Standard Centre of Mass Positions
| Body | CM Position | Measured From |
|---|---|---|
| Uniform rod (length L) | Either end | |
| Uniform disc / ring | Geometric centre | — |
| Triangular lamina (height h) | Base | |
| Semicircular ring (radius R) | Centre of full circle | |
| Semicircular disc (radius R) | Centre of full circle | |
| Uniform solid hemisphere (radius R) | Centre of flat face | |
| Hollow hemispherical shell (radius R) | Centre of flat face |
Memory Pattern
Note the decreasing sequence of CM distances from the centre for curved shapes:
- Semicircular ring: $2R/\pi \approx 0.637R$ (all mass at edge)
- Semicircular disc: $4R/3\pi \approx 0.424R$ (mass spread inward)
- Solid hemisphere: $3R/8 = 0.375R$ (mass fills volume)
- Hollow hemispherical shell: (mass at surface only)
Key Formula for CM
For any finite system:
For a body with a cavity: treat the cavity as a negative mass at the cavity's CM position.$