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I am in 12th grade right now. We have a chapter on Rotational dynamics in which it is clearly stated that it is for rigid bodies. I understand that, Moment of Inertia will remain constant only for rigid bodies. But in real world not all the bodies are rigid! So how do we deal with those problems in real life?

What if I want to know about the dynamics of a ball which is attached to a spring and I am rotating the spring with variable acceleration. The motion of the ball will be something like performing SHM while rotating in a circular motion. approximately... I guess)

Edit: What are the dynamics in case of non-rigid body?

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  • $\begingroup$ There is a more complete and more complex theory for the mechanics of non-rigid bodies. If you want to solve problems like that of balls connected by springs, then you can use Lagrangian mechanics to work in the conditions of how the spring connects the masses. If you want to analyze elastic (or inelastic) continuous bodies, there is continuum mechanics. You would encounter both in your university level physics classes, if you chose to become a physicist and you would also get to learn about continuum mechanics as a mechanical engineering student. $\endgroup$
    – CuriousOne
    Commented Feb 16, 2016 at 6:55
  • $\begingroup$ @CuriousOne Hmm.. So I guess I should skip this one for now. Thank you for the information $\endgroup$
    – brainst
    Commented Feb 16, 2016 at 6:56
  • $\begingroup$ Depends on your level of interest and how good you are with multivariate calculus. I would say that understanding Lagrangian mechanics is certainly within your reach in 12th grade if you have the motivation. It is certainly something you should have heard about and maybe spent a couple hours on (look at the Wikipedia entry). Continuum mechanics, in my experience, is more of a "snoozer" unless you have a real need for it, which is mostly within engineering and in certain areas of physics that deal with fluids or the mechanical properties of solids under mechanical stress. $\endgroup$
    – CuriousOne
    Commented Feb 16, 2016 at 7:02
  • $\begingroup$ You will probably meet a non rigid body when discussing the conservation of angular momentum for an ice skater. $\endgroup$
    – Farcher
    Commented Feb 16, 2016 at 7:46
  • $\begingroup$ Non-rigid body as in an elastic body, or as in a non-solid fluid? $\endgroup$
    – John Alexiou
    Commented Aug 7, 2017 at 13:55

2 Answers 2

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This is a great question, but I think it is too broad. There is a variety of techniques used to idealize real life (complex) situations. It depends really on what assumptions you are willing to live with, and what modeling tools you have at hand. Ultimately for real life simulations, you want your hand on some commercial MBD (Multi Body Dynamics) software and a lot of time and money to put together a decent model that doesn't blow up or isn't "too chaotic" to be useful.

Besides computer modeling, there is my favorite subject: Symbolic modeling of multiple connected rigid bodies. That is, building all the equations of motion and kinematics for a system of bodies and figuring out what influence each parameter has on the results.

If you are looking at elastically suspended bodies (bodies held together by springs) then you have to make assumptions such as the springs are massless, and the bodies are rigid and you can formulate all the spring forces as a function of the body positions and velocity (for damping).

But in real life (for example with engine valvetrains), the mass and inertia of the springs are critical to the dynamic behavior and so people have developed techniques such as "multi-mass springs" and "quarter beam methods" to include such effects. Real life springs resonate, clash and surge.

The same may apply to systems with thin beams that cannot be considered rigid but have to include the flexibility in the model. Frankly, it is exciting that this is an active area of research so many years after Newton and Euler described the equations of motions for rigid bodies. If you are interested you can do a PhD in rigid body modeling. As I said, this is a very broad and complex subject.

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You are Actually correct, In real world there is no perfect rigid body. Every Body can be deformed more or less by application of force. $\text{These solids, in which the changes produced by external force are negligibly small,}$ $\text{are usually considered as}$ $\text{rigid body.}$ That ball you have to know about that dynamics should be satisfy above conditions

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  • $\begingroup$ Hmm.. Then how do we deal with such problems in real life? I added this question in the edit. :D $\endgroup$
    – brainst
    Commented Feb 16, 2016 at 6:53

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