Wheel Displacement in Gaining Velocity

## Question:

A wheel has an initial angular velocity clockwise of 10 rad/s and
a constant acceleration clockwise of 3 rad/s/s. Determine how
many revolutions it will take for the wheel to reach an angular
velocity clockwise of 15 rad/s. How long will be required to
achieve this angular velocity?
## Answer:

Because the acceleration is constant we know that the average
acceleration is equal to the constant value, so the time to
change velocity by 5 rad/s is just the change in velocity divided
by the acceleration. In this case 5/3 = 1.67
s. The displacement during that time is
1/2*a*t^{2} + v0*t = 1/2*3*2.78 + 10*1.67 = 4.167 + 16.7
= 20.867 rad.
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