What is the Angular Equivalent of E=mc^2?

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SUMMARY

The discussion centers on the search for an angular equivalent of the equation E=mc^2. Participants outline analogies between linear and angular quantities, such as mass to moment of inertia, and velocity to angular velocity. The conversion of linear kinetic energy to rotational kinetic energy is highlighted with the formula ##\frac{1}{2}mv^2 \rightarrow \frac{1}{2} I \omega^2##. However, it is concluded that E=mc^2 does not have a direct angular counterpart, as energy is a broader concept applicable to both linear and angular motion.

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  • Understanding of linear and angular motion concepts
  • Familiarity with moment of inertia and angular velocity
  • Knowledge of kinetic energy equations
  • Basic grasp of physics terminology related to energy
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Physics students, educators, and professionals interested in the relationships between linear and angular motion, as well as those exploring advanced mechanics concepts.

neuralnova
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Many linear quantities have angular counterparts.

Mass --> Moment of inertia
velocity --> angular velocity
acceleration --> angular acceleration
force --> torque
momentum --> angular momentum

E = mc^2 --> ? = I ?^2

Even a loose analogy would do.
 
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Linear kinetic energy -> rotational kinetic energy
 
Or mathematically, ##\frac{1}{2}mv^2 \rightarrow \frac{1}{2} I \omega^2##.
 
Sure -- I should have included those in my list, as I did already know about them. I'm looking for something more daring. ;)
 
neuralnova said:
I'm looking for something more daring.
mc^2 is not related to linear or angular motion, so I'm not sure in what sense there can be an "angular counterpart".
 
Energy isn't linear by default, it's a more general concept that can be applied to both linear and angular motion.
 

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