Recent content by Amit1011

These are the all pages on which I made attempt to solve this question from start to finish, apparently I couldn't finish it. Most of it will seem like illegible on first sight, but it isn't illegible to me. On the 3rd page, at the bottom, where I had written with pencil first, but then felt...

No need to Shout.. ! For a moment there, felt like I am sitting in a class getting shouted on by an Angry teacher who thinks that the student asking the question has not done his due. Let me post the pages on which I've been working to prove that wrong.

Substituting ## 1-cos\theta = 2sin^2\frac{\theta }{2} ## is the first thing I tried when I was doing it on paper; however, couldn't make a dent. I understand that putting a=0, reduces it to the simpler version of the differential equation. But the present differential equation is not getting...

I tried to solve the differential equation by paper pen.. couldn't make it work. I then tried wolfram alpha, it just showed various forms of the same equation, but not the solution. Is there any way that this differential equation could be solved ? If somebody knows, kindly let me know.

Yes, you've put it quite nicely; only in the last line, it should have been: find $$\theta =f(t)$$

Yes, it is exactly how you described it. But I thought about it; figured that if the particle has some charge on it and it is in an Electric field, then also, it will experience a force whose magnitude could be ma. But what you assumed about the frame of reference being non-inertial is how the...

Differentiating eq1 mentioned above, and using eq 2, i got : $$v\frac{dv}{d\theta}=R\frac{dv}{dt}$$ From this, i got:$$ \frac{d\theta}{dt}=\sqrt{(2/R)(g(1-cos\theta )+asin\theta)}$$ After this point, I am not able to understand what substitution or may be other method could be used to solve...

I was already aware when I was attempting it by myself, that at theta exactly =0, the equation will not not be solvable, because the particle will be in equilibrium, though unstable equilibrium. However, I used Wolfram alpha, to solve it. It gave the equation that I used to plot the graph.

This is exactly the differential equation that I figured out while I was attempting to solve it. On solving this equation, the equation I got was θ≈4 cot^(-1)(e^(-3.1305 sqrt(1/R) t)) , which I've posted in my original post. By plotting it in a mathematical software(Geogebra), what I saw, I've...

It's an Is there any software where I could plot it.? I don't know how to solve this differential equation.

when theta_0 tends to 0, but is not exactly equal to 0, it will definitely start to slide down the surface of the sphere. It will continue to be on the surface of the sphere until theta = 48.18 degrees(approx). It will then fly off in parabolic path. I'm trying to find the equation between theta...

That is the assumption I'm also using, but limiting it to theta_0 tends to zero

Well, that much is clear. Suppose, at t=0, theta is infinitesimally close to zero. Starting with this assumption, what will be the equation between theta and time.?

Will the particle not fly off from the surface of the sphere, were it to slide down under influence of gravity ? It will fly off when theta = Cos^(-1) (2/3), i.e. at about 48 degrees. But until that happens, theta will vary wrt time.

I started by using this equation (by energy conservation): v^2 = 2gR(1-cos(theta)), where R is the radius of the sphere, and g = 9.8 m/sec^2. Next equation I used is dv/dt =gSin(theta). Solving both these equation gave this formula: θ≈4 cot^(-1)(e^(-3.1305 sqrt(1/R) t)) When I plotted, it, It...