====== 3. Moment of inertia of a flywheel ======
[[https://colab.research.google.com/drive/1mVmVE4wY7OsXLviG2Ht6e4ddznz1XtHZ?usp=sharing|Report sample in Google Colab]]

===== - Introduction and theory =====

$$ mgh = \frac{1}{2} m r^2 \omega^2 + \frac{1}{2} I \omega^2 + n_1 W $$

$$ \frac{1}{2} I \omega^2 = n_2 W \Rightarrow W = \frac{I\omega^2}{2n_2} $$

$$ I = \frac{2mgh - mr^2\omega^2}{\omega^2\left(1+\frac{n_1}{n_2}\right)} $$

$$ \frac{\omega+0}{2} = \frac{2\pi n_2}{t} \Rightarrow \omega = \frac{4\pi n_2}{t} $$

$$ h = 2\pi r n_1 $$
===== - Method and data =====
{{:courses:phy101l:flywheel.png?nolink|}}

Number of rotations before the mass falls, $n_1=$

Radius of the axle, $r=[(a+vb)/2]$ cm; where $a$ is the main scale reading, $b$ is the Vernier scale reading, and $v$ is the Vernier constant.

^ Mass [g] ^ $n_2$ ^ $t$ [s] ^
| 1000 |  |  |
| 1500 |  |  |
| 2000 |  |  |
| 2500 |  |  |

===== - Angular velocity =====

===== - Moment of inertia =====
Mean

$$ \mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i. $$

Standard deviation

$$ \sigma = \sqrt{ \frac{1}{N} \sum_{i=0}^{N-1} (x_i-\mu)^2}. $$

The final result of an experiment is quoted as

$$ \text{ value } = \mu \pm \sigma. $$
===== - Discussion and conclusion =====
  - Why does the flywheel come to a stop?
  - Why are the 4 measurements of moment of inertia different?
  - When does the flywheel reach its maximum velocity?
  - What does the standard deviation (numpy.std) of $I$ tell you?