What is the power expression for a motor given torque and angular velocity, and what unit is the angular velocity?

• A. P = ω/τ; ω in cycles per second.
• B. P = τ·ω; ω in rad/s.
• C. P = τ+ω; ω in degrees per second.
• D. P = ω-τ; ω in meters per second.

Answer: (B)

Power in a rotating system is the rate at which torque does work. If a constant torque acts as the angle changes, the small amount of work is dW = τ dθ, so the power is P = dW/dt = τ dθ/dt = τ ω. That makes P = τ ω the correct expression, with the angular velocity measured in radians per second. Using rad/s keeps the units consistent so the result comes out in watts (since torque is in newton-meters and 1 watt = 1 newton-meter per second). If you use cycles per second or degrees per second, you’d need a conversion to rad/s to get the right power. The other forms—adding, subtracting, or dividing by ω—don’t represent the rate of doing work.