Angular and Tangential Velocity

In circular motion, an object follows a path at constant distance from a center. Examples include a coin on a rotating turntable, the tip of a clock hand, or a stone whirled on a string.

At every instant, the object has a tangential velocity $\vec{v}$ that points along the tangent to the circular path. This is the direction the object is moving at that moment. The radius vector $\vec{r}$ points from the center to the object's current position.

The diagram shows $\vec{r}$ pointing from the center to the object and $\vec{v}$ pointing in the direction of motion. They form a 90° angle.

Why must $\vec{v}$ be perpendicular to $\vec{r}$?

Circular motion requires constant radius. The distance from the center never changes.

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