| Topic: |
Science > Physics |
| User: |
"Wiredchop" |
| Date: |
28 Feb 2006 06:00:37 AM |
| Object: |
Conservation of momentum -specific case |
Hi everyone,
I'm struggling with a simple model I'm trying to create. It concerns
the momentum change in a ball/racket interaction, specifically tennis.
I know the mass of the ball and racket, the I value of the ball around
it's centre, and three I's around the COM of the racket according to
three commonly used local axes.
What I'm trying to do is balance the momentum of the system before and
after impact, my thoughts initally are, that the linear momentum of the
COM and ball before and after impact will be conserved, but I'm
struggling to conserve angular momentum.
I know the angular velocities of the ball and racket before and after
impact in every direction. I'm thinking that angular momentum can be
conserved about the COM of the racket according to the rackets local
angular velocities and the balls linear momentum at its impact point on
the racket face according to L = r x p (r is also known). What is
really confusing me, is how does this angular momentum relate to the
angular momentum or spin of the ball. I know the spin around the centre
of the ball itself, but how is this related to the angular momentum of
the racket? Is it conserved seperately or can it be related somehow?
To be honest the angular momentum from the spin of the ball is very
small, and may be disregarded and still achieve a good result, but it
would be nice to relate certain momentum components to spin generation
etc.
I read a post on angular momentum from a few years back that went near
400 posts, it helped a little but still didn't answer the spin
question.
Any help is GREATLY appreciated.
Thanks
Simon C
.
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| User: "Spaceman" |
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| Title: Re: Conservation of momentum -specific case |
28 Feb 2006 09:21:20 AM |
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"Wiredchop" <Wiredchop@hotmail.com> wrote in message
news:1141128037.620185.306310@i39g2000cwa.googlegroups.com...
Hi everyone,
I'm struggling with a simple model I'm trying to create. It concerns
the momentum change in a ball/racket interaction, specifically tennis.
I know the mass of the ball and racket, the I value of the ball around
it's centre, and three I's around the COM of the racket according to
three commonly used local axes.
What I'm trying to do is balance the momentum of the system before and
after impact, my thoughts initally are, that the linear momentum of the
COM and ball before and after impact will be conserved, but I'm
struggling to conserve angular momentum.
I know the angular velocities of the ball and racket before and after
impact in every direction. I'm thinking that angular momentum can be
conserved about the COM of the racket according to the rackets local
angular velocities and the balls linear momentum at its impact point on
the racket face according to L = r x p (r is also known). What is
really confusing me, is how does this angular momentum relate to the
angular momentum or spin of the ball. I know the spin around the centre
of the ball itself, but how is this related to the angular momentum of
the racket? Is it conserved seperately or can it be related somehow?
To be honest the angular momentum from the spin of the ball is very
small, and may be disregarded and still achieve a good result, but it
would be nice to relate certain momentum components to spin generation
etc.
I read a post on angular momentum from a few years back that went near
400 posts, it helped a little but still didn't answer the spin
question.
Any help is GREATLY appreciated.
Sounds like you need to look up stuff on rotational kinetic energy.
:)
.
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| User: "Randy Poe" |
|
| Title: Re: Conservation of momentum -specific case |
28 Feb 2006 09:16:41 AM |
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Wiredchop wrote:
Hi everyone,
I'm struggling with a simple model I'm trying to create. It concerns
the momentum change in a ball/racket interaction, specifically tennis.
I know the mass of the ball and racket, the I value of the ball around
it's centre, and three I's around the COM of the racket according to
three commonly used local axes.
What I'm trying to do is balance the momentum of the system before and
after impact,
There's a human body involved as well. In any such interaction
involving striking a ball, you're taught to "follow through"
for maximum effect. You'd have to model what that means
carefully.
my thoughts initally are, that the linear momentum of the
COM and ball before and after impact will be conserved, but I'm
struggling to conserve angular momentum.
No reason for conservation to be happening, as the arm
is there to provide additional energy. You aren't just
throwing the racket at the ball. You're still holding it at
the moment of impact.
Then there's the whole thing about the "sweet spot,", which
is the impact point that maximizes momentum transfer. As I
recall from playing tennis (badly) many years ago, if you
hit it anywhere else there is a significant amount of
vibration induced in the racket and your arm.
My first cut at this would be an elastic collision with an
infinite-mass object consisting of arm and racket.
- Randy
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| User: "tadchem" |
|
| Title: Re: Conservation of momentum -specific case |
28 Feb 2006 06:56:46 PM |
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Also, angular momentum depends on the selected axis.
If there were no player (i.e. if this were a mid-air collision between
a ball and a racquet) the preferred axis would pass through the center
of mass of both of them.
