Classical mechanics-coordinates

  • Thread starter rsaad
  • Start date
  • Tags
    Classical
In summary, the conversation is discussing the coordinates and position of the centre of mass (CM) for two spheres connected by a dumbbell. The formula for determining the position of the CM is given as (R1m1+R2M2)/(M1+M2) with the origin at the CM. The conversation also clarifies the relation between R1 and R2 and their relationship to the distance R between the spheres. Ultimately, the conversation highlights the use of parentheses in the formula and the distinction between coordinates and distances in determining the position of the CM.
  • #1
rsaad
77
0

Homework Statement



Attached is the picture of a dumbbell. I do not understand how the coordinate of M1 is
M2 R/ (M1 + M2)

It is not an assignment question but an example from a book.
 

Attachments

  • newdoc.pdf
    149 KB · Views: 206
Physics news on Phys.org
  • #2
The origin is at the centre of mass. You certainly know how to determine the position of the CM?

ehild
 
  • #3
CM= (R1m1+R2M2)/M1+M2
because CM=0, I get M1 R1 = -R2 M2
which further gives me
R1= RM2 / (M2-M1)

=|
 
  • #4
rsaad said:
CM= (R1m1+R2M2)/M1+M2
because CM=0, I get M1 R1 = -R2 M2
which further gives me
R1= RM2 / (M2-M1)

=|

What do you mean on R1 and R2? If they are coordinates of the spheres with respect to the CM, the formula is correct, but use parentheses. (R1m1+R2M2)/(M1+M2)=0

How are R1 and R2 related to the distance R between the spheres?

ehild
 
  • #5
R= R_1 + R_2
where R_i is the distance to M_i from CM.
 
  • #6
In the book R_1 = R M2/ (M1 + M2) but mine is R1= R M2 / (M2-M1)
 
  • #7
If x1, x2 are coordinates of m1, m2, respectively, the x coordinate of the CM is (x1m1+
x2m2)/(m1+m2).
If they are distances from the CM, the coordinate of m2 is negative: m1R1-M2R2=0

ehild
 
Last edited:

1. What is classical mechanics?

Classical mechanics is the branch of physics that deals with the motion of macroscopic objects, such as everyday objects like cars and baseballs. It is based on Newton's laws of motion and can be used to predict the behavior of objects in a wide range of situations.

2. What are coordinates in classical mechanics?

Coordinates in classical mechanics refer to the variables used to describe the position, velocity, and acceleration of an object. These can include position coordinates (such as x, y, z), velocity coordinates (such as vx, vy, vz), and acceleration coordinates (such as ax, ay, az).

3. How are coordinates used in classical mechanics?

Coordinates are used in classical mechanics to mathematically describe the position, velocity, and acceleration of an object in a given system. By measuring the values of these coordinates, we can make predictions about the behavior of the object and understand how it will move over time.

4. What are the most commonly used coordinate systems in classical mechanics?

The most commonly used coordinate systems in classical mechanics are Cartesian coordinates (x, y, z), cylindrical coordinates (r, θ, z), and spherical coordinates (r, θ, φ). These systems allow us to describe the position and motion of an object in three-dimensional space.

5. How does classical mechanics relate to other branches of physics?

Classical mechanics is the foundation of many other branches of physics, such as thermodynamics, electromagnetism, and quantum mechanics. It provides the fundamental principles and equations that govern the behavior of macroscopic objects and forms the basis for understanding more complex systems in other areas of physics.

Similar threads

  • Advanced Physics Homework Help
Replies
5
Views
2K
  • Advanced Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
863
  • Electrical Engineering
Replies
17
Views
1K
  • Advanced Physics Homework Help
Replies
5
Views
791
  • Advanced Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Advanced Physics Homework Help
Replies
2
Views
4K
  • Introductory Physics Homework Help
Replies
15
Views
961
  • Introductory Physics Homework Help
Replies
1
Views
1K
Back
Top