Physics Notes: Moments and Equilibrium Concepts

Translational Equilibrium

  • Definition: An object is in translational equilibrium if it is not accelerating in any direction.

  • Condition: The net force acting on the object must be zero (F_net = 0). This means that all resolved forces in a direction cancel each other out.

Eg: A 2.5 kg box is at rest. Two people push it with 10 N each.

  • The forces acting are:

    • Applied forces: 10N from left and right.

    • Reaction force from ground = 25 N (upwards)

    • Weight of the box = 25 N (downwards)

    Since the resolved forces in any direction cancel each other, the net force is zero and the box remains at rest.

Moment of a Force

  • Definition: is the product of force and perpendicular distance from that reference point, usually a pivot.

The moment of a force with reference to a point is: the turning effect of a force, the ability of the force to make something turn/rotate at an axis through a reference point

Formula: Moment (M) = Force (F) x Perpendicular distance (d) from the pivot.

Units: SI unit of moment is Newton metre (Nm).

  • The direction of the moment can be either clockwise or anti-clockwise.

  • Example Calculation:

  • If a force of 8 N is applied at a distance of 3 m from the pivot, Moment = 8 N × 3 m = 24 Nm (anti-clockwise).

Centre of Gravity

  • Definition: The center of gravity (COG) is the point where the total weight of an object can be considered to act.

  • Example: For a uniform plank, if the pivot is at its COG, it will remain in equilibrium. If the pivot is off-center, the plank will rotate due to the moment created by the weight acting at COG.

Rotational Equilibrium

  • Condition: An object is in rotational equilibrium if the net moment about any reference point is zero.

  • For rotational equilibrium, Total Anti-clockwise (ACW) moments = Total Clockwise (CW) moments.

  • Steps to Determine:

  1. Calculate total ACW moments.

  2. Calculate total CW moments.

  3. Compare the two sums.

  • Example:

  • If 4N force at 2m creates an 8 Nm clockwise moment and 2N at 4m creates an 8 Nm anti-clockwise moment, we achieve rotational equilibrium.

Static Equilibrium

  • Condition: An object is in static equilibrium when it satisfies both translational and rotational equilibrium conditions.

  • This means:

    1. F_net = 0 (translational equilibrium)

    2. M_net = 0 (rotational equilibrium)

  • Example:

  • For a beam with weights acting downwards and tensions upwards, set up equations for forces and moments to find unknowns and confirm equilibrium.

  • Scenarios to consider when evaluating static equilibrium:

  • Object at rest.

  • Object in translational motion without rotation or vice-versa.

  • Both types of motion occurring simultaneously.