Physics problem

engrymbiff · 2011-05-30 04:52:16

A particle with mass m lies on a circular plate at the distance R from the center point. At time t = 0 the plate begins rotating around a fixed vertical axis through the center. The angular velocity is given by dΘ / dt = αt, where α is a constant. Static friction rate between the plate and the particle is μ. At what time t = T does the particle remains at rest relative to the plate?

gAr · 2011-05-30 06:07:16

Hi engrymbiff,

??

Bob · 2011-05-30 06:20:22

hi engrymbiff

My first thought was simply to apply circular motion formulas. But ... the particle is accelerating along the tangent too, ... so I think the equations are more complicated.

When the speed is slow (just after the start) there will be no slipping. Friction with the surface is the only force in the plane of the plate and, as such, will have to provide the acceleration required. As the speed increases, a point will be reached when the force required to maintain the acceleration will become equal to and then exceed all that friction can provide. Then the particle will slip.

At what time t = T does the particle remains at rest relative to the plate?

I think this should read

At what time (t = T) does the particle cease to remain at rest relative to the plate.

normal reaction of plate on particle = mg

=> Max friction = μmg

let w = dΘ / dt = at .... tangential velocity, v = wr

acceleration towards centre

tangential acceleration

resultant acceleration is then given by

so at point of slipping

From this you can get an expression for T

I think

Bob

Last edited by Bob (2011-05-30 06:37:20)

gAr · 2011-05-30 15:12:50

Hi Bob,

Thanks, I think that's right.
I misunderstood the question.

Bob · 2011-05-30 19:44:44

hi gAr

Thanks for saying that. I was a bit worried about this one.

Back in my youth (you'll be too young to know about this) there was a thing called a wind up gramophone record player with bakerlite 78 rpm discs.

If you put something on the disc surface and wound up the clockwork, it gradually came up to speed, and at a certain point threw the object off the disc. Of course, you had to make sure you didn't use your Dad's favourite platter.

Nothing like a practical experiment to establish the rules.

My experiment to investigate standing waves in strings was even more weird.

Bob

gAr · 2011-05-30 20:05:06

Hi Bob,

I need to go through a physics text book again to verify the answer, I was finding physics problems tough when I was studying. But now, I'm very much interested!

Yes, I have heard about gramophones, but never seen one.

Lucky that today's computers can simulate most of the experiments!

Bob · 2011-05-31 00:54:03

hi gAr

I need to go through a physics text book again to verify the answer

I'd be grateful as I've never worked out this case before.

Lucky that today's computers can simulate most of the experiments!

hhmmm maybe.

A simulation is only as good as the programming that went into it. If the programmer hasn't factored in something, then the results won't be right. Not blaming the programmer of course. One can only work with existing kinowledge. I prefer the 'real world'; that's how it really is ... apparently, according to my perception ... which has been known to be wrong occasionally ... whoops I seem to be arguing on the wrong side!

Bob

gAr · 2011-06-01 23:22:11

Hi Bob,

I guess the solution is little simpler:

?

Bob · 2011-06-01 23:28:09

hi gAr

How are you today?

In post #3 I wrote:

My first thought was simply to apply circular motion formulas.

If you take out my factor for tangential motion, our formulas are the same.

But hang on. Who said you could ignore tangential motion?

This particle is moving in a circle but at an increasing speed => it is accelerating relative to the tangent => some of the friction must be the force to supply this acceleration.

Bob

Last edited by Bob (2011-06-01 23:37:33)

gAr · 2011-06-02 01:39:55

Hi Bob,

I'm fine. How are you?

And thanks, you cleared my doubts!

Bob · 2011-06-02 04:12:17

hi gAr

Congratulations on becoming a Supermember !

Ok, I'm glad I've dispelled your doubts. Now about mine ...........

Bob

gAr · 2011-06-02 04:23:37

Hi,

Gee, thanks! Didn't realize that was my 1000th post!

Are you saying you have doubts?!

Bob · 2011-06-02 04:53:09

hi gAr

A lifetime of conditioning on the receiving, then the other end, of the educational process, in various schools requires that I get a tick at the conclusion of my work. engrymbiff has gone silent. Are you convinced my maths is correct? Else: perhaps the Jedi Master will contribute.

Bob

gAr · 2011-06-02 05:01:49

Hi Bob,

The maths is correct, but I'll need to through more examples on nonuniform circular motions to comment overall.

I'll get back to this later!

Math Is Fun Forum

#1 2011-05-30 04:52:16

Physics problem

#2 2011-05-30 06:07:16

Re: Physics problem

#3 2011-05-30 06:20:22

Re: Physics problem

#4 2011-05-30 15:12:50

Re: Physics problem

#5 2011-05-30 19:44:44

Re: Physics problem

#6 2011-05-30 20:05:06

Re: Physics problem

#7 2011-05-31 00:54:03

Re: Physics problem

#8 2011-06-01 23:22:11

Re: Physics problem

#9 2011-06-01 23:28:09

Re: Physics problem

#10 2011-06-02 01:39:55

Re: Physics problem

#11 2011-06-02 04:12:17

Re: Physics problem

#12 2011-06-02 04:23:37

Re: Physics problem

#13 2011-06-02 04:53:09

Re: Physics problem

#14 2011-06-02 05:01:49

Re: Physics problem

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