Which formula expresses the power transmitted by a shaft in terms of torque and angular velocity?

Which formula expresses the power transmitted by a shaft in terms of torque and angular velocity?

• A. P = ω / T
• B. P = T ω
• C. P = T ω^2
• D. P = ω T^2

Answer: (B)

Power transmitted by a shaft is the rate at which torque does work as the shaft rotates. The small amount of work from a tiny rotation dθ is dW = τ dθ. Since angular velocity ω = dθ/dt, the instantaneous power is P = dW/dt = τ dθ/dt = τ ω. So the power equals the torque times the angular velocity: P = T ω. The units work out as well: torque in N·m and angular velocity in rad/s yield watts. For example, a torque of 50 N·m at 6 rad/s gives 300 W. The other forms mix the quantities in ways that don’t match the relationship or the units.

Power transmitted by a shaft is the rate at which torque does work as the shaft rotates. The small amount of work from a tiny rotation dθ is dW = τ dθ. Since angular velocity ω = dθ/dt, the instantaneous power is P = dW/dt = τ dθ/dt = τ ω. So the power equals the torque times the angular velocity: P = T ω. The units work out as well: torque in N·m and angular velocity in rad/s yield watts. For example, a torque of 50 N·m at 6 rad/s gives 300 W. The other forms mix the quantities in ways that don’t match the relationship or the units.