AP Physics 1 / Unit 5: Torque and Rotational Dynamics
5.4 Rotational Inertia
Notes
Rotational inertia $\displaystyle I=\sum mr^2$ measures resistance to changes in rotation. Mass farther from the axis increases $I$.
- Hoop: $MR^2$. Solid disk: $\displaystyle \frac{1}{2}MR^2$. Solid sphere: $\displaystyle \frac{2}{5}MR^2$.
- Parallel axis theorem: $I=I_{cm}+Md^2$.
Practice
Which has the largest $I$ for the same mass and radius?
All mass at the rim.
Two 1 kg masses at 2 m from the axis. $I=$
$2(1)(4)$.
Moving mass closer to the axis makes $I$:
Depends on $r^2$.
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