Physics Olympiad

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Important formulas for the physics olympiad.

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1
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Vis-viva equation

v velocity of orbiting object
r distance between orbiting bodies
a semi major axis of the orbit

<p><span>v</span> velocity of orbiting object<br><span>r</span> distance between orbiting bodies<br><span>a</span> semi major axis of the orbit</p>
2
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Period of Orbit

T orbital period
a semi major axis

<p><span>T</span> orbital period<br><span>a</span> semi major axis</p>
3
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Capstan Equation

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

<p><span>T</span><sub><span>1</span></sub><span>​</span> smaller tension<br><span>T</span><sub><span>2</span></sub><span>​</span> larger tension<br><span>μ</span> coefficient of friction<br><span>θ</span> wrap angle in radians</p>
4
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Euler’s Identity

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5
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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.

<p>r repeated root<br><br>note: use this if the discriminant of the characteristic equation (<span>ar2+br+c=0) is 0. Plug in the repeated root and use initial conditions to solve.</span></p>
6
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