University:
Santa Fe College
Course:
PHY 2004 | Applied Physics 1
Academic year:

2024
Views:

449

Pages:

5
Author:

Jabin F.

How to solve general problems of Mechanics/Dynamics. 1st Approach: using equation of motion (EOM) ① Newton's equation of motion Fundamental Approach F = dp/dt If mass is constant then F = ma Note: In relativistic mechanics mass is variable. ② Lagrange's equation of motion d/dt (∂L/∂q̇ᵢ) - ∂L/∂qᵢ = 0 where L = T - V Lagrangian ③ Hamilton's equation of motion q̇ᵢ = ∂H/∂pᵢ ṗᵢ = -∂H/∂qᵢ where H = Σpᵢq̇ᵢ - L Hamiltonian 2nd Approach: using conservation laws ① Conservation of linear momentum if F = 0 then p = constant => Σp_initial = Σp_final Figure: A diagram with two masses (m₁ and m₂) connected by a spring. Forces F are acting on both masses in opposite directions. Text: In figure shown, forces on m₁ & m₂ are not zero. So their individual momentum is not conserved. However, total force on m₁ & m₂ together is zero. So sum of their momentum is conserved. Equations: If ΣF = 0 then Σp = constant If ΣF ≠ 0 then Σp ≠ constant Conservation of angular momentum: If τ = 0 then L = constant If Στ = 0 then ΣL = constant ΣL_initial = ΣL_final