Angular momentum of a particle system

In summary, the angular momentum of the system of particles pictured in Figure P.10 about the origin at 0 is 4k.
  • #1
jhu2011
2
0

Homework Statement



Calculate the total angular momentum of the system of particles pictured in Figure P.10 about the origin at 0. Figure is at www.webassign.net/reese1/p10-10.gif.


Homework Equations



L = r X p

p = mv

The Attempt at a Solution



Since you are taking a vector product, there is no i or j component to the angular momentum, meaning there will just be k perpendicular to the plane. I read somewhere that when doing a system of particles, you should take the angular momentum of each separate particle and then add it up. However, when I do this I don't get the right answer... Using L = r X p:

For 1st 3m: -4i + 2j X -3i = 6k
For 1st 2m: 1i + 2j X 2i = -4k
For 2nd 2m: 1i -2j X 2j = 2k

And 6 - 4 + 2 = 4k, which is NOT the right answer. I don't know what I've done wrong...
 
Physics news on Phys.org
  • #2
jhu2011 said:

Homework Statement



Calculate the total angular momentum of the system of particles pictured in Figure P.10 about the origin at 0. Figure is at www.webassign.net/reese1/p10-10.gif.

Homework Equations



L = r X p
p = mv

The Attempt at a Solution



Since you are taking a vector product, there is no i or j component to the angular momentum, meaning there will just be k perpendicular to the plane. I read somewhere that when doing a system of particles, you should take the angular momentum of each separate particle and then add it up. However, when I do this I don't get the right answer... Using L = r X p:

For 1st 3m: -4i + 2j X -3i = 6k
For 1st 2m: 1i + 2j X 2i = -4k
For 2nd 2m: 1i -2j X 2j = 2k

And 6 - 4 + 2 = 4k, which is NOT the right answer. I don't know what I've done wrong...

Welcome to PF.

Your 3rd r vector should be <1.2i, -2j> shouldn't it?
 
  • #3
LowlyPion said:
Welcome to PF.

Your 3rd r vector should be <1.2i, -2j> shouldn't it?

Indeed it should be. That 1.20 is so close to the 1.00! I got the correct answer now. Thanks a lot!
 

FAQ: Angular momentum of a particle system

What is angular momentum?

Angular momentum is a physical quantity that describes the rotation of a particle or system of particles around a fixed point. It is a vector quantity that takes into account the mass, velocity, and distance from the axis of rotation.

How is angular momentum calculated?

Angular momentum is calculated by multiplying the moment of inertia (a measure of the distribution of mass around the axis of rotation) by the angular velocity (the rate of change of angular displacement).

What is the conservation of angular momentum?

The conservation of angular momentum states that the total angular momentum of a system remains constant as long as there are no external torques acting on it. This means that the angular momentum of a system will remain the same unless there is an external force causing a change in rotation.

How does angular momentum relate to rotational motion?

Angular momentum is a crucial concept in rotational motion as it describes the rotational equivalent of linear momentum. Just as an object in motion will continue to move with constant velocity unless acted upon by a force, an object in rotational motion will continue to rotate with constant angular velocity unless acted upon by a torque.

What are some real-life examples of angular momentum?

Some examples of angular momentum in everyday life include spinning tops, spinning wheels on a bicycle, and the rotation of the Earth around its axis. It is also a fundamental concept in sports such as figure skating, where the skater's angular momentum helps them maintain their spin.

Similar threads

Back
Top