Learning Materials

Features

Discover

# Dynamic Systems

Suzie plays basketball with her brother Tom (an inquisitive toddler.)  Suzie drops the ball; it bounces and eventually stops. If asked, "who dropped the ball?". Tom says, "Suzie." To go further, as inquisitive toddlers do, Tom asks, "Why"...

#### Create learning materials about Dynamic Systems with our free learning app!

• Flashcards, notes, mock-exams and more
• Everything you need to ace your exams

To help Tom understand why the ball dropped and how it bounced and stopped, we look at the influences around Suzie and the ball. To make it simpler, we may group Suzie, Tom, a basketball court, a ball, and the ground, calling the group a "system."

## Definition of Dynamic Systems

To understand the fundamental concept of systems, we first need to know what a system is. When studying something in physics, we want to consider exactly the things relevant to what we are studying and ignore everything else. The things we include in what we are studying are called our system. Plainly put,

A system is an object or collection of objects.

We treat the objects in our system as if they had no internal structure. The internal structure of the objects should have no bearing on the final solution of the problem and can be ignored. Everything that is not part of our system is considered the environment.

A system can be a person and an automobile, a person and a skateboard, or even a classroom with desks and chairs. When calculating the acceleration of a system, we can use Newton's second law of motion. The properties and interactions of their substructures determine the properties of systems. When individual parts are not important for modeling the system's behavior, the system itself may be referred to as an object. According to Newton's first law of motion, only external forces affect a system's motion. That is because the law says an object at rest tends to stay at rest, and an object in motion tends to stay in motion. Since we have this distinction, defining the boundaries of a system should be done before we can understand what forces are affecting its motion.

For all systems and circumstances, energy, charge, linear momentum, and angular momentum are conserved except for an isolated or closed system, where conserved quantities are constant. We call an "interaction" a force caused by other objects outside the system, or the transfer of some quantity between the system and its environment. When solving a problem you consider the situation and make your own decision about the boundary between a system and its environment. The main characteristic of a dynamic system is a function that describes what future states follow from the current state.

Remember that a collection of particles where internal interactions change little or not at all, or where changes in these interactions are irrelevant to the question or problem being solved, can be treated as an object.

Some elementary particles are fundamental particles, (e.g., electrons). Protons and neutrons are composed of fundamental particles and might be treated as either systems or objects, depending on the question being addressed in the problem being solved.

The electric charges on neutrons and protons result from quark compositions.

### What are the Basic Types of Systems?

There are three types of basic systems: Open, Closed, and Isolated systems. Below we will discuss some of the properties of each and how they relate to one another.

We start our discussion with open systems

An open system is a physical system where matter and energy can enter or leave the system. External forces outside the system are not balanced.

Consider the following diagram of a heated flask. If our system is the beaker, then we have energy being added to the system in the form of heat, and matter leaving in the form of water vapor.

Model of an open system Wikicommons Public Domain

Closed systems are more restricted compared to open systems. Energy can still enter or leave the system, but now we add the restriction that matter cannot.

A closed system is a physical system where no matter can enter or leave the system. Additionally, external forces must balance.

In our diagram, we now put a stopper on the top of the flask. Now air cannot be exchanged between the environment and the system, though heat can still enter and leave through the glass.

An example of a closed system Wikicommons, Public Domain.

Note that in a closed system you can have external forces, we just require that the net force on our system is zero.

Tip: A closed system refers to a system that doesn't lose mass, energy, charge, etc., so conserved quantities are considered to be constant. On the other hand, an open system refers to exchanges of energy, charge, etc., with the object(s) surrounding since the amount of the previously stated quantities can increase or decrease without replacement.

Finally, we come to our most restricted type of system. Isolated systems, where, you may have guessed, we add a further restriction that both matter and energy cannot enter or leave the system. In practice, we cannot have a system that exchanges no energy with its environment, but it is still a useful tool for modeling some systems.

An isolated system is a type of closed system where neither matter nor energy can transfer into or out of the system.

We return once again to our flask, but this time we place our flask within a sealed vacuum flask. Heat and matter are now restricted from entering or leaving our system.

Example of isolated system Wikicommons Public Domain

An isolated system does not interact with its surroundings. Its total energy and mass stay constant.

### Real-Life Examples of Systems

Properties of open, closed, and isolated systems Wikicommons

Examples of Systems StudySmarter Originals

## Dynamic Systems

Now let's take a look at what dynamic systems are.

A dynamic system means the motion of systems under the influence of forces.

### Examples of Dynamic Systems

A dynamic system is a system where motion occurs, as opposed to static conditions with no motion. Dynamic systems are constantly moving or must change states to be useful.

Examples of Dynamic Systems include:

• Automobiles
• Computers
• A Swinging Pendulum
• Motions of Celestial Bodies

To make a prediction about a system's future behavior, an analytical solution of equations, or their integration over time through a computer simulation is completed. The study of dynamical systems is the focus of dynamical systems theory, which has applications to a wide variety of subject fields (Math, Physics, Biology, Chemistry, Engineering, History, and Medicine). Dynamical systems are a fundamental part of chaos theory, logistic map dynamics, and the edge of chaos concept. (to name a few).

