Moment of Force (Torque) and Couple
Understanding rotational effects of forces
What is Moment of Force (Torque)?
Moment of force, often called torque, is a measure of the tendency of a force to rotate an object about an axis, fulcrum, or pivot. It's a vector quantity, meaning it has both magnitude and direction.
Where:
τ = Torque (N·m)
r = Position vector (distance from axis to force application)
F = Force vector
θ = Angle between force vector and lever arm
The animation above demonstrates how applying a force at a distance from the pivot point creates rotational motion. The longer the lever arm (distance from pivot), the greater the torque for the same amount of force.
What is a Couple?
A couple is a system of forces that results in a moment (torque) but no resultant force. It consists of two equal and opposite forces that don't share the same line of action, creating pure rotation without translation.
Where:
M = Moment of the couple (N·m)
F = Magnitude of one of the forces
d = Perpendicular distance between the forces
The animation shows how two equal and opposite forces acting at different points create pure rotational effect. The moment of the couple depends on the magnitude of the forces and the distance between them.
Key Differences
Torque (Moment of Force)
• Caused by a single force
• Requires a pivot point
• Can produce both rotation and translation
• Depends on the point of application of force
Couple
• Caused by two equal and opposite forces
• Doesn't require a pivot point
• Produces pure rotation without translation
• Moment is independent of the reference point
Applications in Real Life
Torque Examples
• Turning a wrench to loosen a bolt
• Pedaling a bicycle
• Opening a door
• Seesaw in playground
Couple Examples
• Steering wheel of a car
• Turning a screwdriver
• Adjusting a faucet
• Rotating the lid of a jar
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