What is the Degree of Freedom of a System?

In summary, the conversation discusses the concept of degrees of freedom (DOF) in a system and how to determine the number of DOF for two given systems. The main question is whether the spring in the first system should be considered when counting the DOF. It is concluded that the number of DOF is determined by the number of independent coordinates needed to describe the position of each particle or component in the system, and not by the velocities. Therefore, the first system has 4 DOF and the second system has 1 DOF.
  • #1
DarkDrag0nite
15
0
This is not really the homework. It is the university examination problem. The problem here is many teachers/professors answer differently and not much detailed. And we don't know who was the exact professor who create these problems.

Homework Statement



Instuction: Find the number of "Degree of Freedom (dof)" in the system.

First System

47295.jpg


Second System
(Please ignore unreadable words, they're Thai language but you can understand by their variables)

47327.jpg


Homework Equations



I don't think there is any relevant equation here.

The Attempt at a Solution



For the First System:

Absolutely, 2 Boxes (M1 and M2) can move left and right. So there are 2 dof.
The 2 sphere (m1 and m2) with the rope can move in circular. So there are 2 dof.
I'm not sure if we also consider 2 sphere that they can move left and right or not ?
If we do, so 6 dof. If not, so 4 dof.
What's should I answer ? 6 or 4 dof ?

For the Second System:

There are two pulleys stuck together (m and M) so we consider as one object which can rotate in 1 circular direction. So there is 1 dof.
The box (MB) can move up and down. So there is 1 dof.
Here is problem, some professors said that the box can move in 3 axis which is 3 dof. Is it reasonable ?
I myself think the box should have only 1 dof which corresponds to the system.
Should answer to this system be 2 dof or 4 dof ?

Any help is appreciative. (I will be at school and not be able to reply for 2 days)
 
Physics news on Phys.org
  • #2
Anybody please ?

Maybe I didn't give much information about variable.
R = radius of the pulley
k = spring constant (I don't think we really need it)
M, m = mass of the object
 
  • #3
With the systems you showed consider the variables you would need to completely account for both the kinetic and potential energy of the system in question. For a spring you need to know how much it is compressed. For a mass that moves horizontal you need a velocity. For the pendulum you need a velocity for the motion of the pivot point and another coordinate for the angular position. So for the first example you need four position coordinates and four velocities. So eight degrees of freedom for the first example?

If this is not right I hope it is corrected.
 
  • #4
Spinnor said:
With the systems you showed consider the variables you would need to completely account for both the kinetic and potential energy of the system in question. For a spring you need to know how much it is compressed. For a mass that moves horizontal you need a velocity. For the pendulum you need a velocity for the motion of the pivot point and another coordinate for the angular position. So for the first example you need four position coordinates and four velocities. So eight degrees of freedom for the first example?

If this is not right I hope it is corrected.

I get the idea. But do we count DOF from the spring too ?
 
  • #5
Have you learned any methods for analyzing the number of Degree of Freedom for a system? --- any theorems?

Without more details (such as what motions MB can have) these appear to have no particular correct answer.

If no other instructions were given, I would be inclined to think that the motions are in the plane of the page.
 
  • #6
DarkDrag0nite said:
I get the idea. But do we count DOF from the spring too ?

I would like to be corrected, but with four position coordinates and four velocities we can completely account for both the kinetic and potential energy for all parts of the first system and that number eight gives you the degrees of freedom?
 
  • #7
SammyS said:
If no other instructions were given, I would be inclined to think that the motions are in the plane of the page.

No other instructions were given in this exam.

Have you learned any methods for analyzing the number of Degree of Freedom for a system? --- any theorems?

I'm currently in high school and never learn such these theorems. I know only DOF is how many axis the object can move/rotate. (Of course, my friends know nothing) Wikipedia and many website do not give enough information. Could you please advise me ?

Thank in advance.
 
  • #8
Spinnor said:
I would like to be corrected, but with four position coordinates and four velocities we can completely account for both the kinetic and potential energy for all parts of the first system and that number eight gives you the degrees of freedom?

I've checked. For the first system, there is four choices:
1. 2DOF
2. 3DOF
3. 4DOF
4. 6DOF
For the second system, it is writing test.

Anyway, Please ignore the choices. The choices are usually incorrect.
 
  • #9
DarkDrag0nite said:
I've checked. For the first system, there is four choices:
1. 2DOF
2. 3DOF
3. 4DOF
4. 6DOF
For the second system, it is writing test.

Anyway, Please ignore the choices. The choices are usually incorrect.

I looked in "Lagrangian Dynamics" a Schaums outline for a definition of degrees of freedom and it looks as though I was wrong but on the right track. In what I wrote above you only need to count how many coordinates you need to completely describe the position of the systems parts and not the velocities. So it looks like the answer is 4DOF.

From page 15 of the book:

"degrees of freedom of the system. This is defined as: The number of independent coordinates (not including time) required to specify completely the position of each and every particle or component part of the system."

Now we both know %^)
 
  • #10
Spinnor said:
From page 15 of the book:

"degrees of freedom of the system. This is defined as: The number of independent coordinates (not including time) required to specify completely the position of each and every particle or component part of the system."

Now we both know %^)

Thank you so much ! This is exactly what I'm looking for. :)
 

FAQ: What is the Degree of Freedom of a System?

1. What is the definition of degree of freedom of a system?

The degree of freedom of a system refers to the minimum number of independent variables required to describe the state or motion of the system. It represents the number of ways in which a system can move without violating any constraints.

2. How is the degree of freedom related to the number of particles in a system?

The degree of freedom is directly proportional to the number of particles in a system. As the number of particles increases, the degree of freedom also increases, as there are more ways in which the particles can move.

3. What is the significance of degree of freedom in thermodynamics?

In thermodynamics, the degree of freedom is used to determine the number of thermodynamic variables needed to completely describe the state of a system. This helps in understanding the behavior of a system and predicting its equilibrium state.

4. What is the difference between translational and rotational degree of freedom?

Translational degree of freedom refers to the movement of a system as a whole, while rotational degree of freedom refers to the rotational motion of a system around an axis. In general, rotational degree of freedom is applicable to systems with a defined shape, while translational degree of freedom is applicable to all systems.

5. How does the number of constraints affect the degree of freedom of a system?

The number of constraints in a system decreases the degree of freedom. This is because constraints limit the movement of the system, reducing the number of independent variables needed to describe its state. In some cases, constraints can even reduce the degree of freedom to zero, resulting in a completely fixed system.

Similar threads

Replies
26
Views
3K
Replies
5
Views
5K
Replies
1
Views
2K
Replies
8
Views
4K
Replies
2
Views
3K
Replies
3
Views
4K
Replies
1
Views
2K
Back
Top