\omega is the angular velocity of the disk, v is the translational velocity. v and \omega are constants. Integration extends over the area of the disk with \vec{r} vectors starting at the center.
Hi,
How do integrate this? I wish to see it step by step and I'm glad for any help i can get.
\int_{ \vec{r}\in{A}} \frac{ \vec{v}+ \vec{\omega}\times\vec{r}}{| \vec{v}+ \vec{\omega}\times\vec{r}|}d^{2}r
where A is area of disk with radius R.
[\frac{b}{x}] it is entier function. I can not solve second case... It is harder than first. Can I do (\frac{x}{a}-1)\frac{b}{x}\leq{[\frac{x}{a}]\frac{b}{x}}\leq{\frac{b}{a}} and use |f(x)-g|\leq{\epsilon} so g=\frac{b}{a}?
Hi,
How can I calculate left and right-sided limits?
\frac{x}{a}[\frac{b}{x}]
\frac{b}{x}[\frac{x}{a}]
\frac{x}{\sqrt{|sinx|}}
in point x=0.
Thanks for help.
I used to function calculator and I received:
\int{\frac{A+Bcosx}{\sqrt{A^{2}+B^{2}+2ABcosx}}}=\frac{(B^{4}-4AB^{3}+4A^{2}B^{2})x^{5}}{5(24B^{4}+96AB^{3}+144A^{2}B^{2}+96A^{3}B+24A^{4})}-\frac{B^{2}x^{3}}{3(2B^{2}+4AB+2A^{2})}+x+O(x^{7})+C
I think what I can neglect O(x^{7})... Is it correct?
Hi!
I have big problem with solve this equation:
m\frac{d^{2}x}{dt^{2}}+ksinx=0
I can't go ahead, because I don't know how solve this
\frac{dx}{\sqrt{cosx}}=\sqrt{\frac{2k}{m}}dt
Phizyk
I apologize to bad equation C=C_{1}+C_{2}
It's wrong... You have a good solution, because
V=\frac{q}{C}
and V_{1}=\frac{q}{C_{1}} V_{2}=\frac{q}{C_{2}}
and V=V_{1}+V_{2}
so \frac{1}{C}=\frac{1}{C_{1}}+\frac{1}{C_{2}}
\frac{dR}{d\theta}=cos\theta{cos(\phi+\theta)}-sin\theta{sin(\phi+\theta)}=0
but
cos(\phi+\theta)=cos\theta{cos\phi}-sin\theta{sin\phi}
sin(\phi+\theta)=sin\phi{cos\theta}+cos\phi{sin\theta}
to equation
\frac{dR}{d\theta}=cos\phi(cos^{2}\theta-sin^{2}\theta)-2sin\theta{cos\theta}sin\phi=0...