Hockey Puck

[drew]

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

[davieddy]

Now you've got ME suffering from this malaise.

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

David

[davieddy]

Originally Posted by davieddy

Now you've got ME suffering from this malaise.

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

David

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

Trivial (except I expect to Mally)

David

[drew]

Originally Posted by davieddy

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

Trivial (except I expect to Mally)

David

Friction is not proportional to speed. The puck will come to rest in finite time.

[R.D. Silverman]

Originally Posted by drew

Friction is not proportional to speed. The puck will come to rest in finite time.

And it will then be bestowed by Don Rickles.

[davieddy]

Originally Posted by drew

Friction is not proportional to speed. The puck will come to rest in finite time.

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

[davieddy]

Originally Posted by R.D. Silverman

And it will then be bestowed by Don Rickles.

Should us Brits have heard of this guy?

David

[drew]

Originally Posted by davieddy

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

That's true, but in the interest of mathematics, let's say it is.

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

[cheesehead]

Originally Posted by drew

Friction is not proportional to speed. The puck will come to rest in finite time.

Indirectly invoking Zeno's Paradox, eh?

[davieddy]

Originally Posted by drew

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

Drew

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

David

[drew]

Originally Posted by davieddy

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

David

Be my guest. My analysis involved a cylinder, but I don't believe it matters.