A wheel is rotating about an axis that is in the z -direction. The angular veloc

Question

A wheel is rotating about an axis that is in thez-direction. The angular velocity z is -6.00 rad/sat t = 0, increases linearly with time, and is+4.00 rad/s at t = 14.0 s . We have taken counterclockwise rotation to be positive.

Part A.) Is the angular acceleration during this time interval positive or negative?

Part B.) During what time interval is the speed of the wheel increasing?

Part C.) During what time interval is the speed of the wheel decreasing?

Part D.) What is the angular displacement of the wheel at t = 14.0 s ?

Explanation / Answer

A)Here, angular velocity increases from -ve to +ve. Hence angular acceleration during this time interval is positive.

Angular acceleration can be calculated by, = (-o)/t = (4 -(-6))/14 = 0.714 rad/s2

C) The angular velocity first decreases from 6 rad/s (in opposite direction) to 0 rad/s, so that the wheel comes to rest for an instant. So the time interval during which this happens is:

We know that =o+t Here o = 6 and = 0 , = 0.714

=> t = 6/0.714 = 8.4 sec

Hence speed decreases from t = 0 to t = 8.4 sec

B) Speed increases from 0 rad/s to +4 rad/s

t = 4/0.714 = 5.6 sec

Hence speed increases from t = 8.4 s to t = 8.4+5.6 = 14 s

D) Angular displacement, d = ot+(1/2)t2 = -6*14+(1/2)*0.714*14*14 = -14.028 radians

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