Cross products vanish Classical Mechanics

AI Thread Summary
The discussion centers on the vanishing of cross terms in the context of an object moving in the x-y plane, specifically referencing equation 8.9. The key reason for this is the definition of the center of mass, which simplifies the calculations in the center of mass frame of reference. Participants suggest examining equations 5.56 and 5.58 for further clarity, emphasizing that in this frame, the position vector r' becomes zero. A question arises regarding the integral of the cross product of r' and v', prompting a deeper exploration of the mathematical implications. Understanding these concepts is crucial for grasping the mechanics involved in the problem.
KEVmathematics
Messages
5
Reaction score
0
As seen in the picture, this question is about an object moving in the x-y plane. But I don't get why in equation 8.9 the cross terms vanish? If anyone can help me, that would be really nice.
 

Attachments

  • question.jpg
    question.jpg
    36.9 KB · Views: 463
Physics news on Phys.org
... they vanish due to the definition of "center of mass".
The text explains with maths in the passage right below eq8.9.
Have you tried working out the cross terms for some example?
 
The book answers your question already. You need to think about the center of mass in the center of mass frame of reference. Also the author suggests hou look at equation 5.56
 
Equation 5.58 is just R_cm = sum m_i r_i / M.

I get why r' is zero in the frame of the center of mass. But if that's the case, why is the integral of the cross product of r' and v' not equal to zero also?
 
Thread 'Is 'Velocity of Transport' a Recognized Term in English Mechanics Literature?'

Thread 'Is 'Velocity of Transport' a Recognized Term in English Mechanics Literature?'

Here are two fragments from Banach's monograph in Mechanics I have never seen the term <<velocity of transport>> in English texts. Actually I have never seen this term being named somehow in English. This term has a name in Russian books. I looked through the original Banach's text in Polish and there is a Polish name for this term. It is a little bit surprising that the Polish name differs from the Russian one and also differs from this English translation. My question is: Is there...
View full post »

Thread 'Is calling fictitious forces "not real" just about terminology?'

Hi there, im studying nanoscience at the university in Basel. Today I looked at the topic of intertial and non-inertial reference frames and the existence of fictitious forces. I understand that you call forces real in physics if they appear in interplay. Meaning that a force is real when there is the "actio" partner to the "reactio" partner. If this condition is not satisfied the force is not real. I also understand that if you specifically look at non-inertial reference frames you can...
View full post »

Similar threads

A Exploring Infinitesimal Rotations in Classical Mechanics
Replies
8
Views
2K
Hamiltonian Mechanics: why paths in state space never cross each other
Replies
9
Views
2K
What is the derivative of velocity with respect to position?
Replies
14
Views
7K
Advice on Resources -- A really good classical mechanics book?
Replies
9
Views
3K
The Cross Product and Angular Momentum
Replies
6
Views
3K
I Question on analytic mechanics
Replies
3
Views
1K
Classical Rotation: Referencing Rotational Motion in Mechanics
Replies
5
Views
1K
Prerequisite mathematics for intermediate mechanics?
Replies
4
Views
2K
Challenging Susskind's "rule" for classical mechanics
Replies
10
Views
2K
Can the kinetic energy be a function of the position vector?
Replies
8
Views
4K

Hot Threads

Recent Insights

Back
Top