USEFUL EQUATIONS Velocity in polar coordinates Acceleration in polar coordinates Center of mass (COM) of a rigid body Volume element in cylindrical coordinates Kinetic energy Work Potential Energy (for conservative forces) where Angular momentum Torque Fixed axis rotation: COM Moment of inertia for a uniform bar COM Moment of inertia for a uniform hoop COM Moment of inertia for a uniform disk COM Moment of inertia for a uniform sphere Scalar parallel axis theorem Moments of inertia tensor (permute x→y→z) Euler’s Equations (permute 1→2→3) Time derivative between inertial and rotating frames Fictitious force in an accelerating frame Fictitious force in a rotating frame (Ω constant) Taylor Expansion of f(x)

Useful Equations (III)

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