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.