# Learning Time! by Snively '11

I walk you through a physics/dynamics problem.

Oftentimes the best way to learn something is to teach it. I’ve decided to try this approach to study for my 2.003 test coming up.

WARNING WARNING WARNING!!! Physics content ahead! If you’re afraid of physics, well, frankly, keep reading because you may just learn something important. If you like physics, well keep reading, because you’ll enjoy it. If you don’t really care, stay for the pretty pictures, mmmk? Mmmk.

Alright here’s the problem as its posed to us:
A wheel of diameter R, consisting of a thin uniform rim of mass M and six thin uniform spokes mass m, is released from rest at the top of a hill of height h.

What is the angular velocity of the wheel when it reaches the bottom, assuming that it rolls without slipping?

I’ve played with my tablet and written up the answers nice and pretty-like (in color!). Before you look at that though, let’s do a quick game plan.

1) Energy. Since the wheel starts high and ends low it looks a lot like we can use energy. There’s nothing but gravity doing work so we can use conservation of energy. Everything in orange is energy. Remember, energy before equals energy after. That extra term on the right that you may not be familiar with is called the “Rotational Energy” and involves the moment of inertia and omega (angular velocity (what we’re solving for!)).

2) Moment of Inertia. We need to find it. For the wheel. This involves finding the moment of inertia for the rim and adding the inertia for each of the 6 spokes. How do we find the spokes’ moments of inertia? Parallel axis theorem!

3) Putting it all together. Plug your moment of inertia into the energy equation and solve for angular velocity omega.

Here’s my solution:

This is just one of many problems I’m reviewing and going over while studying for the test I have in this class on Wednesday. My current strategy is to just shove everything into energy and angular momentum equations until I get the variables I want. We’ll see how this works.

Back to coloring!

### 52 responses to “Learning Time!”

1. Ahana says:

@ Wesh m, agreed. IIT is a good place. IITians are not good people.

Magic Algebra->Witchcraft->Sweet.

2. i like mit.. says:

IIT = good
MIT = BEST

3. Banerjee says:

4. wesh m says:

@banerjee(from India?)-Not necessarily.Hey don’t try to do what you think (or what people tell you)is suitable for mit. Just do whatever you enjoy.

If you are really interested in rotational energy then there is no reason why you shouldn’t learn about it.Otherwise- go play a video game and relax.

5. Anonymous says:

First!

6. Anonymous says:

that is the most awesome table i have ever seen.

7. Alim says:

Sweet Science!

8. I LUV mit says:

Jesus these kids are quite illusioned with all this MIT-best-tech-school-ever syndrome. Lookee banerjee, I’m not disappointing you, but I think that if you really interested in practical undergrad education, then choose Princeton and GWU, way ahead of most colleges in US, in terms of thier path-breaking research. I’m not saying MIT is not what it seems, but the real stuff is really over there.

9. Snively says:

In response to I LUV mit
Hopefully everybody applying to MIT has done enough research to understand all of their options and which schools have an undergraduate program that they’d prefer. As for coming on to MIT’s website and telling people to go look at other websites, kinda not cool.

10. Alexander says:

That is so freaking AWESOME!!!!

11. Ahmed says:

May I interest you in a floating bed?

12. Anonymous says:

Ahmed, would it sink if I got on it?

13. I LUVed mit says:

Agreed! But I’m not selling something, even if it be an idea; I’m just trying to widen the horizons. And here we’ve a kid who wants to secure a position in MIT, whereas he’s still in only tenth grade. This is sure an obsession.

Nevermind, anyway, thanks for tip to be really cool.

14. Ahmed says:

Nope, it’s suspended by magnets and held in place by steel rods (or cables, forgot which).

15. Sigh says:

That Omega is obscene…

16. Anonymous says:

Bravo!! *claping hands*

17. Shufeng says:

I am a big fan of the *Magic Algebra* you have there in Step 3! Nicely done =D

18. Sigh says:

Of course, no offense intended.

19. HAHA LMAO!! The problem says “a wheel of diameter R” That could be very miss leading come test time. I would have expected a wheel of radius R.

20. Snively says:

@RZf
Actually, the solution provided mentions that and says they didn’t dock people for using R as the radius. That was sneaky of them though, good catch.

21. Indian says:

i missed the height of the wheel in calculating the potential energy(V1) of the wheel, in the energy conservation equation in first step….that was a silly mistake

Did same problem in 11th grade, while preparing for IIT-JEE 2008.

I lke your way of explaining things snively, i am usually pretty bad at teaching OTHERS, not myself.

23. Anonymous says:

get lost u damn IITians. You just know how to cram things.

24. Efolse '11 says:

Also go to GWU if you want to pay the most expensive college tuition in the US… *roll eyes*

25. @anonymous:
sure may be someday an iitian would teach you how to really cram things….
we are used to do this level physics in half-consciousness… and that we are able to do with practice and not by craming…. it takes days n nights of practice to make an iitian…

26. scanner says:

Snively, you have to do more stuff like this (I love Physics, but also for other classes). Seeing what kinds of things you learn is very important.

27. Liz says:

Snively!! I am enthused that you put up a fun physics problem (and I sincerely hope more problems are to come). I wish I had such fun psets.

