Problem based on Equilibrium of Rigid Body

Описание: Problem based on Equilibrium of Rigid Body
A rigid body is in equilibrium when the sum of all external forces acting on it is zero (translational equilibrium) and the sum of all external moments (torques) about any point is also zero (rotational equilibrium). These two conditions, expressed as ∑F = 0 and ∑M = 0, ensure the body has no linear or angular acceleration, remaining at rest or moving with constant velocity.  

Conditions for Equilibrium 

Translational Equilibrium: 

The vector sum of all forces acting on the rigid body is zero.

∑F = 0

This means the body's linear momentum remains constant; it experiences no linear acceleration.

Rotational Equilibrium: 

The vector sum of all moments (torques) acting on the rigid body about any arbitrary point is zero.

∑M = 0

This means the body's angular momentum remains constant; it experiences no angular acceleration.

Types of Equilibrium

Static Equilibrium: 

A rigid body is in static equilibrium if it is at rest and remains at rest. 

Dynamic Equilibrium: 

A rigid body is in dynamic equilibrium if it is in motion with constant linear velocity and constant angular velocity. 

Importance of Rigidity

In a rigid body, forces can cause either linear acceleration or rotation. For a body to be in equilibrium, neither of these accelerations must be present. 

Forces must be applied at specific points to produce moments that balance the existing moments. The body must not deform, so any deformation is negligible or irrelevant.