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We have been studying centripetal forces and accleration in my class, and my teacher has shown me how to derive centripetal acceleration as v^2/r using change in velocity over time. I recently got into angular velocity vs. linear velocity in my math class, and I know that angular velocity is the change in the central angle(in radians) over time. But is this not SPEED? Speed is distance traveled over time, which is like the change in the central angle. Velocity is change in displacement over time.

With this lack of clarity, I became confused with the formula for centripetal acceleration as change in velocity over time. The "velocities" we seemed to be using actually appear to me now as speeds.

So here are my two questions:

1) Should it be angular speed not velocity since it is really distance traveled around a circle over time and not displacement over time?

and

2) In the formula for centripetal acceleration, v^2/r, is the centripetal velocity suppossed to be termed centripetal speed since it is also the distance traveled around the circle over time? If not, then the displacement over time for an object traveling around a circle (velocity) is much less than the distance over time (speed), right?