Physics Angular Velocity Question?

NetherCraft 0

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

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