Forest UCM MnAM

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Conservation of Momentum


[math]\sum \vec{F}_{ext} = 0 = \vec{\dot{P}}_{tot}[/math]


[math]\vec{P}_{tot} = \sum_i^N \vec{p}_i = \sum_i^N m_i\vec{v}_i = [/math] =constant where N = sumber of particles in the systetm

Inelastic Collision of 2 bodies

Inelastic collision DO NOT conserve energy


Elastic Collision of 2 bodies




Center of Mass


Angular Momentum


Sample Problems

circular motion

One end of a string is attached to a mass [math]m[/math] that is moving in a circle of radius [math]r_0[/math] on a frictionless table. The string passes through a hole in the table such that I can hold the string while the particle is moving around in a circle on top of the table.

I pull on the sring until it is a length [math]r[/math] from the hole in the table to the mass.

What is the object's angular velocity after this movement.

Is angular momentum conserved?

The string is the only foce acting on the mass [math]m[/math]. The force is along the string. This means that

[math]\vec r \times \vec F = 0 = \mathcal T[/math]
[math]L_i = L_f[/math]
\vec{r}_0 \times \vec p_i = \vec{r} \times \vec p_f
[math]r_0 mv_i = L_f[/math]

Since r changes though v needs to change such that

[math]r_0 mv_i =r m v_f[/math]
[math]v_f = \frac{r_0 }{r} v_i [/math]