28. I Love IIT says:

To–too an iitian
IIT is a very creativity killing zone, for anyone who dares to get in. As for as the intellectual vitality of any IIT guy is concerned, they are just a mere bunch of idiots, who learn to memorize at least 1500 problems in PMC, of Tripos Examination of Cambridge U, London, (diluted of course), supplemented to them by numerous coaching factories situated in Western India. Over 80% admitted students are from these coaching factories; leading profs in despair commenting- Given a problem, these guys even think alike.

And I’m neither from MIT nor IIT, which in all probable cases, suits me.

29. wesh m says:

@whoever posted before me- bravo!

@egoistic iitians–SHUT UP.

This is not the place to boast about your intellectual prowess.You can do that to all those gullible Indians(did you even read the post?)But not at MIT.So back off.

30. wesh m says:

That table is freaking awesome.(It’s a table isn’t it?)

31. Ehsan says:

Snively the Teacher?

32. Snively says:

@IITian
Sorry you feel that way. Look into it, you’re wrong.

33. Anonymous says:

Magic Algebra = TI-89?

34. Why couldn’t you just use PE=mgh, KE=1/2*mv^2 and solve for ω=v/r?

I know you can’t do it that way because I tried and came up with a vastly different answer than yours… I assume the MOI’s have something to do with it?

Also, @ ‘Rieman Zeta Function’, good catch, I would have missed that one, and it’s spelled ‘Riemann.

Also:
LOLOMGWTFBBQ MIT>IIT!!!!!!!!!!!!!!!111!!!!11!!!11!!!!11!1!1one!!onetwo!!!randomleetspeak
J/K, , it’s just that saying random statements without providing sufficient logical backup seems… trollish. Tell why IIT is better than MIT or vice versa. Although as Snively said, this isn’t really the place for that discussion.

Excellent post Snively! Physics = awesome.

35. Hey, I’m a strangelet produced by the Large Colliding Hadron that just posted, and I just my excessively dumb mistake in not realizing that rotational energy isn’t part of the KE=.5mv^2 at the end, it’s an additional energy variable- that’s it, isn’t it?

‘Newayz, GTG, need to go find some nucleons and incite an Ice-Nine scenario.

36. iitian says:

look into what.r u mad .or u r also too rich to answer.

it sucks

37. Ahana says:

OMG. IIT, great. MIT, great. Both are great institutions on totally different scales. So get over it.

38. Banerjee says:

@ wesh m: Yup, I’m (a girl) from India. And yes, I’m interested in Rotational Energy, so I looked it up and asked my dad. And guess what, He went to IIT (coincidence, huh?).

@ I LUV MIT: Thanks for the advice. I’ll look into those Universities when I apply. And I’m not obsessed with MIT, I just think that they happen to have a really good Mechanical Engineering program.

39. Ashwath says:

It’s sad that conversations like this on IIT vs. MIT have to be conducted on the MIT website. Why can’t people accept that they’re both excellent institutions with great students? Deriding either is a sign of immaturity and is pretty pathetic.

40. Javal says:

I don’t think including the R/2 for the height of the centre of mass is necessary.

You’re dealing with change in P.E and that is affected by the change in height of the mass, the centre of mass still goes through a height of h, if you went through the *MAGIC ALGEBRA* i think you’d find that the R/2’s fall out. Just a little thing i noticed. I suppose including it is more thoroough though. 2 am babbling from me. Physics is fun. .

Ashwath:

IIT is soo not an excellent institution.
Good attempt at diplomacy though.

42. Anonymous says:

@IIT LOVERS, if u are in IIT, then plz concebtrate on your studies rather than visiting the undergrads site. Moreover, many of the IITians do come @ MIT to pursue thier masters. that proves which is superior. i suppose u get what i mean.

43. IITian says:

MIT SUCKS
IIT ROCKS
WE ARE THE BEST EVERYONE KNOWS IT. EVEN U PEOPLE. U SHOULD BE ASHAMED OF YOURSELVES. MIT STUDENTS R FILTHY RICH THATS HOW THEY GET IN.

44. Allen says:

Dude, use better notation! That’s the first thing they taught me in 8.012. WTF is T!!!!! and V!!!!
Please email me back at [email protected]

45. Peace maker says:

all those who think iit is good…should not come to mit blog site(stay with iit only, now dont say that iit doesnot have such a good discussion board thts why u r visiting mit blogsphere)…

and leave only mit lovers here, so tht we dont waste discussing who is better…

That IIT lover guy is a seriously embarrassing halfwit.

47. lulu says:

T is kinetic energy
V is potential energy

that’s actually the more universal notation. I always have to remember to write K and U when I’m talking to 8.012 students.

48. Anonymous says:

A lot of hate going on in here…

Maybe people should just focus on the actual topic and not on which school is better. Arguing over the internet is like fighting a five year old: even if you win you still look like an idiot.

49. Anonymous says:

Nice. Michael what kind of tablet did you use for that? Looks neat.

50. Matt A. says:

Messy Algebra!!! Huzzah!! And I worked it, it really is magical how it condenses. I was a little fuzzy when I first looked at it, but the second time I saw exactly what happened (alas, my school couldn’t offer a Physics C course, and Rotational Kinetic Energy is not on the B exam, although we did learn it, I just forgot it until now.)

51. The last line,

IIT pwned MIT.

52. Ishaan says:

The only solution….
the only conclusion..

M.I.T=Great
I.I.T=Jealous