A modeling approach to the 8.01 final exam equation sheet.
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Interactions
General Definitions
Work
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\begin
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[ W = \int_
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^
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\vec
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\cdot d\vec
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]\end
Potential Energy
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\begin
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[\Delta U = -W_
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= -\int_
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^
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\vec
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_
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\cdot d\vec
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]\end
Power
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\begin
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[P = \vec
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\cdot\vec
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]\end
Impulse
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\begin
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[ I = \int_
Unknown macro: {t=0}
^
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\vec
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(t)\:dt ]\end
Torque
\vec
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_
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= \vec
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_
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\times\vec
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_
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\qquad \qquad |\vec
_
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| = |\vec
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_
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||\vec
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_
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| \sin\theta = r_
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F = r F_
]\end
[ \vec
_
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= - G\frac{m_
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m_{2}}{r_
^{2}}\hat
_
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\qquad\qquad U_
(r) = - G\frac{m_
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m_{2}}{r_{12}}]\end
[ F = mg \mbox
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\qquad \qquad U
= mgy ]\end
[ \vec
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_
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= \vec
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+ \vec
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]\end
[ 0 \le f_
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\le f_
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= \mu_
N \mbox
Unknown macro: { (directed opposite net force neglecting friction)}
]\end
[ f_
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= \mu_
N \mbox
Unknown macro: { (opposes motion with respect to the surface)}
]\end
[ F = k|\Delta x| \mbox
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\qquad \qquad U
= \frac
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k x^
]\end
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