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class09

# class09 - Announcements Reading for Wednesday 3.1-3.6 First...

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Announcements Reading for Wednesday: 3.1-3.6 First Mid-term is next week (Feb. 9 th , 7:30pm). It will cover Chapters 1&2. Support Haiti: On Facebook: CU Stands with Haiti Momentum The classical definition of the momentum p of a particle with mass m is: p =m u . In absence of external forces the total momentum is conserved (Law of conservation of momentum): n . 1 const i i = = p Due to the velocity addition formula, the definition p =m u is not suitable to obtain conservation of momentum in special relativity!! Need new definition for relativistic momentum! Review: Transformation rules and conservation of momentum y u 1 u 2 m m y' u ' 1 u ' 2 m u u 1y v = u 1x x S x' m S' 1x 2 / 1 ' c v u v u u x x x - - = ( 29 2 / 1 ' c v u u u x y y - = γ Relativistic: Classical: u' x = u x – v u' y = u y Conservation of momentum is extremely useful in classical physics. For the new definition of relativistic momentum we want: 1. At low velocities the new definition of p should match the classical definition of momentum. 2. We want that the total momentum ( Σ p ) of an isolated system of bodies is conserved in all inertial frames. Relativistic momentum Classical definition: dt d m r p = Say we measure the mass 'm' in its rest-frame (' proper mass' or ' rest mass' ). Since we measure 'm' it's rest- frame we agree on the same value for 'm' in all frames. Relativistic definition: proper dt d m r p Assume we take the derivative with respect to the proper time t proper , which has the same meaning in all frames. This definition fulfills the conservation of momentum in SR! To prove it you can apply the relativistic velocity transformation.

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class09 - Announcements Reading for Wednesday 3.1-3.6 First...

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