Starting from rest at t = 0 s, a wheel undergoes a constant angular acceleration. When t = 1.6 s, the angular velocity of the wheel is 5.9 rad/s. The acceleration continues until t = 19 s, when the acceleration abruptly changes to 0 rad/s2. Through what angle does the wheel rotate in the interval t = 0 s to t = 47 s?

Question

Damon · Accepted Answer

v = Vi + a t

theta = theta zero + Vi t + (1/2) a t^2

when t = 0, v = 0
v = a t
5.9 = a(1.6)
so a = 3.69 radians/s^2

now at 19 seconds:
v = 0 + 3.69 (19) = 70.1 radians/s
theta = 0 + 0 t + (.5)(3.69)(19)^2
= 666 radians

NOW continues at 70.1 rad/s for
47 - 19 = 28 seconds
so goes 28*70.1 = 1963 radians more

1963 + 666 = 2629 radians