Physical meaning of the cross product
📘 Conceptual notes
WHAT IS TORQUE?
Torque (or the moment of a force) measures the tendency of a force to rotate a body about an axis. Given the position vector from the axis to the point where the force is applied, the torque is the cross product . Its magnitude depends on the arm, the force, and the angle between them.
🔧 Analogy: a wrench on a bolt
Picture a wrench tightening a bolt. Doubling the arm (r)
or pushing twice as hard (F) doubles the torque. Pushing the wrench
along its own length (θ = 0°) won't turn the bolt — only the perpendicular component
of F counts, and that's the meaning of the sin θ factor.