How Does Angular Velocity Change with Time in a Rotating Disk?

[kappcity06]

Figure 10-21b is a graph of the angular position of the rotating disk of Fig. 10-21a.

Figure 10-21

(a) Is the angular velocity of the disk positive, negative, or zero at t = 1 s?
positive
negative
zero
(b) Is the angular velocity of the disk positive, negative, or zero at t = 2 s?
positive
negative
zero
(c) Is the angular velocity of the disk positive, negative, or zero at t = 3 s?
positive
negative
zero
(d) Is the angular acceleration positive or negative?
positive
negative

 

[andrevdh]

The angular velocity is per definition

$$\omega = \frac{d\theta}{dt}$$

which means that the angular velocity is the gradient of the tangential to the angular position versus time curve.