Apply the concepts of force and torque on a body at equilibrium.

7.1 Define equilibrium

  • Equilibrium is the condition of balance - in mechanics the term can be applied to balanced forces(translational equilibrium) or to balanced torques (rotational equilibrium). Thus for complete equilibrium there must be both translational equilibrium (balanced forces) AND rotational equilibrium (balanced torques).
  • The science of STATICS is the study of stationary objects which are in (complete) equilibrium. Such objects are said to be in static equilibrium (as opposed to dynamic equilibrium).

7.2 Define translational equilibrium (ΣF = 0 )

  • An object in translational equilibrium is acted on by balanced forces, thus the net force is zero (ΣF = 0) and the object has no translational (straight line) acceleration (though it may have rotational acceleration).

7.4 Define rotational equilibrium (Στ = 0 ).

  • An object in rotational equilibrium is acted on by balanced torques, thus the net torque is zero (Στ = 0) and the object has no rotational acceleration (though it may have translational acceleration).
  • A pair of equal and opposite forces acting on the same object but not acting along the same line will cause no translational acceleration but will cause rotational acceleration. Such a pair of forces is called a couple.

7.6 The concepts of lever arm and torque.

  • Torque is the quantity that measures how effectively a force causes rotation.
  • Torque is represented by the Greek letter τ (tau),
  • The torque is, of course, proportional to the size of the force.
  • The torque depends on (and is proportional to) the distance (r) from the axis of rotation to the point where we apply the force.
  • The torque also depends on the angle between the line of action of the applied force and the line from the axis to the point where the force is applied. The torque is greatest when this angle is a right angle (think about closing a door) and zero when the lines are parallel.
  • The relation between torque τ, force, distance and angle is given by τ = F r sin θ
  • The distance r sin θ is known as the LEVER ARM - it corresponds to the perpendicular distance from the axis of rotation to the line of axis of the force.
  • Thus torque is equal to the product of force times lever arm τ = F (r sin θ)
  • Lever arm is sometimes called moment arm or moment of force.
  • Since torque is the product of a force and a distance its units are newton meters (Nm)
  • It is possible to assign a direction to torque in accordance with the rules of vector cross products, implying that torque is a vector quantity.