# Rigid Bodies in Equilibrium

## Rigid Bodies in Equilibrium

# Introduction to Rigid Bodies

- A
is an idealised concept where the body does not deform under the application of force.*rigid body* refers to a state where the resultant force and torque acting on a rigid body are zero.*Equilibrium*- If a body is in equilibrium, it means that it is either at rest or moving with a constant velocity.

# Conditions for Equilibrium

- There are two conditions required for a rigid body to be in equilibrium:
- The vector sum of all forces acting on the body must be zero -
.*translational equilibrium* - The sum of all torques, or moments, about any point must also be zero -
.*rotational equilibrium*

- The vector sum of all forces acting on the body must be zero -

# Centre of Mass

- The
is a point in a rigid body where the total weight of the body can be assumed to act.*centre of mass* - For symmetric bodies, the centre of mass is at the geometric centre.
- For an irregular shape or system of particles, the position of the centre of mass can be calculated using the formula:
*∑miri / ∑mi*- where ‘mi’ represents the mass of the i-th object and ‘ri’ represents its distance from the reference point.

# Resultant Force

- A single force that has the same effect as all the forces acting on the body is termed as the
.*resultant force* - The resultant force is found by vector addition of all the forces acting on the body.

# Torque of a Force

- The
, or the moment of a force about a point, is a measure of the rotational effect of the force about the point.*torque* - The torque τ is calculated by multiplying the force ‘f’ by the perpendicular distance ‘r’ from the point to the line of action of the force.
- τ = r f sin(θ)

# Principles of Moments

- According to the principle of moments, for a body to be in equilibrium, the sum of clockwise moments about any point needs to be equal to the sum of anticlockwise moments about that same point.

# Free Body Diagrams

are visual representations used to analyze the forces and torques acting on a rigid body.*Free body diagrams*- These diagrams include all the forces acting on the body, as well as their direction and point of application.

# Solving Equilibrium Problems

- Step 1: Draw a free body diagram that represents the problem.
- Step 2: Identify all the forces acting on the body and write down the equations of equilibrium.
- Step 3: Use the equations of equilibrium to solve for the forces or moments, as required.
- Use the principles of vector addition and principles of moments to solve these problems.