Hockey Puck
 

A hockey puck is simultaneously rotating and translating on an ice rink. Under what conditions will it stop rotating before translating, or vice-versa?

And since this is such a pedantic group, I'll state the following assumptions:

- The puck is perfectly rigid.
- All motion is constrained to the plane of the ice, which is perfectly flat and level
- The only forces present are Earth's gravity, the pressure from the ice that opposes gravity, and friction with the ice
- Mass and pressure are distributed uniformly over the puck's area
- Friction is ideal...for each surface element, the frictional force is a constant fraction of the force normal to the ice, in a direction opposite its velocity.


Once you find the answer, are there other interesting generalizations that can be made?


I'll try to refrain from commenting in the ensuing discussion until I post my solution. I found the answer fascinating when it occured to me, so I ended up exploring it to a greater depth.

Drew

Laziness versus interest
 

Now you've got ME suffering from this malaise.

Wouldn't a friction force density (shear stress) of -k[B]v[/B] be more tractable
than -k[B]v[/B]/v ?

David

[quote=davieddy;96156]Now you've got ME suffering from this malaise.

Wouldn't a friction force density (shear stress) of -k[B]v[/B] be more tractable
than -k[B]v[/B]/v ?

David[/quote]

So tractable I've done it in my head. Both translation velocity and
rotation rate decrease as e[sup](-kAt/M)[/sup] where A is area of puckand M is
mass.

Trivial (except I expect to Mally)

David

[QUOTE=davieddy;96180]So tractable I've done it in my head. Both translation velocity and
rotation rate decrease as e[sup](-kAt/M)[/sup] where A is area of puckand M is
mass.

Trivial (except I expect to Mally)

David[/QUOTE]
Friction is not proportional to speed. The puck will come to rest in finite time.

[QUOTE=drew;96185]Friction is not proportional to speed. The puck will come to rest in finite time.[/QUOTE]

And it will then be bestowed by Don Rickles.

[quote=drew;96185]Friction is not proportional to speed. The puck will come to rest in finite time.[/quote]

But the distance and angle travelled are of course both finite
in my case.

To resort to pedantry again, friction isn't independent of speed either:)

If I do get round to your problem, I hope the answer is as intriguing
as you suggest.

David

[quote=R.D. Silverman;96199]And it will then be bestowed by Don Rickles.[/quote]

Should us Brits have heard of this guy?

David

[QUOTE=davieddy;96238]To resort to pedantry again, friction isn't independent of speed either:)[/QUOTE]
That's true, but in the interest of mathematics, let's say it is. :smile:

It's still a much better model than a proportion of speed.

[quote=drew;96185]Friction is not proportional to speed. The puck will come to rest in finite time.[/quote]Indirectly invoking Zeno's Paradox, eh? :smile:

[quote=drew;96083]
Once you find the answer, are there other interesting generalizations that can be made?

Drew[/quote]

I can make a good generalization about the solution to my
frictional force. Namely the puck could be any shaped prism you want.

David

[QUOTE=davieddy;96244]I can make a good generalization about the solution to my
frictional force. Namely the puck could be any shaped prism you want.

David[/QUOTE]
Be my guest. :grin: My analysis involved a cylinder, but I don't believe it matters.