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TriTertButoxy
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Why is it in kinetic theory one uses the velocity variable, instead of the momentum variable? Wouldn't this cause problems when trying to generalize to relativistic systems?
Archosaur said:I think I understand your question.
Momentum is in the equation. It's just hiding.
You could think of the equation for kinetic energy as [tex]KE = \frac{1}{2}pv[/tex]
because [tex]p = mv[/tex]
I don't know if this answers your question.
Velocity is a measure of an object's speed and direction, while momentum is a measure of an object's mass and velocity combined. In other words, velocity tells us how fast an object is moving and in which direction, while momentum tells us how much force an object has as a result of its mass and velocity.
Kinetic theory states that all particles in a substance are constantly in motion, and their speed and direction of movement determine their momentum. The faster and heavier a particle is, the more momentum it will have. This theory also explains why increasing the temperature of a substance can increase the average velocity and therefore the momentum of its particles.
Yes, in a relativistic system, velocity and momentum can change due to the effects of time dilation and length contraction. As an object approaches the speed of light, its velocity will increase but its momentum will decrease due to the increase in mass. This is known as relativistic momentum.
The conservation of momentum states that in a closed system, the total momentum remains constant. This means that if two objects collide, their combined momentum before the collision will be equal to their combined momentum after the collision. This applies to velocity as well - the total velocity of all objects in a closed system will remain constant, even if individual velocities change.
In classical systems, velocity and momentum are directly proportional, meaning that as one increases, so does the other. However, in relativistic systems, velocity and momentum are not directly proportional due to the effects of time dilation and length contraction. Additionally, in classical systems, the mass of an object remains constant, whereas in relativistic systems, the mass can change due to the increase in velocity.