Starting from rest, a spinning disk accelerates constantly to a final rotational speed, ω , in a period of time, Δ Δ t. What expression best represents the revolutions the disk has turned through? A) ω Δ Δ t /2 π B) Δ4 ω Δ t 4 π C)Δ22 ω Δ t 2 2 D) Δ ω Δ t E) 2Δ 2 π ω Δ t

the correct one is B,   θ  =    w t    [rev]

Explanation:

This is a rotational kinematics exercise

        w = w₀ + α t

        w² = w₀² + 2 α θ

indicate that part of rest whereby the initial angular velocity is zero

        w = α t       -> α = w/t

        w² = 2 α θ

we substitute

        w² = 2 (w / t) θ

         w = 2 θ / t

        θ = w t / 2

This angle is given in radians, let's reduce to revolutions = 2π rad = 1 rev

        θ = w t / 2 rad (1 rev / 2π rad)

        θ  =    w t    [rev]

when checking the answers, the correct one is B, even though he has some mistakes in his writing