# Degrees of Freedom in Physics: Theory & Solutions

• chimay
In summary, the conversation discusses using a method to solve problems in basic physics by analyzing the two degrees of freedom of a system and combining the results. The person is looking for information on this approach and its theoretical background, specifically in rotational dynamics and constraint equations. They mention Halliday, Resnik, and Krane as potential sources and ask for a detailed discussion and mathematical formulation of this approach. The concept of applied science is suggested as a potential term to search for.
chimay
Hi,

in my previous course on basic Physics we learned to solve problems concerning simple mechanical systems like this:

The method consists in analyzing separately the two degrees of freedom of the system, computing for each degree the acceleration of each body (or whathever) and the sum both of them to obtain the overall result.
Can someone tell me where I can find information about this approach? What does assure me that the sum of the quantities give me the correct result? I would like to understand in detail where the theoretical backgroud lies.

Thank you.

PHYSICS
halliday resnick krane vol 1

you need to understand rotational dynamics for this and also constraint equations

chimay
Halliday, Resnik? Boy, that brings memories from several decades ago...but not enough to know what the OP is talking about...

...then again, simply from the "degrees of freedom" point of view, the reason why you can combine the results is precisely because these two quantities are independent from each other...otherwise, they wouldn't be degrees of freedom...it is like solving for the x position AND the y position of an object and combining the two quantities to know exactly where the object is in space.

Does this help?

keywords: degrees of freedom, state variables.

chimay
Thank you, very helpfull.

Where can I find quite a detailed discussion about these topics?
I am looking for a general approach of this kind and its mathematical formulation.

Thank you a lot

chimay said:
Thank you, very helpfull.

Where can I find quite a detailed discussion about these topics?
I am looking for a general approach of this kind and its mathematical formulation.

Thank you a lot

Would it be that you are looking for the term, "Applied Science", the application of formulas for specific uses found in engineering.

Applied Science
https://en.wikipedia.org/wiki/Applied_science

chimay

## 1. What is the concept of degrees of freedom in physics?

Degrees of freedom in physics refers to the number of independent variables or parameters that are required to fully describe the state of a physical system. It is a measure of the system's complexity and the number of ways in which it can move or change.

## 2. How is the concept of degrees of freedom used in physics?

Degrees of freedom are used in various areas of physics, such as thermodynamics, mechanics, and statistical mechanics. They help in analyzing and understanding the behavior of physical systems, including the movement of particles, energy transfer, and phase transitions.

## 3. Can you provide an example of degrees of freedom in a physical system?

One example is a simple pendulum, which has two degrees of freedom - the angle of the pendulum and its angular velocity. These variables determine the position and motion of the pendulum at any given time.

## 4. What is the difference between constrained and unconstrained degrees of freedom?

Constrained degrees of freedom are restricted by external forces or conditions, such as boundaries or constraints imposed on a system. Unconstrained degrees of freedom are free to vary without any restrictions or limitations.

## 5. How do degrees of freedom affect the behavior of a physical system?

The number of degrees of freedom in a system determines its energy and entropy, which in turn affect its behavior. For example, a system with more degrees of freedom will have a higher energy and more possible variations, leading to a more complex and dynamic behavior.

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