Class 9 > Unit # 04: Turning Effect of Forces > Equilibrium & Conditions of Equilibrium

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Turning Effect of Forces - Equilibrium and its Conditions

Q.10 Define Equilibrium and its types.

Equilibrium

"When a body does not possess any acceleration—neither linear nor angular—it is said to be in equilibrium."

Examples: A book lying at rest on a table, a paratrooper moving downwards with terminal velocity, or a chairlift hanging stationary on supporting ropes.

Types of Equilibrium

There are two primary types of equilibrium:

1. Static Equilibrium
2. Dynamic Equilibrium

1. Static Equilibrium

When a body is completely at rest, it is said to be in static equilibrium.

Example: A wall hanging, buildings, bridges, or any object resting stationary on the ground.

2. Dynamic Equilibrium

When a moving object is in uniform motion and does not possess any acceleration (neither linear nor angular), it is said to be in dynamic equilibrium.

Example: Uniform downward motion of a steel ball through a viscous liquid, or a paratrooper descending with steady terminal velocity after jumping from a helicopter.

Q.11 State and explain 1st and 2nd condition of equilibrium.

1. First Condition for Equilibrium (Translational Equilibrium)

"A body is in the first condition of equilibrium if the vector sum of all the forces acting on the body is equal to zero."

Suppose $n$ number of forces $\vec{F}_1, \vec{F}_2, \vec{F}_3, \dots, \vec{F}_n$ are acting on a body. According to the first condition of equilibrium:

$\vec{F}_1 + \vec{F}_2 + \vec{F}_3 + \dots + \vec{F}_n = 0 \implies \sum \vec{F} = 0 \quad \text{--- (i)}$

Where $\Sigma$ (Sigma) represents summation. In terms of rectangular components along the $x$ and $y$ axes, this condition can be resolved into two scalar equations:

$\sum F_x = F_{1x} + F_{2x} + F_{3x} + \dots + F_{nx} = 0$

$\sum F_y = F_{1y} + F_{2y} + F_{3y} + \dots + F_{ny} = 0$

2. Second Condition for Equilibrium (Rotational Equilibrium)

"A body is in the second condition of equilibrium if the sum of all the torques acting on the body is equal to zero."

Suppose $n$ number of torques $\tau_1, \tau_2, \tau_3, \dots, \tau_n$ are acting on a body. According to the second condition of equilibrium:

$\tau_1 + \tau_2 + \tau_3 + \dots + \tau_n = 0 \implies \sum \tau = 0 \quad \text{--- (ii)}$

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