Differences

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--- courses:phy101l:3 [2023/07/11 03:23] – asad
+++ courses:phy101l:3 [2023/10/31 03:36] (current) – [4. Moment of inertia] asad
@@ Line 1: / Line 1: @@
 ====== 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
-===== - Discussion and conclusion =====
+$$ \mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i. $$
+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?