Throw in a player and the axis becomes indeterminate (somewhere betwee
the ground and the player's wrist, depending on style) and eenergy and
momentum are not conserved as both depend on the player as an outside
source.
Tom Davidson
Richmond, VA
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| User: "Wiredchop" |
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| Title: Re: Conservation of momentum -specific case |
01 Mar 2006 03:45:57 AM |
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Thanks for all the responses guys,
Firstly, I'm doing research on a lot of freely suspended rackets, and
so for the most part no players involved :-) Probably should have
mentioned this, will look into rotational kinetic energy thanks, was
just mostly unsure about referring the ball spin to a specific point or
axis, when the COM of the racket is used in every other case.
In terms of player interaction, momentum won't be conserved if the
player's involved but by monitoring trends in momentum transfer,
playing styles can be assessed.
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| User: "tadchem" |
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| Title: Re: Conservation of momentum -specific case |
01 Mar 2006 04:32:20 AM |
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Oops. Perhaps I should have made this a little more clear.
If there were no player (i.e. if this were a mid-air collision between
a ball and a racquet) the preferred axis for the angular momentum of
the system would pass through the center of mass of the system, defined
as both the ball and the racquet.
[I derived an expression once for the viscosity of gas mixtures based
(among other things) on the conservation of *angular* momentum in a
bi-molecular collision.]
Tom Davidson
Richmond, VA
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| User: "Sam Wormley" |
|
| Title: Re: Conservation of momentum -specific case |
28 Feb 2006 08:18:57 AM |
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Wiredchop wrote:
Hi everyone,
I'm struggling with a simple model I'm trying to create. It concerns
the momentum change in a ball/racket interaction, specifically tennis.
I know the mass of the ball and racket, the I value of the ball around
it's centre, and three I's around the COM of the racket according to
three commonly used local axes.
What I'm trying to do is balance the momentum of the system before and
after impact, my thoughts initally are, that the linear momentum of the
COM and ball before and after impact will be conserved, but I'm
struggling to conserve angular momentum.
I know the angular velocities of the ball and racket before and after
impact in every direction. I'm thinking that angular momentum can be
conserved about the COM of the racket according to the rackets local
angular velocities and the balls linear momentum at its impact point on
the racket face according to L = r x p (r is also known). What is
really confusing me, is how does this angular momentum relate to the
angular momentum or spin of the ball. I know the spin around the centre
of the ball itself, but how is this related to the angular momentum of
the racket? Is it conserved seperately or can it be related somehow?
To be honest the angular momentum from the spin of the ball is very
small, and may be disregarded and still achieve a good result, but it
would be nice to relate certain momentum components to spin generation
etc.
I read a post on angular momentum from a few years back that went near
400 posts, it helped a little but still didn't answer the spin
question.
Any help is GREATLY appreciated.
Thanks
Simon C
Some Resources: http://www.google.com/search?q=conservation+momentum+ball+racket
.
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| User: "Wiredchop" |
|
| Title: Re: Conservation of momentum -specific case |
28 Feb 2006 08:39:44 AM |
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Thanks, unfortunately I've got the book those guys wrote and it doesn't
solve this specific case, am working in Sports engineering and have
read quite a lot of the specific papers on the subject. Wanted the low
down from a physics based persepctive
Sam Wormley wrote:
Wiredchop wrote:
Hi everyone,
I'm struggling with a simple model I'm trying to create. It concerns
the momentum change in a ball/racket interaction, specifically tennis.
I know the mass of the ball and racket, the I value of the ball around
it's centre, and three I's around the COM of the racket according to
three commonly used local axes.
What I'm trying to do is balance the momentum of the system before and
after impact, my thoughts initally are, that the linear momentum of the
COM and ball before and after impact will be conserved, but I'm
struggling to conserve angular momentum.
I know the angular velocities of the ball and racket before and after
impact in every direction. I'm thinking that angular momentum can be
conserved about the COM of the racket according to the rackets local
angular velocities and the balls linear momentum at its impact point on
the racket face according to L = r x p (r is also known). What is
really confusing me, is how does this angular momentum relate to the
angular momentum or spin of the ball. I know the spin around the centre
of the ball itself, but how is this related to the angular momentum of
the racket? Is it conserved seperately or can it be related somehow?
To be honest the angular momentum from the spin of the ball is very
small, and may be disregarded and still achieve a good result, but it
would be nice to relate certain momentum components to spin generation
etc.
I read a post on angular momentum from a few years back that went near
400 posts, it helped a little but still didn't answer the spin
question.
Any help is GREATLY appreciated.
Thanks
Simon C
Some Resources: http://www.google.com/search?q=conservation+momentum+ball+racket
.
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