A machinist turns the power on to a grinding wheel, at rest, at time t = 0 s. Th

Question

A machinist turns the power on to a grinding wheel, at rest, at time t = 0 s. The wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 45 rads/s. The wheel is run at that angular velocity for 34 s and then power is shut off. The wheel slows down uniformly at 2.9 rad/s2 until the wheel stops. In this situation, the average angular velocity in the time interval from t = 0 s to t = 25 s is closest to: A machinist turns the power on to a grinding wheel, at rest, at time t = 0 s. The wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 45 rads/s. The wheel is run at that angular velocity for 34 s and then power is shut off. The wheel slows down uniformly at 2.9 rad/s2 until the wheel stops. In this situation, the average angular velocity in the time interval from t = 0 s to t = 25 s is closest to: 14 rad/s 23 rad/s 45 rad/s 54 rad/s 36 rad/s

Explanation / Answer

A machinist turns the power on to a grinding wheel, at rest, at time t = 0 s. The wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 91 rad/s. The wheel is run at that angular velocity for 33 s and then power is shut off. The wheel decelerates uniformly at 2.9 rad/s2 until the wheel stops. In this situation, the average angular velocity in the time interval from t = 0 s to t = 25 s is... The angular position of the grinding wheel is given by: f = ½(?o+?)t So the position at t=25s is found by: f = ½?*t1 + ?*t2 f = ½(91)(10)+(91)(25-10) = 1820 rad And the avg. angular speed is: ? = f/(t1+t2) = 73 rad/s Which of course is different than your given answer. The only times when ?=55 rad/s are at t=12.6s and t=89s.

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