An object can rotate at a constant rate even if its angular acceleration is not constant. This is possible when the angular acceleration changes in such a way that it cancels out the effects of the changing angular velocity.
Angular acceleration (α) is the rate at which the angular velocity (ω) changes with respect to time. If the angular acceleration is not constant, it means that the rate of change of angular velocity is not constant. This can result in a changing angular velocity over time.
However, if the changes in angular acceleration are such that they compensate for each other, it is possible for the object to maintain a constant angular velocity. In other words, if the increases and decreases in angular acceleration are appropriately balanced, they can offset each other's effects on the angular velocity.
One example is when an object undergoes periodic motion or oscillations, such as a pendulum swinging back and forth. In this case, the angular acceleration changes direction at each extreme point of the oscillation. The object experiences a changing angular acceleration during each cycle, but the net effect is that it maintains a constant angular velocity during the oscillation.
In summary, an object can rotate at a constant rate even if its angular acceleration is not constant if the changes in angular acceleration are balanced in such a way that they compensate for each other and maintain a constant angular velocity.