What is the formula relating linear velocity (v) to angular velocity (ω)?

The correct relationship between linear velocity (v) and angular velocity (ω) is expressed through the formula v = rω. In this equation, v represents the linear velocity of a point on a rotating object, ω is the angular velocity in radians per second, and r is the radius of the circular path along which the point is moving.

This formula captures the idea that as an object rotates, the linear speed of a point on the edge of that object depends directly on both how fast it rotates (its angular velocity) and the distance of the point from the axis of rotation (the radius). Thus, if you increase the radius, the linear velocity will increase proportionally for a constant angular velocity. Similarly, if the angular velocity increases, the linear velocity also increases.

In summary, the formula v = rω effectively links angular motion to a linear measure, making it fundamental for analyzing circular motion in physics.