Moment Arm and Torque Calculator Explained
The Moment Arm Calculator calculates the torque produced by a force applied at a distance from a pivot point. Torque describes the tendency of a force to rotate an object.
Moment Arm Formula
The standard torque formula is:
- τ = torque
- F = applied force
- d = distance from the pivot
- θ = angle between force and lever arm
Perpendicular Moment Arm
The effective moment arm is the perpendicular distance from the pivot to the force line of action:
Then torque can also be written as:
Example Calculation
Force = 100 N Lever arm distance = 0.5 m Angle = 90°
Since sin(90°) = 1:
Why the Angle Matters
| Angle | Effect on torque |
|---|---|
| 0° | No torque, because the force acts along the lever arm. |
| 30° | Only part of the force contributes to rotation. |
| 90° | Maximum torque for the same force and distance. |
| 180° | No torque, because the force again acts along the lever arm. |
Real-World Examples
- Wrench: A longer wrench increases torque for the same applied force.
- Door handle: Handles are placed far from the hinge to increase moment arm.
- Engines: Torque describes rotational output at the crankshaft.
- Levers: Increasing distance from the pivot increases rotational effect.
Frequently Asked Questions
What is a moment arm?
A moment arm is the perpendicular distance from a pivot point to the line of action of a force.
Is moment arm the same as lever arm distance?
Not always. If the force is perpendicular, they are the same. If the force is angled, the perpendicular moment arm is d × sin(θ).
Can torque be negative?
Yes. A negative torque can represent rotation in the opposite direction, depending on the sign convention.
What units does torque use?
In SI units, torque is measured in Newton-meters, written as N·m.