Maxwell's Wheel: Understanding Conservation of Energy and Derivatives

[diracdelta]

Well, I have to do experiment with Maxwell's wheel, but i struggle with theoretical background.
If you don't know what Maxwell's wheel is,
http://www.nikhef.nl/~h73/kn1c/praktikum/phywe/LEP/Experim/1_3_18.pdf

I understand conservation of energy and how we made that equation, but this part i don't get;

Ok, i understand derivative, but how do i get s(t) and v(t).
Thanks!

 

[Doc Al]

You just need a bit of algebra. Hint: first solve for the acceleration.

 

[rude man]

You have a very simple ODE. Solve it for v(t) using the given I.C. for v, then solve for s(t) = ∫v(t)dt using the I.C. for s.

EDIT: go with Doc Al, don't need formal ODE approach. Divide by v and solve for accel.

 

[diracdelta]

Edit:
I see that v derivated is acceleration, so when i divide equation and kill v(t) i get acceleration,
a= mg/(m+I/r²)

should i just double integrate it now for s(t) and once for v(t), yes,i get it.
thanks!

 

[diracdelta]

One more thing
http://www.officeplayground.com/Assets/ProductPreview/pi3600-3799/3653_maxwellswheel_1.jpg
In scheme of wheel, where does ds point to?

 

[Doc Al]

Edit:
I see that v derivated is acceleration, so when i divide equation and kill v(t) i get acceleration,
a= mg/(m+I/r2)

Right!

should i just double integrate it now for s(t) and once for v(t), yes,i get it.

Sure. (Or, since the acceleration is constant, you can use the standard kinematic formulas.)

In scheme of wheel, where does ds point to?

Down.

 

[diracdelta]

Alright. I can't remember why, if ds=d(phi)xr, where x i vector cross multiply. Using right hand rule, it should be perpenicular towards angle and radiaii?