Name: balanced forces and torque in equilibrium
Uploaded: 2023-09-22T11:49:20.000Z
Duration: 1 min 23 s
Channel: JoVE

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,&#160; the net force, the vector sum of all the forces acting on the particle, must equal zero.&#160;&#160;&#160;&#160;
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&#39;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.

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.

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 ...

Education

JoVE Core

Mechanical Engineering

Unit 1

Equilibrium of a Particle

KEY TERMS AND CONCEPTS

balanced forces and torque in equilibrium

Equilibrium depends on balanced forces and balanced torque. An object in equilibrium is either at rest or moving with a constant velocity. These two cases are called static equilibrium and dynamic equilibrium.

Static equilibrium means the object is not moving. Dynamic equilibrium means the object is moving, but its velocity stays constant. In both cases, the forces acting on the object must balance each other.

Different forces can add, subtract, or cancel each other out. When the vector sum of all the forces is zero, the object is in equilibrium. That is why the net force must be zero. A parked car on a level surface is a simple example. Gravity pulls it downward, and the normal force from the ground pushes upward to balance it.

The second condition for equilibrium is zero net torque. Torque is the turning effect of a force, and it can cause rotation. Net torque, or the total moment, must also be zero. A wooden plank on a pivot shows this idea. If two equal masses sit at equal distances from the center, their torques cancel, and the plank stays in static equilibrium.

Balanced Forces and Torque in Equilibrium

balanced-forces-and-torque-in-equilibrium

Equilibrium depends on balanced forces and balanced torque. An object in equilibrium is either at rest or moving with a constant velocity. These two cases are called static equilibrium and dynamic equilibrium. Static equilibrium means the object is not moving. Dynamic equilibrium means the object is moving, but its velocity stays constant. In both cases, the forces acting on the object must balance each other. Different forces can add, subtract, or cancel each other out. When the vector sum...

free-body diagram

Free-Body Diagrams for Force Analysis

Free-body diagrams help analyze the forces acting on an object in mechanics. They give a simple picture of a stationary or moving object and show why it moves the way it does. By turning a complex situation into a clear sketch, they make it easier to write the equation needed to solve the problem. To draw a free-body diagram, first choose the object or system you want to study. Then isolate it from its surroundings and draw it as a dot or a simple outline. Add arrows for every important...

steps for free-body diagram

Free-Body Diagram for Two-Block Motion

A free-body diagram helps analyze two-block motion in mechanics. It shows the forces acting on a system so the net force can be found and the acceleration can be calculated. The example in this lesson uses two blocks linked by a massless string over a frictionless pulley. Block 1 moves across a table while block 2 falls under gravity. The two blocks are treated as one isolated system. External forces are then identified and drawn as vector arrows on the diagram. For block 1, the forces...

free-body diagrams: problem solving

Free-Body Diagrams on Inclined Planes

Free-body diagrams help show the forces acting on an object on an inclined plane. A free-body diagram is a simple drawing that focuses only on the object or system being studied. It leaves out extra details so the force problem is easier to analyze and solve. For an example, a 10 kg block is released on a ramp that is 30° to the horizontal. The coefficient of friction is 0.2. The diagram for this block includes the weight from gravity, the normal force, and the frictional force. These are the...

coplanar forces

Resolving Coplanar Force Components

Coplanar forces act on an object in the same plane. To analyze this kind of system, each force is resolved into x and y components using Cartesian vector form and vector algebra. This makes it possible to test whether the object is in equilibrium. A coplanar system is in equilibrium when the resultant force is zero. That means the sum of the forces in each direction must also be zero. If the forces do not balance, the object is not in equilibrium and will accelerate in the direction of the net...

categories of equilibrium

Types of Equilibrium in Forces

Equilibrium in physics describes how forces act on a body so it stays still or moves at a constant speed. In two-dimensional force systems, equilibrium can be grouped into several categories based on how the forces are arranged. Collinear equilibrium is the simplest case. The forces act along one straight line, so only one force equation is needed in the direction of those forces. The other equations are already satisfied. Coplanar concurrent equilibrium is another category. In this case, all...

key terms and concepts

Learn how balanced forces and zero net torque keep an object in static or dynamic equilibrium, with examples like a parked car and a plank on a pivot.

Balanced Forces and Torque in Equilibrium | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Balanced Forces and Torque in Equilibrium

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