of the merry$-$

go$-$round, C $=2$r$.)$

b$)$ Compute the magnitude of the child$$s acceleration, assuming the child travels at a constant

speed along this circular path.

c$)$ In what direction does this acceleration lie?

d$)$ Suppose the merry$-$go$-$round$$s speed calculated in part $($a$)$ doubles. After this doubling,

what is the new magnitude of the child$$s acceleration?

e$)$ Suppose the child moves closer to the center of the merry$-$go$-$round, at a new radius of $6$

m$.$ Assuming the child is traveling at the doubled speed calculated in part $($d$),$ what is the

new magnitude of the child$$s acceleration?

e$)$ Suppose the child moves even closer to the center of the merry$-$go$-$round, at a new radius

of $3$ m$.$ If the merry$-$go$-$round slows down so that the child is only traveling at a speed of $0\mathrm{.}5$

m$/$s$,$ what is the new magnitude of the child$$s acceleration?