Answer:
α = 0.129 rad / s²
Explanation:
This is a rotation kinematics exercise
Let's start by reducing the magnutes to the SI system
θ = 13 rev (2π rad / 1 rev) = 26π rad
θ = 81.68 rad
let's use the equations
w = w₀ + α t
θ= w₀ t + ½ α t²
we have a system of two equations with two unknowns,
w₀ = w -α t
we substitute
θ = (w-α t) t + ½ α t²
α (t² - ½ t²) = w t - θ
α (½ t²) = w t - θ
α = (w t - θ) 2 / t²
let's calculate
α = (14 6 - 81.68) 2/6²
α = 0.129 rad / s²
