Equilibrium Conditions for a Particle

A particle is in equilibrium when different forces act upon it but its motion does not change with time. This means the particle either remains at rest or continues moving at constant velocity. Equilibrium requires two conditions: the net force must equal zero, and the net torque about any axis through the particle must also be zero.

Static equilibrium occurs when a particle is at rest with zero net force and zero net torque. Dynamic equilibrium occurs when a particle moves with constant velocity while maintaining zero net force and zero net torque. Both states satisfy the same equilibrium conditions but differ in whether the particle is stationary or moving uniformly.

The net force is the vector sum of all forces acting on a particle. If the net force equals zero, the forces are balanced and cannot change the particle's motion. This is the first equilibrium condition. For example, a parked car experiences gravitational force downward and normal force upward from the ground, which cancel each other, resulting in zero net force.

Net torque is the vector sum of all moments acting on a particle about an axis. For equilibrium, net torque must equal zero, preventing rotational motion. When two equal masses sit equidistant from a plank's center on a pivot, they create equal but opposite torques that balance each other, establishing static equilibrium with zero net moment.

Forces acting on a particle can add, subtract, or cancel each other depending on their directions and magnitudes. When the vector sum of all forces equals zero, the forces are balanced and the particle achieves equilibrium. This force balance is essential for both static and dynamic equilibrium conditions.

Yes, a particle can be in dynamic equilibrium while moving at constant velocity. As long as the net force and net torque remain zero, the particle's motion does not change. This differs from static equilibrium, where the particle is at rest, but both satisfy the same fundamental equilibrium conditions.

Free body diagrams represent all forces acting on a particle as vectors. By drawing these diagrams, you can visually verify that forces balance and net force equals zero. This approach helps identify whether equilibrium conditions are satisfied and is essential for free body diagrams problem solving in mechanics.