The vector sum of all the external forces acting on a rigid body is expressed as $\sum F$ and the vector sum of moments of the external forces about a point is given as $\sum M$. The rigid body is in equilibrium if

Question

Prepp Team · Accepted Answer

Conditions for Rigid Body Equilibrium

A rigid body is considered to be in equilibrium when it has no linear or angular acceleration. This state is achieved when the net effect of all external forces and moments acting on it is zero.

Fundamental Equilibrium Equations

For a rigid body to be in static equilibrium, two conditions must be met simultaneously:

The vector sum of all external forces acting on the body must be zero. This prevents linear acceleration. Mathematically, this is represented as:
$\sum \vec{F} = \vec{0}$
The sum of the moments (or torques) of all external forces about any point must be zero. This prevents angular acceleration. Mathematically, this is represented as:
$\sum \vec{M} = \vec{0}$

Conclusion

Therefore, the rigid body is in equilibrium if and only if both the sum of the forces ($\sum F$) and the sum of the moments ($\sum M$) are equal to zero.

This corresponds to Option 3: $\sum F = 0$ and $\sum M = 0$.