Why is a door handle placed far from the hinges? Why is a long spanner better for loosening a tight nut? This lesson explains the physics of turning things, known as moments.

1. Short Notes: Core Concepts

A. Moment of a Force

• Definition: A moment is the turning effect of a force. To cause a rotation, you need a moment.

• Calculation: The size of the moment depends on two things: the size of the force and how far it is applied from the turning point (the pivot).

  • Formula: Moment = Force (F) × Perpendicular distance from the pivot (d)

• Pivot (or Axis of Rotation): This is the point around which the object turns. For a door, it's the line through the hinges. For a seesaw, it's the central support.

• Units: Force is in Newtons (N) and distance is in metres (m). Therefore, the unit for a moment is the Newton-metre (N m).

B. Directions of Moments

• Moments can cause rotation in two directions:

  1. Clockwise Moment: Tries to turn the object in the same direction as the hands of a clock.

  2. Anti-clockwise Moment: Tries to turn the object in the opposite direction.

C. The Principle of Moments (For Equilibrium)

• This is the most important rule for solving problems in this topic.

• Rule: For an object to be balanced (in equilibrium), the total clockwise moments about any pivot must be equal to the total anti-clockwise moments about the same pivot.

  • Formula: Sum of Clockwise Moments = Sum of Anti-clockwise Moments

D. Couple of Forces

• Definition: A couple is a pair of forces that are:

  1. Equal in magnitude.

  2. Parallel to each other.

  3. Acting in opposite directions.

• Effect: A couple produces a pure turning effect (rotation) without causing the object to move from its position.

• Examples: Turning a car's steering wheel with two hands, turning a tap, or using a screwdriver.

2. Tips & Tricks for the Exam

• Identify the Pivot First! In any problem, the first step is always to figure out where the pivot point is. All distances must be measured from this point.

• "Perpendicular" is Key: The distance in the formula M = F × d must be the perpendicular distance from the pivot to the line of action of the force.

• Spanner Question: A very common question is: "Why does a long spanner make it easier to loosen a nut?"

  • Answer: To loosen the nut, you need to apply a certain turning moment. Since Moment = Force × Distance, if you increase the distance (by using a longer spanner), you need to apply less force to achieve the same moment.

3. Important Points & Common Exam Questions

• Seesaw Problems: These are classic applications of the Principle of Moments.

  • Example: A uniform rod AB is 1 m long and balanced at its center (the pivot). A weight of 4 N is hung at end B (0.5 m from the pivot). What weight (x) must be hung at point C, which is 0.4 m from the pivot on the other side, to balance the rod?

  • Solution:

    1. Identify the moments: The 4 N weight causes a clockwise moment. The unknown weight (x) causes an anti-clockwise moment.

    2. Apply the principle: Anti-clockwise Moment = Clockwise Moment

    3. Substitute the formula: (Force × Distance) = (Force × Distance)

    4. x × 0.4 m = 4 N × 0.5 m

    5. x × 0.4 = 2.0

    6. x = 2.0 / 0.4 = 5 N.

• List Real-world Examples: Be ready to give examples of where moments and couples are used in daily life (e.g., wheelbarrow, crowbar, bottle opener, bicycle pedals).