Proof of the Parallel Axis Theorem

[@azmath2059]

After much hunting on the internet, I've finally found an explanation to the Parallel axis theorem that I can understand fully. Thank you Jason

[@mohammadsahil451]

Where are you from.......????

[@himanshugupta9787]

Thanks for the great explanation

[@markkennedy9767]

Hi you might be able to help me out with something i cant figure out:
If I apply the parallel axis theorem to a (non-spinning) body of mass m in uniform circular motion around a point a distance r away, then I get the angular momentum of the body about the point is
(I + mr^2) omega where I is the body's moment of inertia around its COM and omega is the body's angular velocity around the point.
However if we compute the angular momentum by just getting the orbital angular momentum about the point (where the body isn't spinning around its COM), we get r × mv = (mr^2 omega) which is clearly different to what we got above.
Can you point out where I might be making a mistake here.
Your help is greatly appreciated.
Thanks.

[@jasoninnc1]

Thank you very much for the thoughtful proof.

[@spiralfireball8663]

Your name also Joson.

[@fayazrahman731]

Why is it (x - d)?

[@atharva9092]

(x-d)^2 is the same as (d-x)^2

[@davidsha]

This is great!

[@dosomestuff1949]

DUDE ARE YOU THE JASON THAT WENT TO BILL HOGARTH????????

[@unist_jaeeul]

Thank you sir..

[@edmund3504]

beautiful

[@KingXF]

Wow doin me a educate

[@ramanujansrinivasa6234]

Thank You sir

[@fabiospinelli4179]

Wonderful

[@scottyuki9581]

we stan

[@arnavsingh5197]

AWESOME!!!!!!!!!!!!!!!!!!!!!!!!!!!

[@YommiOfficial]

Awesome