equation 33.6 eq:expcav-torsion-period
open in the book ·
parts/03-classical-mechanics/16-exp-cavendish.tex:309
- part of a statement or proof
Rests on
- step_from equation 33.5 eq:expcav-torsion-eom ¶
- step_from equation 9.108 eq:slt-helmholtz-real ¶
Supports
- assumes experiment The Cavendish Torsion Balance ¶
-
depends_on
proposition 33.6
The working formula of the torsion balance
¶
-
depends_on
phenomenon 33.12
The Earth is much denser than its crust
¶
- depends_on phenomenon 33.13 One constant serves the bench and the sky ¶
-
depends_on
phenomenon 33.12
The Earth is much denser than its crust
¶
- depends_on remark 33.5 Why the fibre must be fine, quantitatively ¶
- step_from equation 33.11 eq:expcav-theta-solved ¶
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
- a check failed
- not graded
- declared in the source
- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
step_from |
→ | eq:expcav-torsion-eom | declared — reading off $\omega=\sqrt{\kappa/I}$ from the harmonic solution and inverting $T=2\pi/\omega$ | parts/03-classical-mechanics/16-exp-cavendish.tex:313 |
step_from |
→ | eq:slt-helmholtz-real | declared — reading off $\omega=\sqrt{\kappa/I}$ from the harmonic solution and inverting $T=2\pi/\omega$ | parts/03-classical-mechanics/16-exp-cavendish.tex:313 |
assumes |
← | The Cavendish Torsion Balance | declared | parts/03-classical-mechanics/16-exp-cavendish.tex:4 |
depends_on |
← | The working formula of the torsion balance | declared | parts/03-classical-mechanics/16-exp-cavendish.tex:385 |
depends_on |
← | Why the fibre must be fine, quantitatively | declared | parts/03-classical-mechanics/16-exp-cavendish.tex:347 |
step_from |
← | eq:expcav-theta-solved | declared — substituting $\kappa=4\pi^{2}I/T^{2}$ with $I=2md^{2}$, so that $m$ cancels between torque and inertia | parts/03-classical-mechanics/16-exp-cavendish.tex:406 |