Dynamic systems are systems that involve change.

## Dynamic Equilibrium System

Dynamic equilibrium in a reversible process happens when the forward and the reverse processes occur at the same exact rate thus, dynamic equilibrium is when all forces acting on an object are balanced.

There are three conditions to achieve equilibrium. First, the net external force of the system must be zero. Second, the sum of all external torques must be zero. Finally, we can say the object is in equilibrium when both conditions are met simultaneously. If one is not satisfied, the object is not in equilibrium.

• The equation is: $F\mathit{=}\mathit{0}$
• Static means motionless or stationary
• Dynamic means energetic

The system must maintain constant angular velocity and avoid accelerated rotation to achieve equilibrium.

Dynamic Equilibrium is the state of a given system in which there is no net change.

• Static Equilibrium: occurs when the net force on a motionless object/system is 0
• Dynamic Equilibrium: occurs when the net force on a moving object/system is 0 (no acceleration though, must have a constant velocity)
• If it's not moving or at a constant rate, all forces are balanced

## Examples of Dynamic Equilibrium

Let's take a look at the difference between static and dynamic equilibrium.

Static equilibrium refers to a condition where the reaction occurring in a system is completely halted and there is no movement between the reactants and the products corresponding to the chemical reaction.

If the forces acting on an object cancel each other, in addition to the constancy of content and composition, no movement of the object takes place. This is static equilibrium.

Key Differences - Static and Dynamic Equilibrium

Static vs dynamic equilibrium chart StudySmarter Originals

The resultant force acting on both of these types of equilibria in a system is zero. Generally, neither of these types of equilibrium display visible changes.

Now that we can tell the difference between dynamic and static equilibrium, here are examples of dynamic equilibrium.

Rotating Fan

Rotating fan Wikicommons

A fan rotating with constant velocity is one of the excellent dynamic equilibrium examples.

When the fan is rotating with constant velocity, the angular acceleration and the torque acting on the fan are nullified, thus balanced by the dynamic equilibrium.

Raindrops

Raindrops, Pixabay

The raindrop reaches Earth from the cloud at a certain velocity. The speed of the raindrop increases while falling to Earth because of the acceleration due to gravity.

Each drop of rain moves with the same velocity. Due to air resistance and friction, the raindrop stops accelerating once it reaches terminal velocity.

## Discrete Dynamical Systems

Finally, we consider a specific type of dynamic system. In discrete dynamical systems, we consider the system in snapshots in time. Formally, we say:

A Discrete Dynamical System is a dynamic system where the state of the system evolves in discrete steps.

These could be natural steps where things change at specific times. The United States government is one example of this. It is a system that evolves in time, but it does not change smoothly. There are specific points in time where changes occur. In this example, those points in time are elections. We can also artificially create discrete steps. Consider a census. The population data is updated every ten years. These are discrete steps, and we can make predictions and models based on this data, but the actual population change is far more continuous with people dying and being born every day.

## Dynamic Systems - Key takeaways

• A system is an object or collection of objects without internal structure.

• There are three types of basic systems: Open, Closed, and Isolated.

• Static equilibrium refers to a condition where stability is reached.

• Dynamic equilibrium only occurs in reversible reactions.

#### Flashcards in Dynamic Systems 15

###### Learn with 15 Dynamic Systems flashcards in the free StudySmarter app

We have 14,000 flashcards about Dynamic Landscapes.

What is a dynamic system?

A dynamic system in Physics is usually described as a "particle or ensemble of particles whose state varies over time, thus obeying differential equations involving time derivatives".

What are examples of a dynamic system?

One example of a dynamic system is the human body.

What are the basic types of systems?

The types of systems in physics are open, closed and, isolated.

What is dynamical systems used for?

Dynamical systems are mainly used to model physical phenomena whose state (or instantaneous description) changes over time.

What is the main characteristic of a dynamic system?

The main characteristic of a dynamic system is a function that describes what future states follow from the current state.

## Test your knowledge with multiple choice flashcards

What is the definition of a system in Physics?

What are the three types of basic systems in Physics?

Static equilibrium refers to a condition where the reaction occurring in a system is completely halted and there exists no movement between the reactants and the products corresponding to the chemical reaction.

StudySmarter is a globally recognized educational technology company, offering a holistic learning platform designed for students of all ages and educational levels. Our platform provides learning support for a wide range of subjects, including STEM, Social Sciences, and Languages and also helps students to successfully master various tests and exams worldwide, such as GCSE, A Level, SAT, ACT, Abitur, and more. We offer an extensive library of learning materials, including interactive flashcards, comprehensive textbook solutions, and detailed explanations. The cutting-edge technology and tools we provide help students create their own learning materials. StudySmarter’s content is not only expert-verified but also regularly updated to ensure accuracy and relevance.

##### StudySmarter Editorial Team

Team Physics Teachers

• Checked by StudySmarter Editorial Team