3.1:
Equilibrium Conditions for a Particle
When different forces act upon a particle, but its motion does not change with time, it is said to be in equilibrium. Equilibrium can be categorized as static or dynamic.
If a particle is at rest, it is said to be in static equilibrium, and if it is moving with constant velocity, the particle is said to be in dynamic equilibrium.
For a particle to be in equilibrium, it should satisfy two conditions simultaneously. First, the net force, the vector sum of all the forces acting on the particle, must equal zero.
Second, the net torque acting on the particle about an axis passing through the particle must be zero, indicating that the net moment is also equal to zero.
Consider two equal masses placed at the two ends of a wooden plank equidistant from its center. The plank's center is set on a cylindrical pivot. In such a condition, static equilibrium is established since the net force, and the net torque on the system is zero.
3.1:
Equilibrium Conditions for a Particle
When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can add, subtract, or cancel each other out. If the vector sum of all the forces acting on an object is zero, the object is at rest or is moving with a constant velocity.
The first condition that an object must satisfy to be in equilibrium is that the net force acting on it must be zero. This implies that the vector sum of all the forces acting on the object must equal zero. In other words, the forces acting on the object must be balanced. For example, consider a car parked on a level surface. Even though gravitational force is acting upon the vehicle, the force acting upon it from the ground (the normal force) counterbalances it, resulting in zero net force and equilibrium.
The second condition the object must satisfy to be in equilibrium is that the net torque and, as a result, the net moment acting on it must also be zero. An example of torque causing the rotational movement of an object is a wooden plank on a pivot. Two masses of equal weight on either end create a torque, but since they are equidistant from the center of the plank, the torques balance each other out, resulting in zero net torque and static equilibrium.
Suggested Reading
- Hibbeler, R.C. (2016). Engineering Mechanics ‒ Statics and Dynamics. Hoboken, New Jersey: Pearson Prentice Hall. Pp 87.
- OpenStax. (2023). University Physics Vol. 1. [Web version]. Retrieved from https://openstax.org/books/university-physics-volume-1/pages/12-1-conditions-for-static-equilibrium.