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

more than, less

less than, more