🏠 Home › 📚 CSEC Physics › ⚖️ Moments & Equilibrium

Mastering Moments and Equilibrium

CSEC Physics: Turning Effects

Essential Understanding: A moment is the turning effect of a force. It determines whether a seesaw tips, a bridge holds, or a crane lifts safely. Master the Principle of Moments to solve equilibrium problems where an object is balanced and not moving.

🔑 Key Skill: Calculating Moment (\(F \times d\))
📈 Exam Focus: Principle of Moments calculation
🎯 Problem Solving: Center of Gravity & Stability

Core Concepts

🔄

Moment of a Force

Definition: The turning effect of a force about a point (pivot).

Formula: \[ M = F \times d \]

  • \( F \): Force (Newtons, N)
  • \( d \): Perpendicular distance from pivot (m, m)

Unit: Newton-meter (Nm)

📐

The Pivot (Fulcrum)

Definition: The point around which the body rotates or turns.

CSEC Concept: When calculating moments, the distance \( d \) is always measured perpendicular to the line of action of the force from the pivot.

⚖️

Equilibrium

Definition: A state where an object is at rest or moving with constant velocity (constant speed in a straight line).

Conditions for Equilibrium:

  1. Sum of Forces = 0 (Up = Down, Left = Right)
  2. Sum of Clockwise Moments = Sum of Anticlockwise Moments

The Principle of Moments

For an object in equilibrium (balanced), the total clockwise turning moment must equal the total anticlockwise turning moment about any point.

\[ \sum M_{\text{clockwise}} = \sum M_{\text{anticlockwise}} \]

This is also known as the Law of the Lever.

Interactive Seesaw Lab

🎢

Balance Challenge

Objective: Add weights to the seesaw to balance it. Place weights at different distances to change the moments.

Left Side (Anticlockwise)
Right Side (Clockwise)

Anticlockwise Moment

0 Nm

Clockwise Moment

0 Nm

Balanced

Center of Gravity & Stability

The Center of Gravity (C.G.) is the point through which the entire weight of an object appears to act.

Analysis: The chart above compares different states of stability. In Stable Equilibrium, the C.G. rises when displaced and returns. In Unstable Equilibrium, the C.G. falls and the object topples.

🏗️

Worked Example: Bridge Beam

A uniform beam of weight 100N and length 4m is supported at its ends (Pivots A and B). A load of 200N is placed 1m from Pivot A. Calculate the force at Pivot B.

1
Diagram & Variables: Pivot A is at 0m, Pivot B is at 4m. Weight of beam (100N) acts at center (2m). Load (200N) is at 1m. Reaction at B is \( R_B \).
2
Take Moments about Pivot A: Taking moments about A eliminates the unknown reaction at A.
3
Clockwise Moments (Right side): \( (R_B \times 4) + (100\text{N (weight of beam)} \times 2) \).
4
Anticlockwise Moments (Left side): \( 200\text{N} \times 1\text{m} = 200\,\text{Nm} \).
5
Solve: \( 200 = 4R_B + 200 \Rightarrow 4R_B = 0 \Rightarrow R_B = 0 \, \text{N} \). (The beam is on the verge of tipping up at A!)

Key Examination Insights

Common Mistakes

  • Using the length of the object as the distance instead of the distance from the pivot.
  • Forgetting to include the weight of the beam itself if it’s “uniform”. (Weight acts at the midpoint).
  • Mixing up clockwise and anticlockwise signs.

Success Strategies

  • Always draw a large, clear diagram with labels.
  • Write “Sum Clockwise = Sum Anticlockwise” before every calculation.
  • Choose your pivot wisely: often picking the pivot where an unknown force acts eliminates it from the equation.

CSEC Practice Arena

Test Your Understanding

1
Which of the following is the correct unit for a moment?
Joule (J)
Newton (N)
Newton-meter (Nm)
Meter (m)
Explanation: A Moment is Force \( \times \) Distance. \( \text{N} \times \text{m} = \text{Nm} \). Note that Joules (J) are also Nm, but are reserved for Work/Energy, not turning effects.
2
A 10N force acts perpendicularly 2m from a pivot. What is the moment?
5 Nm
20 Nm
12 Nm
8 Nm
Solution: \( M = F \times d = 10 \times 2 = 20 \, \text{Nm} \).
3
A see-saw is balanced. A child of weight 300N sits 2m from the pivot. If another child sits 3m from the pivot on the other side, what is their weight?
100 N
300 N
450 N
200 N
Solution: Clockwise = Anticlockwise. Let \( W \) be the unknown weight. \( W \times 3 = 300 \times 2 \Rightarrow 3W = 600 \Rightarrow W = 200 \, \text{N} \).
🎯

CSEC Examination Mastery Tip

Choosing the Pivot: When solving complex equilibrium problems (like ladders against walls), you have the freedom to choose any point as the pivot.

  • Always choose the pivot where unknown forces act. This makes their distance zero, so their moment becomes zero, eliminating them from the calculation immediately.
  • This reduces the number of simultaneous equations you need to solve.
Scroll to Top