When is angular momentum not parallel to angular velocity?

Developing some intuition about the direction of a rigid body's angular momentum, with the aid of some examples. We focus particularly on the case when angular momentum and angular velocity are in different directions, and discuss how to understand this scenario in terms of applied torque. The discussion is purely in terms of vector cross products, without referring to the inertia tensor.
The thumbnail shows the angular velocity and angular momentum of a rotating bar, with the small arrows represting the angular momentum contributions of particles at various positions throughout the bar.
To support the channel: ko-fi.com/benyelverton
About me: I studied Physics at the University of Cambridge, then stayed on to get a PhD in Astronomy. During my PhD, I also spent four years teaching Physics undergraduates at the university. Now, I'm working as a private tutor, teaching Physics & Maths up to A Level standard.
My website: benyelverton.com/
#physics #mathematics #dynamics #mechanics #angularmomentum #momentum #spin #vectors #crossproduct #calculus #differentiation #productrule #newstonslaws #torque #inertia #centreofmass #centerofmass #rotation #physicsproblems #conservationlaws #maths #math #science #education

[@christiancorrao6591]

Another good one! Huge fan of the channel! Thanks again

[@DrBenYelverton]

Thanks, I appreciate your support!

[@AmitKumar-xw5gp]

Good video.. Nice explanation.

[@r2k314]

Thanks.

[@haritejanamala4595]

Please leave sources or refer books to read on angular momentum further. Spin and orbital angular momentum in particular.
Great video as usual.

[@mingmiao364]

Goldstein for grad level. Taylor for undergraduate level. Both texts titled *Classical Mechanics*

[@DrBenYelverton]

Thanks, I also have a video on spin and orbital angular momentum here: czcams.com/video/AROKWyI34N0/video.html

[@haritejanamala4595]

Thanks a lot😊

[@user-im3lg5sl6c]

why are we allowed to apply the product rule on cross products?

[@DrBenYelverton]

You can find a couple of methods for proving that result here: proofwiki.org/wiki/Derivative_of_Vector_Cross_Product_of_Vector-Valued_Functions

[@thewhyquestion5589]

Plz provide the proof