1. Equilibrium

✅ Definition:

Equilibrium is the state in which all forces and moments acting on a body are balanced, so the body remains at rest or moves with constant velocity (i.e., no turning or linear acceleration).

🔄 Types of Equilibrium:

⚖️ Conditions for Equilibrium:

A body is in equilibrium if:

1. Resultant Force = 0
   ➤ No net linear movement.

   $$\sum \text{Upward Forces} = \sum \text{Downward Forces}$$

2. Resultant Moment = 0
   ➤ No net turning effect.

   $$\sum \text{Clockwise Moments} = \sum \text{Anticlockwise Moments}$$

🧪 Real-life Examples:

• A balanced see-saw

• A weighing scale at rest

• A building standing still

• A ruler balanced at its center

🔹 2. Centre of Gravity (C.G.)

✅ Definition:

The centre of gravity of a body is the point through which the entire weight of the body seems to act, regardless of its orientation.

📍 Key Facts:

• For regular-shaped objects, the C.G. is at the geometric center.

• For irregular-shaped objects, the C.G. must be found experimentally.

• The weight of an object acts vertically downward through the C.G.

🧪 How to Find the Centre of Gravity (Experimentally):

Apparatus:

• Irregular cardboard shape

• String

• Plumb line

• Pin or nail

• Board to pin on

Steps:

1. Suspend the shape from one point and let it hang freely.

2. Use a plumb line to draw a vertical line from the suspension point.

3. Repeat by suspending from a second and third point.

4. The intersection point of the lines is the center of gravity.

🔄 Stability and Centre of Gravity

⚠️ Factors Affecting Stability:

1. Position of C.G.
   ➤ Lower C.G. = more stable

2. Base Area
   ➤ Wider base = more stable

3. Height of the object
   ➤ Taller object = less stable

🧠 Types of Equilibrium Based on C.G.:

🔧 Applications of Centre of Gravity and Equilibrium:

• Design of vehicles (low C.G. improves safety)

• Cranes and bridges (must maintain equilibrium)

• Sports (athletes adjust C.G. for balance)

• Architecture (wide base and low C.G. for stability)

  1. Equilibrium

  ✅ Definition:

  Equilibrium is the state in which all forces and moments acting on a body are balanced, so the body remains at rest or moves with constant velocity (i.e., no turning or linear acceleration).

  ---

  🔄 Types of Equilibrium:

  Type	Description	Example
  Static Equilibrium	Body is at rest and remains at rest	Book on a table
  Dynamic Equilibrium	Body moves at constant speed in a straight line	Car on a highway at constant speed

  ---

  ⚖️ Conditions for Equilibrium:

  A body is in equilibrium if:

  1. Resultant Force = 0
     ➤ No net linear movement.

     $$\sum \text{Upward Forces} = \sum \text{Downward Forces}$$

  2. Resultant Moment = 0
     ➤ No net turning effect.

     $$\sum \text{Clockwise Moments} = \sum \text{Anticlockwise Moments}$$

  ---

  🧪 Real-life Examples:

  • A balanced see-saw

  • A weighing scale at rest

  • A building standing still

  • A ruler balanced at its center

  ---

  🔹 2. Centre of Gravity (C.G.)

  ✅ Definition:

  The centre of gravity of a body is the point through which the entire weight of the body seems to act, regardless of its orientation.

  ---

  📍 Key Facts:

  • For regular-shaped objects, the C.G. is at the geometric center.

  • For irregular-shaped objects, the C.G. must be found experimentally.

  • The weight of an object acts vertically downward through the C.G.

  ---

  🧪 How to Find the Centre of Gravity (Experimentally):

  Apparatus:

  • Irregular cardboard shape

  • String

  • Plumb line

  • Pin or nail

  • Board to pin on

  Steps:

  1. Suspend the shape from one point and let it hang freely.

  2. Use a plumb line to draw a vertical line from the suspension point.

  3. Repeat by suspending from a second and third point.

  4. The intersection point of the lines is the center of gravity.

  ---

  🔄 Stability and Centre of Gravity

  ⚠️ Factors Affecting Stability:

  1. Position of C.G.
     ➤ Lower C.G. = more stable

  2. Base Area
     ➤ Wider base = more stable

  3. Height of the object
     ➤ Taller object = less stable

  ---

  🧠 Types of Equilibrium Based on C.G.:

  Type	Description	Example
  Stable Equilibrium	Returns to original position when slightly tilted	Wide-base cone
  Unstable Equilibrium	Falls over when disturbed	Pencil standing on tip
  Neutral Equilibrium	Stays in new position when moved	Ball on a flat surface

  ---

  🔧 Applications of Centre of Gravity and Equilibrium:

  • Design of vehicles (low C.G. improves safety)

  • Cranes and bridges (must maintain equilibrium)

  • Sports (athletes adjust C.G. for balance)

  • Architecture (wide base and low C.G. for stability)