Torque Calculator - Torque and Moment of Force

This physics calculator helps you calculate torque and moment of force using various methods. Torque is the rotational equivalent of force and is essential in mechanics and engineering.

Torque Definition

• Torque: Rotational force that causes angular acceleration
• SI Unit: Newton-meter (N⋅m)
• Formula: τ = F × r × sin(θ)
• Direction: Perpendicular to force and radius vectors

Torque Formulas

• Basic: τ = F × r × sin(θ)
• Gravitational: τ = mgr
• Angular Acceleration: τ = Iα
• Work: W = τθ
• Power: P = τω

Applications

• Mechanics: Rotational motion and equilibrium
• Engineering: Machine design and power transmission
• Automotive: Engine performance and vehicle dynamics
• Robotics: Joint control and actuator design
• Construction: Structural stability and load analysis
• Sports: Athletic performance and equipment design

Important Notes

• Torque is a vector quantity
• Direction follows right-hand rule
• Maximum torque when θ = 90°
• Zero torque when θ = 0° or 180°
• Torque causes angular acceleration

Torque Types

• Static Torque: No rotation, equilibrium
• Dynamic Torque: Causes angular acceleration
• Reaction Torque: Equal and opposite response
• Friction Torque: Opposes motion
• Load Torque: External resistance

Common Examples

• Wrench: τ = F × L (length of wrench)
• Door: τ = F × d (distance from hinge)
• Pulley: τ = T × r (tension × radius)
• Motor: τ = P/ω (power/angular velocity)
• Gear: τ = F × r (force × pitch radius)

Torque Relationships

• Angular Acceleration: α = τ/I
• Angular Momentum: L = Iω
• Rotational Energy: E = ½Iω²
• Power: P = τω
• Work: W = τΔθ

Torque Measurement

• Torque Wrench: Direct measurement
• Strain Gauge: Deformation measurement
• Load Cell: Force measurement
• Optical Methods: Angular displacement
• Magnetic Methods: Hall effect sensors

Torque Units

• SI: N⋅m (Newton-meter)
• Imperial: ft⋅lb (foot-pound)
• Metric: kgf⋅m (kilogram-force meter)
• Engineering: in⋅lb (inch-pound)
• CGS: dyn⋅cm (dyne-centimeter)