A Ferris wheel of radius R speeds up with angular acceleration α starting from rest.
Find an expression for the velocity of a rider after the Ferris wheel has rotated through angle ΔΘ
in terms of R, α, ΔΘ
1 Answer

Rotational Kinematics Formulas:
ω_f = ω_i+ α∆t
θ_f = θ_i+ω_i ∆t+(1/2) α∆t^2
Solving for ∆t using the second equation
∆θ = 0+0∆t+(1/2)α∆t^2
∆t = √((2∆θ)/α)
Substituting for the first equation ∆t
ω_f = 0+α√((2∆θ)/α)
Remember = ω=v/R therefore
v/R = α√((2∆θ)/α)
and the answer:
v = Rα√((2∆θ)/α)
Be careful to note: α = alpha (not a)
Hope this helps!
–ckelley