Reduced mass: color-coded derivation of definition

[@lseinjr1]

(for *mobile* users) 00:15 Introduction. 00:30 System 1 variables 𝑀, 𝑁, 𝑎, 𝑏, 𝑑 01:20 System 2 variables μ and 𝑑. 02:23 Center of mass condition 𝑀𝑎 = 𝑁𝑏. 02:51 Add 𝑀𝑏 to each side 03:07 Factor each side 03:20 Use fact that 𝑑 = 𝑎 + 𝑏. 03:39 Divide each side by (𝑀 + 𝑁) to get expression for 𝑏. 03:59 Center of mass condition 𝑀𝑎 = 𝑁𝑏. 04:16 Add 𝑁a to each side 04:30 Factor each side 04:41 Use fact that 𝑏 + 𝑎 = 𝑎 + 𝑏 = 𝑑. 04:56 Divide each side by (𝑀 + 𝑁) to get expression for 𝑎. 05:09 Formula for moment of inertia (I) for System 1 ( = I for System 2 by selection) 05:49 Substitute expressions for 𝑎 (04:56) and 𝑏 (03:39) into moment of inertia formula (05:09) 06:13 Combine fractions with same denominators, factor out 𝑑². 06:32 Factor out 𝑀𝑁 from numerator 07:00 Cancel factor of (𝑀 + 𝑁) from numerator and denominator 07:20 Expression in brackets [] equals reduced mass μ. 07:54 Write expression (07:20) on clean board. 08:12 Take reciprocals of each side 08:28 Break fraction on RHS into two (2) fractions with same denominator. 08:40 Factor each fraction on RHS to get second expression for reduced mass (μ). Don't forget to like, comment, share, and subscribe!

[@130anirudh4]

Thanks very much sir 🙏.

[@veracity-]

Please keep making your videos, they're so unbelievably helpful especially during the quarantine! Just watched your Hückel theory energies videos, so helpful! Thank you!

[@lseinjr1]

Glad you like them!

[@dalegriffiths3628]

Very useful, thanks very much for that derivation.

[@shashvatshukla]

Thank you so much! I'm catching up on physics after having not done it for many years and your video helped me learn this concept very quickly.

[@tunneltrance]

My pchem book brings this topic up but never explains where the concept comes from. If I recall correctly, it basically glosses over reduced mass as a "mathematical manipulation" and that's all the explanation it gives. Thank you for doing this video!!

[@lseinjr1]

You're welcome!

[@krishankant5289]

lovely explaining sir 😀🙏 Thank you😊

[@nxpy6684]

Thank you very much for your helpful explanation, sir!

[@farrela6710]

Thank you very much for your helpful explanation, sir! I hope that you can keep making great videos in the future.

[@lseinjr1]

I hope so too!

[@nothingrequired1150]

Sir thank you so much for the derivation.

[@himanshusachdeva6286]

Thank you

[@manjariprakash30]

At 2:44 how Ma=Nb Could you please explain

[@lseinjr1]

Point O is the "center of mass". Note that if line ab were a lever with a fulcrum at point O, and we apply weights M and N at the ends, the lever would be perfectly balanced (not move). Na = Mb is a direct consequence of O being the center of mass of the system.

[@NishchayG]

9:13 does that mean its like parallel resistance and we can keep on adding another mass(say X) as 1/X ; like 3 mass system... Nice explanation btw!

[@lseinjr1]

Yes, and thank you!

[@user-rd1lu7yx1b]

Sir do you have some videos of molecular symmetry and IR? representation irreducible of vibrations ? I have a exam about that and my teacher doesn't explain good

[@lseinjr1]

Yes. Here are a few: kzbin.info/www/bejne/qH6lf353qbKNqKc kzbin.info/www/bejne/rKnafJWNr5WgZ9E kzbin.info/www/bejne/epi4noSamNhpis0

[@user-rd1lu7yx1b]

@@lseinjr1 thanks sir, you save my life again as you save me with the maxwell relations. i'll graduate next semester and you help me a lot with your videos, thank u very much

[@lseinjr1]

Glad to have helped!