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183_notes:ang_momentum [2021/06/04 04:10] – [Angular Momentum] stumptyl | 183_notes:ang_momentum [2021/06/04 04:12] (current) – [Rotational Angular Momentum] stumptyl | ||
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{{youtube> | {{youtube> | ||
- | ==== Translational Angular Momentum ==== | + | ===== Translational Angular Momentum |
- | As with [[183_notes: | + | As with [[183_notes: |
Given that angular momentum is a measure of rotation, you probably have a sense that an object that rotates about itself can have angular momentum, which is true, and will be discussed in a moment. But, an object that is moving, but not rotating about its center can still have angular momentum about a point. In fact, this is how we define angular momentum, in general. To determine the value of this angular momentum requires that we choose a " | Given that angular momentum is a measure of rotation, you probably have a sense that an object that rotates about itself can have angular momentum, which is true, and will be discussed in a moment. But, an object that is moving, but not rotating about its center can still have angular momentum about a point. In fact, this is how we define angular momentum, in general. To determine the value of this angular momentum requires that we choose a " | ||
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$$\vec{L}_{trans} = \vec{r}_A \times \vec{p}$$ | $$\vec{L}_{trans} = \vec{r}_A \times \vec{p}$$ | ||
- | where the vector $\vec{r}_A$ is the vector that points from the rotation axis to the object in question. The units of angular momentum are kilograms-meters squared per second ($\mathrm{kg\, | + | where the vector $\vec{r}_A$ is the vector that points from the rotation axis to the object in question. The units of angular momentum are **kilograms-meters squared per second ($\mathrm{kg\, |
- | === Magnitude of the translational angular momentum === | + | ==== Magnitude of the translational angular momentum |
{{ 183_notes: | {{ 183_notes: | ||
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$$\left|\vec{L}_{trans}\right| = \left|\vec{r}_A\right|\left|\vec{p}\right|\sin \theta = \left|\vec{r}_{A, | $$\left|\vec{L}_{trans}\right| = \left|\vec{r}_A\right|\left|\vec{p}\right|\sin \theta = \left|\vec{r}_{A, | ||
- | === Direction of the translation angular momentum === | + | ==== Direction of the translation angular momentum |
{{ 183_notes: | {{ 183_notes: | ||
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==== Rotational Angular Momentum ==== | ==== Rotational Angular Momentum ==== | ||
- | As you [[183_notes: | + | As you [[183_notes: |
Consider the spinning ball, person, stool system from the demonstration. In this case, the whole system rotates with the same angular velocity ($\omega$) after the ball was caught. An atom in the ball at a distance of $r_{\perp}$ from the rotation axis is therefore moving with a linear speed $v = r_{\perp}\omega$. Here, $r_{\perp}$ is the perpendicular distance from the rotation axis to the atom in the ball. | Consider the spinning ball, person, stool system from the demonstration. In this case, the whole system rotates with the same angular velocity ($\omega$) after the ball was caught. An atom in the ball at a distance of $r_{\perp}$ from the rotation axis is therefore moving with a linear speed $v = r_{\perp}\omega$. Here, $r_{\perp}$ is the perpendicular distance from the rotation axis to the atom in the ball. |