Angular Velocity and Acceleration Problem

[iwonde]

A wheel is rotating about an axis that is in the z-direction. The angular velocity w_z is -6.00 rad/s at t=0, increases linearly with time, and is +8.00 rad/s at t =7.00s. We have taken counterclockwise rotation to be positive.

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

b.) During what time interval is the speed of the wheel increasing? Decreasing?

c.) What is the angular displacement of the whee at t = 7.00s?

a.) Angular acceleration is positive because alpha = (delta omega)/ delta t = 2 rad/s^s
b.) I'm not sure of how to approach this part. My guess is that the speed is increasing when the rotation is counterclockwise and decreasing when it's clockwise. I need help with this one.
c.) I just plugged t=7s into the equation φ(t) = φ_0 + (ω_0)t + (1/2)αt^2 and I got 7.00 rad.

 

[andrevdh]

If one draws a rough sketch of the angular acceleration of the wheel as a function of time it will form a linear graph. This graph stretches from -6 at t = 0 to +8 at 7 s. The (angular and linear) speed of the wheel decreases up to the point where this graph crosses the time axis. Thereafter it increases. That is it first slows down and momentarily stops rotating. Then its speed increases in the opposite direction.

 

[Google_Spider]

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

The angular velocity changes from -ve to +ve therefore the angular acceleration is +ve.

b.) During what time interval is the speed of the wheel increasing? Decreasing?

When the direction of motion of that wheel changes, it will be at rest for an instant.
Use $$\omega=\omega_o + \alpha t$$
with $$\omega=0$$ and $$\omega_o = -6$$
This will give the time for which speed is decreasing.