183_notes:l_principle

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
183_notes:l_principle [2015/10/14 15:58] – [Net Torque & The Angular Momentum Principle] caballero183_notes:l_principle [2021/06/03 15:49] (current) – [Systems That Experience No Net Torque] stumptyl
Line 1: Line 1:
 +Section 11.4, 11.5 and 11.6 in Matter and Interactions (4th edition) 
 +
 ===== Net Torque & The Angular Momentum Principle ===== ===== Net Torque & The Angular Momentum Principle =====
  
-You have read that [[183_notes:torque|torques can cause rotations]], and that [[183_notes:ang_momentum|angular momentum is a measure of rotation]]. These two concepts are linked together in the last of 3 fundamental principles of mechanics: the angular momentum principle. In these notes, you will read about the relationship between the net torque on a system and how its angular momentum changes. You will also read about systems where there is no net torque.+You have read that [[183_notes:torque|torques can cause rotations]], and that [[183_notes:ang_momentum|angular momentum is a measure of rotation]]. These two concepts are linked together in the last of 3 fundamental principles of mechanics: the angular momentum principle. **In these notes, you will read about the relationship between the net torque on a system and how its angular momentum changes. You will also read about systems where there is no net torque.**
 ==== Lecture Video ==== ==== Lecture Video ====
  
Line 7: Line 9:
 ==== The Angular Momentum Principle ==== ==== The Angular Momentum Principle ====
  
-The net external torque on a system gives rise to changes in the angular momentum of that system. This relationship is given by the angular momentum principle,+**The net external torque on a system gives rise to changes in the angular momentum of that system. This relationship is given by the angular momentum principle,**
  
 $$\dfrac{\Delta \vec{L}_{sys}}{\Delta t} = \vec{\tau}_{ext}$$ $$\dfrac{\Delta \vec{L}_{sys}}{\Delta t} = \vec{\tau}_{ext}$$
Line 13: Line 15:
 This relationship is quite analogous to the relationship between the net external force and the momentum. In fact, the relationship between the angular momentum and the torque can be [[183_notes:ap_derivation|derived from the momentum principle]]. This relationship is quite analogous to the relationship between the net external force and the momentum. In fact, the relationship between the angular momentum and the torque can be [[183_notes:ap_derivation|derived from the momentum principle]].
  
-The angular momentum principle allows you to predict the new angular momentum of a system given information about it's current angular momentum and the torque it experiences in a short time.+The angular momentum principle allows you to predict the new angular momentum of a system given information about its current angular momentum and the torque it experiences in a short time.
  
 $$\vec{L}_{sys,f} = \vec{L}_{sys,i} + \vec{\tau}_{ext}\Delta t$$ $$\vec{L}_{sys,f} = \vec{L}_{sys,i} + \vec{\tau}_{ext}\Delta t$$
Line 24: Line 26:
 ==== Systems That Experience No Net Torque ==== ==== Systems That Experience No Net Torque ====
  
-{{ 183_notes:mi3e_11-033.png?300}}+[{{ 183_notes:week12_cometearthsun.png?300| Comet orbiting two locations. Location A being a star, and Location B being Earth. Identifying areas of interest in relation to net torque.}}]
  
-For some systems, you might be able to choose a location form which to measure the angular momentum where the system experiences no net torque. For example, in the figure to the right a comet orbits a star. The gravitational force vector points from the comet to the star (red arrow).+For some systems, you might be able to choose a location from which to measure the angular momentum where the system experiences no net torque. For example, in the figure to the right a comet orbits a star. The gravitational force vector points from the comet to the star (red arrow).
  
-If you choose the location about which to determine the angular momentum to be the star itself (i.e., location A), then the comet experiences no net torque. Why? Because the position vector that locates the comet points from the star to the comet and is thus along the same line as the gravitational force. The cross product of two parallel or anti-parallel vectors is zero. Hence, the angular momentum of the comet around the star is constant. That constant is not zero; the torque is zero.+If you choose the location about which to determine the angular momentum to be the star itself (i.e., location A), then the comet experiences no net torque. Why? Because the position vector that locates the comet points from the star to the comet and is thus along the same line as the gravitational force. The cross product of two parallel or anti-parallel vectors is zero. __//Hence, the angular momentum of the comet around the star is constant. That constant is not zero; the torque is zero.//__
  
 $$\Delta \vec{L}_{sys} = 0 \longrightarrow \vec{L}_{sys,f} = \vec{L}_{sys,i}$$ $$\Delta \vec{L}_{sys} = 0 \longrightarrow \vec{L}_{sys,f} = \vec{L}_{sys,i}$$
  • 183_notes/l_principle.1444838306.txt.gz
  • Last modified: 2015/10/14 15:58
  • by caballero