Single Degree of Freedom Equation of Motion(Newtons Second Law)

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Discussion Overview

The discussion revolves around the application of Newton's Second Law to a single degree of freedom system involving a rod and a mass. Participants explore whether the mass of the rod should be included in the equations of motion, particularly in the context of equilibrium and moment calculations.

Discussion Character

  • Homework-related
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • The original poster (OP) questions whether the rod's mass must be included in the moment equation about point O, citing conflicting advice regarding neglecting the rod's mass.
  • One participant suggests that the geometry of the system is crucial for determining whether the rod's mass can be neglected, asking for clarification on the setup.
  • Another participant mentions that the moment of inertia of the rod can be neglected if it is significantly smaller than that of other objects in the system, specifically the mass M.
  • The OP expresses confusion over examples that seem to treat the rod's mass differently in various scenarios, indicating a lack of clarity on when to include it.
  • One participant advises writing out the sum of forces and moments to clarify the situation, suggesting that if no mass for the rod is provided, it is likely negligible.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the rod's mass should be included in the calculations. There are multiple competing views on the conditions under which the rod's mass can be neglected, leading to ongoing debate.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the rod's mass and the specific conditions of the problem. The geometry and specific values for the masses involved are not fully defined, which may affect the conclusions drawn.

adhwa
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Homework Statement



Hello guys. Really need your helps. When I construct an equation(moment about point O), do I have to include the rod's mass also? I've heard that I can neglect the rod's mass due to equilibrium equation. On the other hand, I've also heard that I can only neglect mass if the point of mass is supported. Appreciate if you could show me the equation. Thanks in advance. * For some reason I cannot attached the image.*

Homework Equations


The Attempt at a Solution

 
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You have not supplied the geometry.
Is this a mass on the end of a rod, with the pivot at the opposite end of the rod to the mass?

If you suspect you cannot neglect the rods mass, do the calculation both ways and see what difference it makes.

There are two ways to attach an image - you can use the attachment manager, or host the image elsewhere and use the image tags. The attachment manager can be temperamental ... the trick I've found is to submit the post as soon as the attachment is uploaded, then edit the post.

These sorts of problems are not about finding the right equation and then plugging in the numbers, they are about your understanding of the physics of the situation. You can find a lot of equations for moment of inertial in wikipedia as well as notes on how to use them.
 
The OP had posted the image elsewhere, so I am reposting it here:

[STRIKE]https://www.physicsforums.com/attachment.php?attachmentid=42534&d=1325989363[/STRIKE]

You may neglect the moment of inertia of the rod if it is significantly smaller than the moment of inertia due to other objects in the system -- in this case, the M.O.I. due to the mass M. Usually, a problem statement will say either (1) the rod has negligible mass, in which case you can neglect it's mass and M.O.I., or (2) provide you with the mass or M.O.I. of the rod, in which case it should be included in the calculations.

Hope that helps.

EDIT: image is in attachment
 

Attachments

  • adhwa_Thread565894_sm.jpg
    adhwa_Thread565894_sm.jpg
    20.5 KB · Views: 513
Last edited:
Invalid Attachment specified. If you followed a valid link, please notify the administrator
 
Weird, I guess only Mentors and Admins can see images from deleted posts.

A valid image is now attached to my previous Post #3.
 
Oh I see now - it's a weird mass-on-a-spring ... probably they only care about the lever-arm effect for the rod.
 
Ive gone through every material that I have. Please correct me if I am wrong. Based on the rod(attached image), we can create and equation (Moment about point O = I\alpha). From my understanding, We can canceled out Moment about point O of rod's mass (mg*l/2) due to mass*acceleration effect on the other side of the equation. Please enlighten me.
 
Well just write out the sum and see ... assign a mass m to the rod.

(Note: if the problem does not give you a mass for the rod, it is probably negligible.)
To me it looks like your photos contain terms from the rod for each example.
 
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