1. What is the Power-Torque-Speed Relationship?

The fundamental relationship between power, torque, and angular speed is crucial in mechanical and electrical engineering. Power is the product of torque and angular velocity, representing the rate at which work is done.

2. How Does the Calculator Work?

The calculator uses the basic power equation:

Where:

• \( P \) — Power in Watts (W)
• \( \tau \) — Torque in Newton-meters (Nm)
• \( \omega \) — Angular speed in radians per second (rad/s)

Explanation: This equation shows that for a given power output, torque and angular speed are inversely proportional. This is why engines and motors produce higher torque at lower speeds.

3. Practical Applications

Details: This calculation is essential for designing mechanical systems, selecting motors, analyzing engine performance, and understanding gear ratios in automotive and industrial applications.

4. Using the Calculator

Tips: Enter torque in Nm and angular speed in rad/s. For RPM conversions, remember that 1 RPM = 0.10472 rad/s. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: How do I convert RPM to rad/s?
A: Multiply RPM by π/30 (approximately 0.10472). For example, 1000 RPM = 1000 × 0.10472 = 104.72 rad/s.

Q2: What's the difference between power and torque?
A: Torque is a rotational force, while power is the rate at which work is done (torque × angular speed).

Q3: Why does power increase with speed at constant torque?
A: Because power is the product of torque and speed - more rotations per second means more work is being done per second.

Q4: What are typical torque values for electric motors?
A: Small motors might produce 0.1-1 Nm, while industrial motors can produce hundreds of Nm. Always check manufacturer specifications.

Q5: How does this relate to horsepower?
A: 1 horsepower ≈ 745.7 watts. To convert, divide your result in watts by 745.7 to get horsepower.