2) A child sits on a merry-go-round, 1.5 meters from the center. The merry-go-round is turning at a constant rate, and the child is observed to have a radial acceleration of 2.3m/s^2. How long does it take for the merry-go-round to make one revolution?

Answer 1

Circumference=pi * 2r = 3.14 * 3=9.42 m.

d = 0.5a*t^2 = 9.42
0.5*2.3*t^2 = 9.42
1.15t^2 = 9.42
t^2 = 8.19
t = 2.86 s.

Answer 2

radial acceleration=w^2*radius

but w=2PI/period

and we want period.

2.3=(2pi/T)^2 * 1.5
solve for T

Answer 3

8.8