Q: I was wondering if an object’s linear velocity in a circular motion is always expressed as a magnitude, or if the sign depends on the direction that the object is traveling around the circle (e.g., clockwise/counterclockwise.)
A: In a circular motion, the linear velocity is always in the Tangential direction, but Tangential is actually not a constant direction (see the picture). At different positions along the circle, the Tangential directions are different!
Since the direction of linear velocity is clear, we study the magnitude of linear velocity (speed) and then the acceleration which depends on the change of velocity.
In a uniform circular motion, the speed is constant, so there is only centripetal acceleration. But in a non-uniform circular motion, there are both centripetal and tangential accelerations. For more details about the accelerations in circular motion, see my post on
https://www.physicsdoable.com/posts/2020-11-17-highlights-of-questionanswer/
We use Clockwise (negative) or Counterclockwise (positive) to describe the direction of angular velocity in a circular motion, not the direction of linear velocity. Of course, these two velocities do have a correlation!
