Dealing with angular momentum of rigid bodies

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SUMMARY

The discussion focuses on the complexities of angular momentum in rigid body dynamics, specifically the confusion surrounding the application of various formulas. Key equations include the relationship between angular momentum (H) about a point and its dependence on moment of inertia (I) and angular velocity (ω), as well as linear momentum (mVd). The conversation emphasizes the importance of understanding rotational kinematics and the analogies between linear and rotational motion, such as torque (T) and force (F), as well as the significance of mass distribution relative to the axis of rotation.

PREREQUISITES
  • Understanding of basic physics concepts such as force (F = ma) and linear momentum.
  • Familiarity with rotational kinematics and the relationship between torque (T) and angular acceleration (α).
  • Knowledge of moment of inertia (I) and its dependence on mass distribution in rigid bodies.
  • Ability to apply equations for kinetic energy in both linear (1/2mv²) and rotational (1/2Iw²) contexts.
NEXT STEPS
  • Study the principles of rotational kinematics in a first-year physics textbook.
  • Learn about the different moment of inertia values for various geometric shapes.
  • Explore the concept of torque and its applications in rigid body dynamics.
  • Practice problems involving the conversion between linear and angular motion variables.
USEFUL FOR

This discussion is beneficial for students studying dynamics of rigid bodies, physics educators, and anyone seeking to deepen their understanding of angular momentum and its applications in mechanics.

tj00343
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I'm taking dynamics of rigid bodies, I'm having some trouble with impulse and momentum.
Basically ,I know that angular momentum abt. a point ,is the linear momentum multilied by the moment arm .
BUT ,I'm not feeling at all comfortable appliying it
For example , When is H abt. a pt. p = (moment of intertia abt. p )(w) and when is it m*V*d ,and when is it Ig*w +mVg *(d) ,i'm very confused about the whole thing and when to apply what so any clarification on the subject would be very helpfull , preferably I would like the most general case stated and explained,than when to cancel out terms and why to get to more specific cases ...
ANY clarification/comment can be helpfull
Thanks
 
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I think your question is not being answered because it's pretty broad...I'm not even sure where to start to assist.

I'd suggest you read a first year physics book on rotational kinematics, linear and angular relations,rotational variables, stuff like that...

If you understand F = ma for translational motion, you can start by figuring out the rotational analogies: Torque [T} becomes the analogy of force [F] and rotational inertia becomes the analogy of mass. The lattter gets a bit tricky because the distribution of mass relative to the axis of rotation is important. And acceleration [a] becomes angular acceleration, alpha.

So for example, instead of kinetic energy being 1/2mv2 the rotational
analog is 1/2Iw2 where m is replaced by I and v = wr. I has different values for different shapes, even when the total mass is the same.
 

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