A wheel rotating with a constant angular acceleration turns through 13 revolutions during a 6 s time interval. Its angular velocity at the end of this interval is 14 rad/s. What is the angular acceleration of the wheel? Note that the initial angular velocity is not zero. Answer in units of rad/s 2 .

 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

c. newton's third law of motion