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

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 = 6.00 s . We have taken counterclockwise rotation to be positive. b) How long is the time interval during which the speed of the wheel is increasing? Express your answer with the appropriate units. c)How long is the time interval during which the speed of the wheel is decreasing? Express your answer with the appropriate units. d) What is the angular displacement of the wheel from t = 0 s to t = 6.00 s ?

Explanation / Answer

The angular acceleration is constant:
alpha = (omega final - omega initial) / totaltime

So the angular velocity as a function of time is:
omega(t) = omega initial + alpha * t
= omega initial + (omega final - omega initial) * t / totaltime

Solve for the t at which omega(t) = 0

t = - omega initial * totaltime / (omega final - omega initial)

t = 6*6/10 = 36/10 = 3.6 sec

Before that time, the angular speed is decreasing, after that it is increasing that is first 2.4 sec it is decreasing and next 3.6 sec it is increasing

alpha = 10/6 = 1.67 rad/s^2

f^2 = i^2 + 2
= (16-36)/2*1.67 = -6 rad

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.