183_notes:ang_momentum

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision		 Previous revision
Last revisionBoth sides next revision
183_notes:ang_momentum [2021/06/04 04:09] – [Translational Angular Momentum] stumptyl183_notes:ang_momentum [2021/06/04 04:11] – [Translational Angular Momentum] stumptyl
Line 2: Line 2:
 ===== Angular Momentum ===== ===== Angular Momentum =====
  
-Angular momentum is a way to measure the rotation of a system. As we did with kinetic energy (which is a way to measure the motion of a system), we can separate the angular momentum into translational and rotational bits. In these notes, you will read about each of these two bits, how they are defined, and how to deal with systems that have both bits. You will also be introduced to the "into/out of the page" language that we often use in physics to describe the direction of vectors that do not point in the plane.+Angular momentum is a way to measure the rotation of a system. As we did with kinetic energy (which is a way to measure the motion of a system), we can separate the angular momentum into translational and rotational bits. **In these notes, you will read about each of these two bits, how they are defined, and how to deal with systems that have both bits.** You will also be introduced to the "into/out of the page" language that we often use in physics to describe the direction of vectors that do not point in the plane.
  
 ==== Catching a Ball ==== ==== Catching a Ball ====
Line 10: Line 10:
  
 {{youtube>itsnuo1DnRw?large}} {{youtube>itsnuo1DnRw?large}}
-==== Translational Angular Momentum ====+===== Translational Angular Momentum =====
  
-As with [[183_notes:torque#torque|torque]], angular momentum requires that you consider a particular rotation axis. That is, around what point will you determine the angular momentum of the system? In general any point can be chosen, but the point that is chosen will determine the value of the angular momentum.+As with [[183_notes:torque#torque|torque]], angular momentum requires that you consider a particular rotation axis. That is, around what point will you determine the angular momentum of the system? __//In general any point can be chosen, but the point that is chosen will determine the value of the angular momentum.//__
  
 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 "rotation" axis. 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 "rotation" axis.
Line 26: Line 26:
 $$\vec{L}_{trans} = \vec{r}_A \times \vec{p}$$ $$\vec{L}_{trans} = \vec{r}_A \times \vec{p}$$
  
-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 ($\mathrm{kg\,m^2/s}$). This is how angular momentum is defined, but it is convenient to think a bit differently about angular momentum associated with a object that rotates about its own center.+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 ($\mathrm{kg\,m^2/s}$)**. This is how angular momentum is defined, but it is convenient to think a bit differently about angular momentum associated with an object that rotates about its own center.
  
-=== Magnitude of the translational angular momentum ===+==== Magnitude of the translational angular momentum ====
  
 {{ 183_notes:week12_angm2.png?400}} {{ 183_notes:week12_angm2.png?400}}
Line 44: Line 44:
 $$\left|\vec{L}_{trans}\right| = \left|\vec{r}_A\right|\left|\vec{p}\right|\sin \theta = \left|\vec{r}_{A,\perp}\right|\left|\vec{p}\right|$$ $$\left|\vec{L}_{trans}\right| = \left|\vec{r}_A\right|\left|\vec{p}\right|\sin \theta = \left|\vec{r}_{A,\perp}\right|\left|\vec{p}\right|$$
  
-=== Direction of the translation angular momentum ===+==== Direction of the translation angular momentum ====
  
 {{ 183_notes:mi3e_11-010.png?300}} {{ 183_notes:mi3e_11-010.png?300}}
  • 183_notes/ang_momentum.txt
  • Last modified: 2021/06/04 04:12
  • by stumptyl