Torque and Couple
Introduction
Torque and couple are fundamental concepts in rotational dynamics. They describe how forces cause objects to rotate and how pairs of forces produce rotational effects.
Torque
Torque is a measure of the tendency of a force to rotate an object about an axis. It depends on the magnitude of the force, the distance from the axis of rotation (lever arm), and the angle between the force and lever arm.
The formula for torque (τ) is:
τ = r × F = rF sinθ
where:
- r = lever arm or perpendicular distance from the axis to the line of action of the force
- F = magnitude of the force
- θ = angle between the force and the lever arm
Couple
A couple consists of two equal and opposite forces whose lines of action do not coincide. It produces a pure rotation without translation and is characterized by its moment (couple moment).
The moment of a couple (M) is:
M = F × d
where:
- F = magnitude of one of the forces
- d = perpendicular distance between the forces
The couple produces rotational effect without any net force acting on the body.
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