Explanation needed in angular acceleration

[Schwatt!]

Hi all, I am doing some homework from my textbook and I encountered this problem:

"Starting from rest, a disk rotates about its central axis with constant angular acceleration. In 5.0 s, it rotates 25 rad. During that time, what are the magnitudes of (a) the angular acceleration and (b) the average angular velocity? (c) Wha is the instantaneous angular velocity of the disk at the end of the 5.0 s? (d) With the angular acceleration unchanged, through what additional angle will the disk turn during the next 5.0s?"

I have a problem calculating the value for (a). I have the answer but I am not sure why I am right. Using θ = ω0t+ 1/2αt^2 and solving for a, what is the value to be used for θ? Would it be the given 25 rad. or 25 rad/5 s?

 

[Saketh]

$\theta$ is an angle, not an angular velocity.

If all else fails, use unit analysis to check what you should plug in.

 

[Schwatt!]

ok so that would mean to plug in the radian measure but that number does not give the answer; the 25/5 does...

 

[Hootenanny]

ok so that would mean to plug in the radian measure but that number does not give the answer; the 25/5 does...

The 25/5 is the correct quantity, that is what Saketh was hinting at. Since;

$$\omega=\frac{d\theta}{dt} = \frac{25}{5} = 5\;rad.s^{-1}$$