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

answer: option c.

explanation:

the working equation for the angular size is the product of the physical size and 360 degrees divided by the product of two pi and distance from earth. the minimum size would be 0.559 degrees while the maximum size would be 0.49 degrees.