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4.8: Elastic Collisions in the COM Frame
https://phys.libretexts.org/Bookshelves/University_Physics/Mechanics_and_Relativity_(Idema)/04%3A_Momentum/4.08%3A_Elastic_Collisions_in_the_COM_Frame
We did the calculation in the lab frame, i.e., from the point of view of a stationary observer. We could of course just as well have done the calculation in the center-of-mass (COM) frame of Section ...We did the calculation in the lab frame, i.e., from the point of view of a stationary observer. We could of course just as well have done the calculation in the center-of-mass (COM) frame of Section 4.3. Within that frame, as we’ll see below, the relation between the initial and final velocities in an elastic collision is much simpler than in the lab frame.
14.2: Some Equations and Constants
https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_I_(2211)/14%3A_Resources_Tools_and_Additional_Information/14.02%3A_Some_Equations_and_Constants
\end{array}\right)=\left(\frac{\partial f}{\partial x} \hat{x}+\frac{\partial f}{\partial y} \hat{y}+\frac{\partial f}{\partial z} \hat{z}\right)\] \end{array}\right)=\frac{\partial v_{x}}{\partial x}...\end{array}\right)=\left(\frac{\partial f}{\partial x} \hat{x}+\frac{\partial f}{\partial y} \hat{y}+\frac{\partial f}{\partial z} \hat{z}\right)\] \end{array}\right)=\frac{\partial v_{x}}{\partial x}+\frac{\partial v_{y}}{\partial y}+\frac{\partial v_{z}}{\partial z}\] $v_{x}=\frac{u+v_{x}^{\prime}}{1+u v_{x}^{\prime} / c^{2}} \quad \text { (longitudinal) } , v_{y}=\frac{1}{\gamma(u)} \frac{v_{y}^{\prime}}{1+u v_{x}^{\prime} / c^{2}} \quad \text { (transversal) }$
4.6: Totally Inelastic Collisions
https://phys.libretexts.org/Bookshelves/University_Physics/Mechanics_and_Relativity_(Idema)/04%3A_Momentum/4.06%3A_Totally_Inelastic_Collisions
For the case of two particles colliding totally inelastically, conservation of momentum gives: $m_{1} v_{1}+m_{2} v_{2}=\left(m_{1}+m_{2}\right) v_{\mathrm{f}}$ . If the masses and initial velocities...For the case of two particles colliding totally inelastically, conservation of momentum gives: $m_{1} v_{1}+m_{2} v_{2}=\left(m_{1}+m_{2}\right) v_{\mathrm{f}}$ . If the masses and initial velocities of the particles are known, calculating the final velocity of the composite particle is thus straightforward.
4: Momentum
https://phys.libretexts.org/Bookshelves/University_Physics/Mechanics_and_Relativity_(Idema)/04%3A_Momentum
6.E: General Planar Motion (Exercises)
https://phys.libretexts.org/Bookshelves/University_Physics/Mechanics_and_Relativity_(Idema)/06%3A_General_Planar_Motion/6.E%3A_General_Planar_Motion_(Exercises)
Show that you can re-write the equation of motion for the separation between the two objects as $\boldsymbol{F(r )} = \mu \boldsymbol{\ddot{r}}$ , where $\mu$ is the reduced mass that we also encou...Show that you can re-write the equation of motion for the separation between the two objects as $\boldsymbol{F(r )} = \mu \boldsymbol{\ddot{r}}$ , where $\mu$ is the reduced mass that we also encountered when studying collisions in the center of mass frame, Equation 4.8.7, given by $\mu=\frac{m M}{m+M}$ Note that solving the final equation for the separation $\boldsymbol{r}$ is entirely equivalent to solving the equation of motion of a single particle under the action of a central force,…
2: Forces
https://phys.libretexts.org/Bookshelves/University_Physics/Mechanics_and_Relativity_(Idema)/02%3A_Forces
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13.4: Relativistic Energy
https://phys.libretexts.org/Bookshelves/University_Physics/Mechanics_and_Relativity_(Idema)/13%3A_Position_Energy_and_Momentum_in_Special_Relativity/13.04%3A_Relativistic_Energy
The relativistic energy of the particle is an energy contribution due to the mass of the particle.
2.5: Statics
https://phys.libretexts.org/Bookshelves/University_Physics/Mechanics_and_Relativity_(Idema)/02%3A_Forces/2.05%3A_Statics
When multiple forces act on a body, the (vector) sum of those forces gives the net force, which is the force we substitute in Newton’s second law of motion to get the equation of motion of the body. I...When multiple forces act on a body, the (vector) sum of those forces gives the net force, which is the force we substitute in Newton’s second law of motion to get the equation of motion of the body. If all forces sum up to zero, there will be no acceleration, and the body retains whatever velocity it had before. Statics is the study of objects that are neither currently moving nor experiencing a net force, and thus remain stationary.
11: Lorentz Transformations
https://phys.libretexts.org/Bookshelves/University_Physics/Mechanics_and_Relativity_(Idema)/11%3A_Lorentz_Transformations
10.1: An Old and a New Axiom
https://phys.libretexts.org/Bookshelves/University_Physics/Mechanics_and_Relativity_(Idema)/10%3A_Einstein's_Postulates/10.01%3A_An_Old_and_a_New_Axiom
The theory of special relativity is built on two postulates (our axioms for this chapter). The first one also applies to classical mechanics and simply states that: (1) The laws of physics are identic...The theory of special relativity is built on two postulates (our axioms for this chapter). The first one also applies to classical mechanics and simply states that: (1) The laws of physics are identical in every inertial reference frame and (2) The speed of light in vacuum is the same in all inertial reference frames.
5: Rotational Motion, Torque and Angular Momentum
https://phys.libretexts.org/Bookshelves/University_Physics/Mechanics_and_Relativity_(Idema)/05%3A_Rotational_Motion_Torque_and_Angular_Momentum
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