An integral for rotational movement equations

Solar Eclipse
Messages
12
Reaction score
0
Im talking calc and physics in high school right now and I was bored and messed with my formulas but I need some help now.It's for rotational movement.
If I have \varpid\varpi=\alphad\theta and then I take the integral will it be (\varpi^2)/2 = \alpha\theta or did I do it all wrong?
 
Physics news on Phys.org
Solar Eclipse said:
If I have \varpid\varpi=\alphad\theta and then I take the integral will it be (\varpi^2)/2 = \alpha\theta or did I do it all wrong?

Hi Solar Eclipse! :smile:

(have an omega: ω and an alpha: α and a theta: θ :wink:)

Yes, that's fine, if α is a constant, of course (except you left out the "+ C"! :wink:) …

d(something) works the same no matter what the something is, and no matter whether you have d(something-else)s in the same equation. :smile:
 
awesome thank you for the help.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
Back
Top