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 the z-direction. The angular velocity _z is -6.00 rad/s at t =0, increases linearly with time, and is +4.00 rad/s at t = 19.0 s . We have taken counterclockwise rotation to be positive.

1) Is the angular acceleration during this time interval positive or negative?

2) During what time interval is the speed of the wheel increasing?

3) During what time interval is the speed of the wheel decreasing?

4) What is the angular displacement of the wheel at t = 19.0 s ?

Explanation / Answer

1) w = w0 + alpha*t

4 = -6 + alpha*19

=> alpha = 10/19 = 0.52 rad/sec^2

2)

speed of whell increasing all time

3) speed of whell increasing all time

4) theta = w0t + 1/2*alpha*t^2

theta = -6*19 + 0.5*0.52*19^2 = -20.14rad

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