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# Re: [Phys-L] angular momentum

The r vector is changing but the r x mv quantity is not.

Consider a 1 kg mass moving at 1 m/s along the line y = 1 in the xy plane. Suppose we want the angular momentum around the z-axis. As it passes through the y axis, the r vector is one unit long and it is perpendicular to the linear momentum vector. As the object continues along the line, the r vector gets longer but is no longer perpendicular to the linear momentum vector.

As when calculating torques, it may help to envision a "lever arm" -- the perpendicular distance between the "line of action" of the linear momentum and the axis around which the angular momentum is being calculated. Though the magnitude of the r vector steadily increases, that lever arm stays constant.

On 7/21/2014 2:38 PM, Paul Lulai wrote:
I am used to seeing and using...
L=r ×p = r × mv.
What happens when the object has:
v_y_ = +10
v_x_ = 0
And the original position of the object is (5,5) relative to my origin.
Then even though p is constant, the position vector r is constantly changing in both magnitude and direction. In this case, L is not constant.
No torques, no interactions with something outside of my system (the ball and my oddly chosen origin), and L is not conserved.
Why is that?
There seems to be some sort of a condition for the origin. I am not used to that.
Thanks again for the time help.
Paul.

.:. Sent from a touchscreen .:.
Paul Lulai

-------- Original message --------
From: treborsci@verizon.net
Date:07/21/2014 1:05 PM (GMT-06:00)
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] angular momentum

Consider the motion of a ball, free of all forces, to be the constant
velocity path: x=a (a constant), and y= vt (v is its constant speed).
Its angular momentum about the origin (0,0) is simply m*a*v, a constant in
time. In the same way, Its angular momentum about any fixed point is a
constant in time .

Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
treborsci@verizon.net
www.sciamanda.com<http://www.sciamanda.com>
-----Original Message-----
From: Paul Lulai
Sent: Monday, July 21, 2014 1:36 PM
To: Phys-L@Phys-L.org
Subject: [Phys-L] angular momentum

Hello.
I am finding I have some questions about conservation of angular momentum
that I hadn't considered in the past. If I am investigating the angular
momentum of a soccer ball about a point, is angular momentum only conserved
if the ball is orbiting about the center of a circular path or a foci of an
ellipse? Certainly a ball traveling directly west across a field does not
have its angular momentum conserved.
I am completely excluding the idea of impulse, torques, and isolated systems
at this point. I just found I haven't thought about this aspect before.
Thanks for your thoughts.
Paul.
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