Final answer:
The torque produced by an industrial motor with an output of 160 kW and an angular speed of 4400 rev/min is approximately 347.22 Nm.
Step-by-step explanation:
To calculate the torque developed by an industrial motor whose output is 160 kW at an angular speed of 4400 rev/min, we need to use the relationship between power, torque, and angular velocity. The power P in watts (W) can be calculated using the formula P = τω, where τ is the torque in newton-meters (Nm) and ω is the angular velocity in radians per second (rad/s).
First, we convert the angular speed from rev/min to rad/s:
- 4400 rev/min × (2π rad/rev) × (1 min/60 s) = 460.8 rad/s
Next, we rearrange the power formula to solve for torque (τ): τ = P/ω.
Substitute the known values into the equation:
- τ = (160,000 W) / (460.8 rad/s) ≈ 347.22 Nm
Therefore, the torque produced by the motor is approximately 347.22 newton-meters (Nm).