18 lines
626 B
Markdown
18 lines
626 B
Markdown
[[Torque and Rotational Dynamics]]
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For a point mass:$$I=mr^2$$
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$I$ is rotational inertia (kg * $m^2$)
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m is mass
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r is radial distance
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Several discrete objects:
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$$I_{tot}=\Sigma I_i=\Sigma m_i r^2$$
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Kinetic energy from rotation formula:
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$$KE_{rot}=\frac{1}{2}Iw^2$$
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# Parallel Axis Theorem
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Essentially shifting the axis and calculating the new inertia.
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$$I'=I_{cm}+Md^2$$
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- $I$' is rotational inertia about the parallel axis (kg⋅m²)
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- $I_{cm}$ is rotational inertia about the center-of-mass axis (kg⋅m²)
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- $M$ is the total mass of the system (kg)
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- $d$ is the perpendicular distance between the two parallel axes (m) |