Angular velocity is a measure of how quickly an object is rotating around a fixed point or axis. It is defined as the rate of change of angular displacement with respect to time. Angular displacement is the angle through which an object rotates, measured in radians. Therefore, the angular velocity depends upon the rate of change of angular displacement.

Explanation:
The angular velocity of an object is determined by how quickly it rotates, which is measured by the angular displacement. Angular displacement is the change in the orientation of an object with respect to a reference point or axis. It is measured in radians and represents the angle through which an object has rotated.

The rate at which the angular displacement changes over time gives us the angular velocity. It tells us how quickly the object is rotating and in which direction. If the angular displacement is changing rapidly, the angular velocity will be high, indicating a fast rotation. On the other hand, if the angular displacement is changing slowly, the angular velocity will be low, indicating a slower rotation.

Angular acceleration is the rate of change of angular velocity with respect to time. It represents how quickly the angular velocity is changing. While angular acceleration is related to the angular velocity, it is not directly responsible for determining the angular velocity itself. Angular acceleration affects how the angular velocity changes over time, but it is not the primary factor that determines the angular velocity.

Torque is a measure of the force that causes an object to rotate around an axis. It is related to angular acceleration through the equation torque = moment of inertia × angular acceleration. While torque is important in determining how an object's angular velocity changes, it is not directly responsible for determining the angular velocity itself.

In conclusion, the angular velocity depends upon the rate of change of angular displacement. By measuring how quickly the angular displacement changes over time, we can determine the angular velocity of an object.