What is the unit of angular velocity ω in the motor power equation P = τ·ω?

• A. Revolutions per minute
• B. Radians per second
• C. Meters per second
• D. Degrees per second

Answer: (B)

Angular velocity is the rate at which something rotates—how fast the angle changes over time. In the motor power relationship, torque is in newton-meters and power is in watts. To multiply torque by angular velocity and get power in the SI system, the angular velocity must be in radians per second. This choice makes the units line up cleanly: torque (N·m) times angular speed (rad/s) gives N·m/s, which is watts. Since radians are dimensionless, using radians per second keeps the equation dimensionally consistent and yields the correct power unit. Using revolutions per minute or degrees per second would require extra conversion factors to reach radians per second. Hence, radians per second is the appropriate unit for ω here.