Parallel Axis Theorem Derivation

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Content Times:
0:00 The Parallel Axis Theorem
0:44 The Derivation Setup
2:32 Organizing the Integral(s)
5:49 Taking the Integral(s)
8:25 The Parallel Axis Theorem

#RotationalInertia #MomentOfInertia #ParallelAxisTheorem

[erichacop]

Wow fantastic job explaining the proof. You sir are a hero!

[justalazyguy._]

you are such a gem
please keep uploading

[AyalaMrC]

Great episode! I just realized that this is why the moment of inertiavis always smallest when pivoting at its center of mass! It also predicts that when comparing moments of inertia about different points, it is purely the distance from the COM that determines their relative values. All the AP teachers at my APSI for APCM had a hard time justifying why they chose a particular answer on an APCM MC question; they knew it was due to the distance from the COM, but noone could state why.

[cck]

I love the way you explain the theorem. thank you so much.

[bhargavibaskar]

Amazing explanation ever, Thank you so much!!!!

[yashchaphekar]

damn man, amazing derivation! thanks a lot!

[andrewjustin]

6:25 Mr. P where did you come up with that equation? Moreover, I couldn't catch why the integral is to be zero. Please elucidate on that!

[justalazyguy._]

I have a question
what does quantities which are result of cross product have direction, perpendicular to the plane of the productant
like torque what does it mean

[renugahlot]

Sir could you please make a video on angular momentum in case of rotation about fixed axis

[lenawalid]

why is X(cm) and Y(cm) =
and why are they equal to 1/m intergral x dm 6:57

[barameesrisawang]

Thank you Sir - I wonder The theorem can use in case of "A New Parallel is located outside the object - such that simple pendulum
Given : pendulum ball with some radius r and is suspened with a rope (a rope is small mass ) So the center of mass of this system is center of mass of the ball. When we release the ball, then moment of inertia of system is I (cm) + (M+R)^2
[ if the ball is sphere : 2/5MR^2 + (M+R)^2 ], isn't it ?
And The other question - When we consider conservation of energy of The pendulum Should we care about size of the ball pendulum ?
( I think We should because while the ball is moving down with radius R each point mass on the ball have different velocity - mean that
v = omega R Why don't we use 1/2 Iw^2 instead of 1/2mv^2 )
Thank you [ Apologize for my english 'I am not english speaker😄 ]