Centrifugal Force Question

[mondrasek]

A friend of mine ;) has a question that I have been unable to answer so I thought I might pose it here:

Imagine a disk spinning in a horizontal plane. It can be driven by a fixed DC motor so that we can easily measure power. Similar to a direct drive record player. It is my understanding that the power consumed by the motor at a steady RPM will only be that necessary to overcome the losses due to friction, heat, etc.

Now lets place a single weight on the rim of the disk so that it is unbalanced. At the same RPM, is any additional power required to keep the disk spinning, assuming no increases in friction, heat, etc., due to the unbalanced load?

Thanks,

M.

[Bill_Mothershead]

Try a different experiment.

An astronaut in space gently starts a hula-hoop rotating/spinning.
There is no air friction or bearings so it spins forever.
It did, however, take a measurable amount of energy to
start it spinning.

Now duct tape a small mass somewhere on the hula-hoop.
It can be made to spin at the same rate but it wobbles about
a center of gravity that is not the center of the hoop.

It will still spin forever but it did take a little bit more energy
to START it spinning. Neither configuration requires additional
energy to keep it spinning.

[Fletcher]

My friend says, exactly Bill - the horizontal disk with eccentric load has more inertia therefore requires that bit extra energy to get it to rpm - assuming the losses are the same as the control [they are not exactly but for the exercise] it requires the same input to overcome those losses & maintain rpm, once at rpm.

In reality air drag will be greater & the eccentric mass will also have a Cf component creating some small amount of point loading on the opposite side of the bearing so the losses will be slightly larger & therefore the maintenance energy input greater.

[nicbordeaux]

Except that if the turntable is rotating very slightly off dead horizontal and that amount of "off" is tuned to the position/"weight" of the offset single weight, surpising things occur. I doubt that any compu sim is going to be able to handle this, but doing a load of trial and error experiments will show some "abnormal" occurences. Making these "occurences" predictable is another question. Except in the case of a driven turntable with constant power input, and freewheel ability. A stroboscope is a nice tool.

[Fletcher]

If you say so Nick - tilting the turntable requires a change in energy input to more pulse like i.e. on the down hill the eccentric weight gets a gravity assist as it looses Pe then at bdc momentum carries it uphill against the pull of gravity then a pulse input is required to get it back up & thru tdc - just my opinion's as always.

[mondrasek]

So far we all agree. But it continues...

With the same unbalanced disk arrangement we un-fix the motor mount. Instead, it is mounted on a linear slide so that it has one degree of freedom (side to side). Call that axis X. Y would be perpendicular to X in the same plane and Z the axis of our motor shaft.

As the mass of our disk, motor, slide, etc, approach a theoretical zero, the rotating weight should not translate at all in the X, but only back and forth in Y. The motor/slide would translate the same distance (disk diameter, or 2 x weight radius) back and forth in X. Please correct me if I've got anything wrong.

With these ideal conditions (as well as assuming no friction from the slide) again we have no increase in the power needed to keep the same RPM?

In reality, the motor, slide, and disk must have non-zero mass. So the weight would prescribe an oval path as the motor/slide does not fully translate the entire diameter distance along in X, right? Do we see a power increase requirement to maintain the same RPM for this case (still no slide friction)? If so, is the power increase linear or sinusoidal?

[Fletcher]

Well actually mondrasek, IIRC you use & are familiar with WM2D - you can turn off gravity & build a 2D vertical analogue of what you are proposing - use sliding pivots for x & y etc - attach a motor option [or torque] & measure the power input - graph it to see if it is a sine curve or whatever.

What you will be left with is the inertial effects & since the eccentric mass will be accelerated & then decelerated & that process reversed [oscillations] then I would suspect that changing the state/direction of linear motion would consume more energy than following a constant radius path for example - but I'm just guessing & there probably is no change in energy input in these ideal conditions ?!

EDIT:

http://www.besslerwheel.com/forum/downl ... er=user_id

I was looking for something similar [thought it was in Patrick's album] - I remember someone experimenting with shifting the hub/axle & levers - kind of related to what you are investigating it would seem.

I would say that path_finder would be able to build an animation of what you are suggesting, if he were willing & sees this thread - he has lots of intersting actions & some of them prescribe a similar operation, IINM.

[mondrasek]

Thanks Fletcher. I was unaware that WM2D might be useful in this case. I've only used it to investigate gravity wheel type scenarios and have not learned it's capabilities for evaluating torque/power input requirements for rotating systems. And from other posts here I realize there are many other features that I have never used.

