I can't math.

Mathematician & trailblazer Katherine Johnson turns 100

On the image above, Katherine Johnson is calculating spacecraft trajectories… by hand! Astronaut John Glenn trusted her more than computers, and her accuracy in orbital mechanics equations helped NASA to fly the first men to the moon. On top of that, she was a race and gender pioneer.

Johnson turned 100 yesterday (26 Aug), which also coincided with Women’s Equality Day. How incredible?!

Johnson at the opening of Katherine G. Johnson Computational Research Facility at NASA’s Langley Research Center in 2017. Image credit: David C. Bowman/NASA

On the definition of  Angular Momentum

Anonymous asked:

Why is it mr^2 omega and not some other weird formula that is conserved? Why not mr^3 omega or mr^2 omega^2 ?

This is a great question. And to be honest, there is no intuitive answer as to why it is defined this way or that.

What makes the definition special?

Conservation laws can be understood better through the Lagrangian formulation of classical mechanics.

That’s the conservation of momentum for a free particle. It means that this quantity mv remains constant with time (not m2v, not m2v2 ,just mv).

And similarly for a rotating body, one can find that the quantity that remains constant wrt time is the angular momentum.

And that’s the best rationale using modern physics that can be provided for why Angular momentum takes the form that it does.

Any other form would just not be conserved. Sure, you can construct a Lagrangian that would give you the form that you need but that would not  represent anything physical !

Hope that answers your question. Thanks for asking !

** If you have not heard about Lagrangian formulation of classical mechanics, the wiki article on Principle of Least action is a really good place to start..