The figure shows a graph of the angular velocity of a rotating wheel as a function of time. Although not shown in the graph, the angular velocity continues to increase at the same rate until t = 8.6 s. What is the angular displacement of the wheel from 0 to 8.6 s?

θ = 33.54 rad

Explanation:

This is a circular motion exercise

         θ= θ₀ + w₀ t + ½ α t²

suppose that for t = 0 the body is at its initial point θ₀ = 0 and from the graph we see that the initial angular velocity w₀ = -9.0 rad / s

we look for the angular acceleration,

         α =

from the graph taken two points

         α =

         α = 3 rad / s²

we substitute in the first equation

            θ = 0 -9 t + ½ 3 t²

the displacement is requested for t = 8.6 s

           θ = = -9  8.6 + 3/2  8.6²

           θ = 33.54 rad