Fun Facts About Merry-Go-Round Rotation!

Did you know that a merry-go-round rotates from rest with an angular acceleration of 1.04 rad/s²? Let's find out how long it takes to rotate through a certain number of revolutions!

First 1.59 revolutions:

Using the equation θ = ω₀t + 1/2αt², where θ is the number of revolutions, t is the time, α is the angular acceleration, and ω₀ is the angular velocity:

Given: θ = 1.59 rev = 1.59 × 2π = 9.992 rad, ω₀ = 0 rad/s, α = 1.04 rad/s²

Substitute into the equation: 9.992 = 0(t) + 1/2(1.04)(t²)

Solving for t, we get t = 4.38 s.

Next 1.59 revolutions:

For the next 1.59 revolutions:

Given: θ = 3.18 rev = 3.18 × 2π = 19.97 rad, ω₀ = 0 rad/s, α = 1.04 rad/s²

Substitute into the equation: 19.97 = 0(t) + 1/2(1.04)(t²)

Solving for t, we get t = 6.197 s

The time required for the next 1.59 revolutions is 6.197 - 4.38 = 1.817 s.