A merry-go-round rotates from rest with an angular acceleration of 1.30 rad/s2. (a) How long does it take to rotate through the first 3.00 rev? s (b) How long does it take to rotate through the next 3.00 rev? s

(a) t=5.384s

(b) t=2.23s

Explanation:

Given data

Initial angular speed of merry go round ω₀=0 rad/s

Angular acceleration of merry go round α=1.30 rad/s²

For Part (a)

Using the equation  of angular motion for constant angular acceleration

Θ=ω₀t+(1/2)at²

The time that the merry takes to complete 3 revolutions is 5.384 seconds

For Part (b)

Using the equations of angular motion for constant acceleration to find the time for the round to complete 6 revolutions

Θ=ω₀t+(1/2)at²

The time that the round takes to finish the second three revolutions is

if you already have the answer to (a), then just work out how many periods there are in 1 minute, and that's the answer to (c).