Relation Between Linear And Angular Velocity — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Relation between Linear and Angular Velocity Applies to particles in circular motion or points on a rotating rigid body. Assumes the radius is constant for the instant calculation. Start with the definition of arc length: s = r theta. Differentiate both sides with respect to time: ds/dt = r (d theta/dt). Identify ds/dt as linear velocity (v) and d theta/dt as angular velocity (omega). Result: v = r omega. Angular velocity must be in radians per second (rad/s), not degrees/s or RPM. Velocity calculated is tangential to the path. Using degrees per second instead of radians per second for omega. Confusing tangential velocity with angular velocity. Assuming this formula applies to non-circular curved motion without using the instantaneous radius of curvature.