Linear Momentum

physics/Linear Momentum/Change in Linear Momentum and Impulse.md

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+[[Linear Momentum]]
+
+# Summary
+* Net force equals $\vec F_{net}=\frac{\Delta \vec p}{\Delta t}$
+* Impulse is average force over time interval: $\vec J = \vec F_{avg}\Delta t$
+* Impulse-momentum theory is impulse = change in momentum: $$\vec J=\Delta \vec p = \vec p-\vec p_0$$
+* Integral of a force vs time graph equals impulse, slope of momentum vs time graph = net force
+* Impulse units are N * s (kg * m/s)
+* When mass is constant F=ma comes from Impulse-Momentum theory
+

physics/Linear Momentum/Conservation of Linear Momentum.md

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+[[Linear Momentum]]
+
+Total momentum of system stays the same when there is no external force acting on it.
+
+# Summary
+* Total momentum is vector sum
+* If net external force is 0, then momentum stays the same.
+* Momentum is conserved in every action
+* Nonzero net external force transfers momentum in or out of system, which is impulse.
+* Center of mass velocity stays constant when no external force.
+
+# Center of Mass Velocity
+$$\vec v_{cm}=\frac{\Sigma \vec p_i}{\Sigma m_i}$$
+Treats whole system like momentum is concentrated in one point.
+

physics/Linear Momentum/Elastic and Inelastic Collisions.md

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+[[Linear Momentum]]
+
+# Summary
+* Elastic collision: total kinetic energy stays the same
+* Inelastic collision: energy is lost to things like heat and sound
+* Perfectly inelastic collision: objects stick together and share one velocity
+* Momentum is conserved in every collision where net external force is zero
+* "Lost" kinetic energy just transforms into different forms, so total energy is preserved.
+
+Perfectly inelastic collisions:
+$$v_f=\frac{m_1v_1+m_2v_2}{m_1m_2}$$
+![[Pasted image 20260819112153.png]]
+# Elastic Collision Energy Conservation Formula
+$$\frac{1}{2}m_1v^2_{1i}+\frac{1}{2}m_2v^2_{2i}=\frac{1}{2}m_1v^2_{1f}+\frac{1}{2}m_2v^2_{2f}$$
+

physics/Linear Momentum/Linear Momentum.md

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+[[physics]]
+Linear momentum: $$\vec p=m\vec v$$
+$\vec p$ is momentum in kg * m/s
+
+# Summary
+* Momentum: $\vec p=m\vec v$
+* It's a vector
+* Doubling either mass or velocity doubles momentum
+* In one dimension, assign positive and negative signs
+* Collision is an interaction where forces between objects are much larger than net external force on system
+* Explosion is interaction where internal forces push parts of a system apart
+