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If two eggs are given out of which one is hard boiled egg and the other is raw egg. When both of them are allowed to spin on a tabletop, the egg which spins slower must be the raw egg because the liquid inside it tries to get away from the axis of rotation increasing the value of moment of inertia (I). To remain the angular momentum L conserved in absence of ...

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The way I see it this problem is similar the problem of column of water and the pressure rising due to gravity pulling down on the liquid - in which case pressure, $P$, is given by $P = h \rho g$ where $h$ is the height of liquid, $\rho$ is the density and $g$ the acceleration due to gravity - but you probably knew this already. The point I want to make ...

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This is d'Alembert's principle. The basic, very general idea is to take Newton's second law applied to an accelerating mass, and write it as $F-ma=0$. That is, we take the $ma$ term and pretend it's another force balancing the $F$ term. This allows us to think about the dynamic, accelerating mass as if it's a static system. The $ma$ term is what's referred ...

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In this case, by inertial force, they do not refer to the pseudoforce from an non intertial reference frame. Instead, by inertial force, they refer to the force due to the momentum of the fluid. This is usually expressed in the momentum equation by the term (ρv)v. So, the denser a fluid is, and the higher its velocity, the more momentum (inertia) it has.

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There are only exact solutions when only using two bodies (namely Kepler orbits), however when you use any more bodies there will be no general solution. These systems of more than two bodies can be approximated numerically, like you tried, by using discreet time steps. But now you enter the realm of numerical integration for ordinary differential equations. ...

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A simulation does not have a prescribed position $x(t)$. The forces are known, and the position and velocity is found by considering a small time step $\Delta t$ and finding the acceleration $a=\frac{\sum F}{m}$ to act on this step. For each step then  \begin{aligned} t & \rightarrow t + \Delta t \\ x & \rightarrow x + v \Delta t \\ v & ...

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First, I take it from your question that you are working to make a simulation of bodies in 2D with gravitational forces between them, like say earth and moon - or sun and earth - is that correct? If this is the case then you are going to have a problem using $v=v_0+at$ and similar formulae because the acceleration will not be constant. $v=v_0+at$ and ...

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