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The figure shows a graph of the angular velocity of a rotating wheel as a functi

ID: 1283317 • Letter: T

Question

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 = 7.9 s. What is the angular displacement of the wheel from 0 to 7.9 s?

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 = 7.9 s. What is the angular displacement of the wheel from 0 to 7.9 s?

Explanation / Answer

The angular acceleration is given by the change in velocity over the change in time.
Using from the graph t0 = 0s, t1 = 3s:
acc = (0 - (-9)) rad/s / (3 - 0) seconds
acc = 9rad/s / 3 seconds
acc = 3 rad/s^2

Then you can use the rotational analog of the displacement formula
linear displacement:
x = v0 t + .5 a t^2
angular displacement:
r = omega0 t + .5 acc t^2

r = (-9 rad/s) t + .5 (3 rad/s^2) t^2
r(6.7s) = (-9 rad/s) 6.7s + .5 (3 rad/s^2) (6.7s)^2
r(6.7s) = -60.3 rad + 67.335 rad
r(6.7s) = 7.035rads

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