Linear Momentum
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[[Linear Momentum]]
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# Summary
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* Net force equals $\vec F_{net}=\frac{\Delta \vec p}{\Delta t}$
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* Impulse is average force over time interval: $\vec J = \vec F_{avg}\Delta t$
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* Impulse-momentum theory is impulse = change in momentum: $$\vec J=\Delta \vec p = \vec p-\vec p_0$$
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* Integral of a force vs time graph equals impulse, slope of momentum vs time graph = net force
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* Impulse units are N * s (kg * m/s)
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* When mass is constant F=ma comes from Impulse-Momentum theory
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[[Linear Momentum]]
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Total momentum of system stays the same when there is no external force acting on it.
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# Summary
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* Total momentum is vector sum
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* If net external force is 0, then momentum stays the same.
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* Momentum is conserved in every action
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* Nonzero net external force transfers momentum in or out of system, which is impulse.
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* Center of mass velocity stays constant when no external force.
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# Center of Mass Velocity
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$$\vec v_{cm}=\frac{\Sigma \vec p_i}{\Sigma m_i}$$
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Treats whole system like momentum is concentrated in one point.
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[[Linear Momentum]]
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# Summary
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* Elastic collision: total kinetic energy stays the same
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* Inelastic collision: energy is lost to things like heat and sound
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* Perfectly inelastic collision: objects stick together and share one velocity
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* Momentum is conserved in every collision where net external force is zero
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* "Lost" kinetic energy just transforms into different forms, so total energy is preserved.
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Perfectly inelastic collisions:
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$$v_f=\frac{m_1v_1+m_2v_2}{m_1m_2}$$
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![[Pasted image 20260819112153.png]]
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# Elastic Collision Energy Conservation Formula
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$$\frac{1}{2}m_1v^2_{1i}+\frac{1}{2}m_2v^2_{2i}=\frac{1}{2}m_1v^2_{1f}+\frac{1}{2}m_2v^2_{2f}$$
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[[physics]]
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Linear momentum: $$\vec p=m\vec v$$
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$\vec p$ is momentum in kg * m/s
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# Summary
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* Momentum: $\vec p=m\vec v$
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* It's a vector
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* Doubling either mass or velocity doubles momentum
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* In one dimension, assign positive and negative signs
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* Collision is an interaction where forces between objects are much larger than net external force on system
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* Explosion is interaction where internal forces push parts of a system apart
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