# Kinematics: Circular Motion

What is the difference between angular velocity and angular speed? Is angular velocity after one complete rotation zero? Is the magnitude of angular velocity always equal to angular speed?

Angular velocity is a Vector quantity and angular speed is a scalar quantity.angular speed may be can constant but angular velocity not necessarily remaining constant as $$\mathbf{\omega}=\mathbf{r}\text{x}\mathbf{v}$$.But $$\mathbf{v}$$ changing with time due to changing direction.

Angular velocity is a vector quantity, and angular speed is defined as its magnitude (and therefore a scalar quantity).

If you are talking about uniform circular motion, the angular velocity after one complete rotation is not zero, but rather a constant (non-zero) vector.

What is the difference between angular velocity and angular speed?

One is a vector term, the other is a scalar term.

• Angular speed is just "how fast" you spin
• Angular velocity is "how fast" you spin a specific direction about an specific axis.

Just like usual speed is the "how fast", while velocity is "how fast" and "in which direction".

Is angular velocity after one complete rotation zero?

No... Why would it? Angular velocity is just the spinning speed (about a specific axis) at some moment in time. Why should that spinning speed (or that axis) be zero after one full rotation?

If you asked about the average, then it would be a different matter.

Is the magnitude of angular velocity always equal to angular speed?

Yep. That's how we define them.