Wheel Displacement in Gaining Velocity


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?


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*t2 + v0*t = 1/2*3*2.78 + 10*1.67 = 4.167 + 16.7 = 20.867 rad.

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