I (mentally) figured out the answer to "my friend's" initial question shortly after posting here. But, as usual, that lead to more scenarios and questions to be considered. Currently that involves the translation/forces on the hub/axle of a rotating wheel in relation to an unbalanced/offset rim weight as you have somewhat surmised. I was intrigued to realise that a free spinning "wheel" that requires no input power (except to overcome frictional loses) could be described by one where the axle shifts side to side and a point on the wheel shifts equidistant but normal to that. Though it makes complete sense from a mathematical point of view, it is a fairly unique way of thinking about a wheel for me.

So a free spinning wheel can be described as two sine waves: One where the axel is translating/oscillating, and one where a point on the rim is translating/oscillating (both 90 degrees out of phase and at 90 degree angles), right?

[rlortie]

Not very popular now days although Wal-Mart still sells them. Back in the fifties and early 60's no sane girl would be caught dead without her hula-hoop

So a free spinning wheel can be described as two sine waves: One where the axel is translating/oscillating, and one where a point on the rim is translating/oscillating (both 90 degrees out of phase and at 90 degree angles), right?

Ralph

[mondrasek]

Of course, Ralph. But in the case of the hula-hoop, there is energy being imparted to hoop by the girl. So that energy is needed to overcome some sort of loss that we normally ignore in the "ideal" situation (without friction, air resistance, etc.). What are the non-ideal losses? (semi-rhetorical question - but something I would like to understand).

Also, in the hula-hoop example, the hoop is not rotating like a wheel around a central axle. It is fixed to an inner wheel: the girl's waist. So it does something similar to a "Spirograph" motion. I can't even fathom the dynamics involved there.

[nicbordeaux]

Also, in the hula-hoop example, the hoop is not rotating like a wheel around a central axle. It is fixed to an inner wheel: the girl's waist. So it does something similar to a "Spirograph" motion. I can't even fathom the dynamics involved there.

In the scenario you are describing with the woman's waist rotating, I don't think the "why" or "how" matter that much, you just need to lay back and enjoy it.

The dynamics ? Surely similar to having a small dia bicycle hub rotating at some speed, and resting upon that hub a rim with no spokes, it's a simple friction drive. The rims rotates. Unless your definition of dynamics is beyond my comprehension. Probably the case.

[mondrasek]

Surely similar to having a small dia bicycle hub rotating at some speed, and resting upon that hub a rim with no spokes, it's a simple friction drive.

Except that the small dia bicycle hub would not rotate. Instead it must move in a circular path. And the rim with no spokes also does not simply rest on that hub, but also moves in a circular path as well as rotating. It is those somewhat more complex movements and relationships that I would find difficulty with trying to describe. Or maybe it is as simple as you say and I just think it is more complex.

[nicbordeaux]

Only thing I can say is that I built a setup to test something silly. This was angle iron to edge of table, drilled on the "front" to accept a bike hub spindle. To said hub I affixed a centally drilled piece of alloy profile 80 cm long. Bit like a propellor. On each end of profile I had a weight, balanced setup. To this I have a stator bord, "behind". Planning to mount a alloy rim to the board as a way of fixing magnets and stuff, I had this rim resting upon stator board, and whilst happily spinning "propellor" to get an idea of decay behavior, rim fell off edge of stator board and fell onto middle of bicycle hub. Where, much to my amazement (don't take much to amaze me if it's mechanics or stuff like that) I saw the "propellor" happily spinning away, and the wheel rim rotating on spinning hub. Rims of the old types have labels on them, so this is why I noticed.

Probably irrelevant, but FWIW... because what happens in a vertical plane is perfectly transposable into a horizontal plane, just a question of F impulse at critical moment , and rpm. Second part of http://www.youtube.com/watch?v=182feHKEB7U

[mondrasek]

Well WM2D appears to have done a fine job. Here is a 1 meter diameter disk where the axle is free to slide side to side. The "weight" is the smaller circle on the rim. For this shot the weight is 100 kg and the disk and slide block are at .0001 kg. The disk is made to spin at 1 rad/sec. Motion is as expected: The weight moves up and down and the axle moves side to side. But the power curve of the motor is anything but what I expected. While the average power is zero, the curve shows a sinusoidal wave of positive and negative power at twice the frequency of rotation. This is the curve of one full rotation of the disk/weight from the shown start and stop position.