3.1 Torque

Torque

  • a force that causes an object to rotate → turning or twisting force
  • ⬆️ torque means it requires less effort, or less force to do something (e.g. pushing a door open)
  • tau (𝛕) measured in newton-metres (N m or N·m)
  • AKA moment of a force
  • unlike linear, doesn’t produce translational motion (Δx, Δy, Δz) but instead rotational motion (Δθ)

 

 no torque if you apply force at pivot (door hinge) because r⟂ is 0

 

 

Torque terminology

  • axis of rotation (pivot, pivot point, fulcrum): the line around which an object rotates (e.g. line formed by a door hinge, a wheels axle)
  • radius (r): the position vector from the pivot to the point where the force is being applied
  • line of action: an imaginary line extending out both ends of the force vector
  • perpendicular distance (AKA force arm) (r⟂ or d): shortest distance between pivot point and line of action
  • lever arm/moment arm: roughly equivalent to r, like it’s the actual physical ‘arm’ of a lever - we DON’T say it is perpendicular distance

Determining torque

  • magnitude (size) of torque is affected by 3 factors:

  

  1. the size of the applied force: ⬆️ force = ⬆️ torque
  2. the perpendicular distance: ⬆️ distance = ⬆️ torque
  3. the angle between the applied force and lever arm (𝜃 sometimes ɸ): ⬆️ sinθ = ⬆️ torque
    • this is why F pushing directly towards the pivot/centre of mass (180°) or pulling directly away from it (0°) has no torque and why 90° = max torque