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Angular acceleration is a measure of how rapidly the angular velocity of an object is changing. In simple terms, it's like how much faster or slower something is spinning per second.
Imagine starting up a merry-go-round. Initially, when you push it, it speeds up, and this speeding up is due to angular acceleration. The moment you stop pushing, it starts to slow down unless acted upon by more force.
For the problem at hand, the disk experiences angular acceleration because it's going from rest (not moving) to rotating over time. The calculation used here applies the formula for angular displacement, which is given by:- \[ \theta = \omega_0 t + \frac{1}{2} \alpha t^2 \]Since the initial angular velocity \(\omega_0 = 0\) (because it starts from rest), this simplifies to \(\theta = \frac{1}{2} \alpha t^2\). Solving for \(\alpha\) allows us to determine that the angular acceleration is 2 \(\text{rad/s}^2\). This means every second, the spinning speed of the disk increases by 2 radians per second.

Average angular velocity provides an overall picture of how fast something was rotating over a period of time. It's different from instantaneous angular velocity because it doesn't tell you about the speed at any specific moment, but rather gives the speed averaged over the entire time.
If you think about a car trip, the average speed is like saying how fast you were traveling for the whole trip, even if sometimes you were stopped or sometimes going faster.
In the situation described, the average angular velocity can be determined using:- \[ \overline{\omega} = \frac{\theta}{t} \]Here, \(\theta\) is the total angle the disk turned (25 radians) over time \(t\) of 5 seconds. Plugging in these values, the average angular velocity is 5 \(\text{rad/s}\). This tells us that on average, the disk turned 5 radians every second over the 5 seconds.

Instantaneous angular velocity is the speed of rotation at a particular moment. It’s like checking your car’s speedometer to see exactly how fast you’re going at that very instant.
While average angular velocity considers something like the whole trip of a disk, the instantaneous angular velocity tells us exactly how fast it was spinning at the end of the 5 seconds.
In this problem, to find the instantaneous angular velocity at the end of 5 seconds, we use the formula:- \[ \omega = \omega_0 + \alpha t \]Given that the initial velocity \(\omega_0\) is 0 and angular acceleration \(\alpha\) is 2 \(\text{rad/s}^2\), we substitute to get \(\omega = 2 \times 5 = 10 \text{rad/s}\). This means that right at the end of 5 seconds, the disk is spinning at 10 radians per second. This value might offer more detail than the average because it tells us exactly how the rotational speed builds to this point.