Data Source and Methodology
Primary reference: OpenStax, University Physics Volume 1, 2016, Chapter 10 (Rotational Motion) — Sections on Torque and Power. https://openstax.org/details/books/university-physics-volume-1
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.
The Formula Explained
Torque from force and lever arm:
$$\\tau = r \\times F \\times \\sin(\\theta)$$
Torque from power and angular speed:
$$\\tau = \\frac{P}{\\omega}, \\quad \\text{with} \\; \\omega = 2\\pi\\,\\frac{n}{60} \\; \\text{(rad/s)}$$
Convenient engineering form (power in kW, speed in rpm):
$$\\tau\\,[\\mathrm{N\\cdot m}] \\approx 9550\\,\\frac{P\\,[\\mathrm{kW}]}{n\\,[\\mathrm{rpm}]}$$
Glossary of Variables
- τ (Torque): Rotational equivalent of force, output in N·m and lbf·ft.
- F (Force): Applied force magnitude; supported units: N, lbf.
- r (Lever arm): Perpendicular distance from axis to line of action; units: m, ft.
- θ (Angle): Smallest angle between r and F, in degrees (0–180).
- P (Power): Mechanical power at the shaft; units: W, kW, hp.
- ω (Angular speed): rad/s; related to rpm by ω = 2π·rpm/60.
- rpm (Revolutions per minute): Rotational speed used with motors and drives.
How It Works: A Step-by-Step Example
Suppose a 120 N force is applied at the end of a 0.35 m wrench, perpendicular to the wrench.
- Inputs: F = 120 N, r = 0.35 m, θ = 90°.
- Formula: τ = r × F × sin(θ).
- Compute: τ = 0.35 × 120 × sin(90°) = 42 N·m.
- Convert to lbf·ft: 42 × 0.737562 = 30.98 lbf·ft (approx).
Power-based example: 2 kW at 1500 rpm ⇒ τ ≈ 9550 × 2 / 1500 = 12.73 N·m.
Frequently Asked Questions (FAQ)
What inputs do I need to compute torque from force?
Provide the force magnitude, lever arm length, and the angle between them. The tool accepts N or lbf for force and m or ft for length.
When should I use the power and RPM method?
Use it for rotating machinery when you know shaft power and rotational speed. It is common for motors, pumps, and gearboxes.
Does direction (clockwise vs counter-clockwise) matter?
Sign convention matters in analysis, but this calculator returns torque magnitude. The direction depends on your coordinate system.
Why does the angle reduce torque?
Only the component of force perpendicular to the lever arm contributes to torque. That component is F·sin(θ).
Are N·m and J the same unit?
They are dimensionally equivalent (kg·m²/s²), but they represent different physical quantities. Use N·m for torque, J for energy.
How accurate are conversions between N·m and lbf·ft?
The tool uses exact constants: 1 lbf = 4.4482216152605 N and 1 ft = 0.3048 m, ensuring high-precision conversions.
Can this tool compute power if I have torque and RPM?
Yes, rearrange P = τ·ω. Currently the interface focuses on torque output, but the formula is provided for completeness.