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Important formulas for the physics olympiad.
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Vis-viva equation
v velocity of orbiting object
r distance between orbiting bodies
a semi major axis of the orbit

Period of Orbit
T orbital period
a semi major axis

Capstan Equation
T1 smaller tension
T2 larger tension
μ coefficient of friction
θ wrap angle in radians

Euler’s Identity

Repeated Root Solution 2nd Order DE
r repeated root
note: use this if the discriminant of the characteristic equation (ar2+br+c=0) is 0. Plug in the repeated root and use initial conditions to solve.


