i = mrr vs i=mr experiment

[Tarsier79]

OK, got the experiment done, and happy with the results on the 4th pass...

A brief description first...(see image below)

Weights are placed on a low mass crossbar to change its inertia. The crossbar is attached to a hub(video head drum), which is driven, via pulleys with a weight falling from a fixed height. The bar is mounted horizontally to counter differences of acceleration due to imbalance and gravity.

If I=mr, half the weight at twice the radius will have the same inertia.

Commonly accepted fact, is that I=mrr, which, if this is the case, then the inertia of the half weight at double the radius will have an increased inertia.

[Tarsier79]

Here are photos of the setup for those not able to view the You Tube.

The 3rd photo "weights in balance" shows that the weights are in fact in a ratio of distance/weight of 1:2

For those with access to You Tube: http://www.youtube.com/watch?v=Y8Kf7d7-XLc

[Tarsier79]

Problems:

Originally, I used cotton thread for the pulleys, which was very low friction, but kept snapping. Knowing very little about fishing, or the imperial system, I purchased some 50 Lb line (a bit thick). Using the line increased friction significantly, but for the purpose of this experiment, providing the friction remains constant, it shouldn't affect the outcome.

The pulleys are mounted on tie-wire, which is simple, and it works, but adds to friction and variations in time. Also, the amount of force on the pulleys also increased friction, so the angle the line enters and leaves each pulley had to remain constant for consistent results

The rotating setup is sitting on some weights to elevate it. Unfortunately, when this moved, it caused another time difference (up to a second) when the line wasn't running straight between pulleys.

My reaction time starting and stopping the stopwatch.

You may notice some of these problems in the video:
http://www.youtube.com/watch?v=8pXROkhm5Dc
The results in this video are not the results below.


In the end, I finally got results I was happy all the above problems were minimised, and repeated sucessfully to within 39 ms at worst. (Even with errors, the results always showed the same conclusion)

For the dropping mass to fall 45cm:

no weights on bar: 3.25 seconds

2 x 0.48kg weights at 24.5 cm radius: 9.26 seconds

2 x 0.24kg weights at 49 cm radius: 12.90 seconds


I was hoping to be able to extrapolate from these results the approximate inertia of the bar and hub, and confirm by measurement, but due to the unknown, and noticable friction of my makeshift pulley system, the results probably won't be that accurate.

[Fletcher]

Well done Kaine.

Another way to check those results in a vertical environment [won't make any difference being vertical] with readily available materials [to most] is to use a bike wheel without the tyre - mount a cross member of wood so that it exactly bisects the wheel circumference - mark it like a ruler with zero at the center etc - place two masses at 1 unit distance from axle opposite each other & again 1/2 masses at 2 units distance from axle.

Use thin fishing nylon [braided if you really want] wrapped around the wheel groove - suspend a drive mass - start from the same height each time & record fall time - run multiple tests & average the results to get a good sample size.

Just like you've done.

Hey, wait, you could do that with a Blue48 & a bit of tinkering !

[Tarsier79]

Now that you say that, That would have been easier... Particularly since I have a few bike rims lying around. I guess sometimes you get the blinkers on, and can't see the most efficient way to prove something.

[pequaide]

We have a torque wrench here in the lab and it complies with the laws of levers. I collected some data from it. In order to get the same reading (as from the full length of the torque wrench) you must apply twice the force at half the distance along the wrench’s lever arm.

If you are going in the other direction the lever arm can apply half the force at twice the distance. Are you trying to show that it can only apply a fourth of the force at twice the distance. Doesn’t the laws of levers already defines what force is going to be applied at twice the distance along the lever arm.

How about measuring the forces at half and full length. Do you have a force gauge that you could just measure the force at the lengths in question?

The actual mass or inertia of an object will not change because of location.  So the only thing that can change is the force applied to the mass.  And the laws of levers defines the quantity of force that is applied along the length of the lever arm.

I notice that there is a certain amount of bar flexing in the half masses at full length, is it possible that some of the force is consumed in loading the bar before motion occurs. The flex is not so noticeable at half length and full mass.

You would also have a little more air resistance for the faster moving half masses.

[Tarsier79]

The bar is attached to a video head drum containing 2 bearings and is unaffected by this size load. more weight is actually applied to the bearings with the larger weight.

I don't think the wind resistance affects the outcome too much, as playing with the bar, it resists acceleration, and deceleration similarly.

Your observations with the torque wrench: This is force x radius. If you used a torque wrench to accelerate two wheels with a different mass distribution, then it would show the difference in force required to accelerate these at the same rate.


Inertia isn't a force.
http://www.youtube.com/watch?v=by-7kkAu2Pg

[pequaide]

79 quote:Inertia isn't a force.

No of course it isn't, but it is a resistance to a change in motion and motion is caused by force. Obviously an object placed on the end of a stick does not have a change in inertia. It is still just as massive and still just as hard to move. The only thing that can change is the quantity of force that you can apply to the object.

Or course a rim mass wheel is harder to rotate than a wheel with its mass distributed near the axial, but each individual gram has the same inertia. It is just harder to apply force to the grams outside near the rim than grams of mass near the axial. The gram don't magically have a change in inertia but their distance from the center just make it harder to apply force through the axial.

[Art]

.

Very nice experiment and build Tarsier . You're my kind of PMer !

In relation to " inertia isn't a force " however , my opinion is that a force is a force of course of course and is there for possible use .

Can you replace your horizontal bar with a long straight spring that you can mount sliding weights on and then compare results with those you obtained with the rigid bar ? .

All of the force s should be "conserved " by the spring so there should not be any difference . But in my opinion there will be if the results are similar to what happens to spring
mounted weights on a vertically rotating platform .

regards
Art

[Tarsier79]

Thanks, but the build was far from perfect, and just built to prove a point.

Im not sure what you are getting at with the springs, are you expecting the springs to give something to the rotation?

[Art]

No , not right away anyway : )

On second thoughts I realised my suggestion arose from my current obsession with flexible pivots/springs
and doesn’t relate very well to your original intention for the experiment , but since a good thread can lead anywhere I’ll keep going .

If you turn your rotary bar arrangement from horizontal to vertical and replace the bar with a very flexible rod or spring you basically end up with MT 18 but with only two arms instead of the four in the drawing and without the stops or anvils .

Since your system is driven by the weight in the Prime Mover jpg I think it should allow a reliable measurement with which to judge the effects of different shaped spring arms .

If one can measure the time required for the prime mover weight to drop and the speed of rotation of the rotary bar assembly ( by video possibly ? ) , then all you would need is Newton with an iPod to get a little closer to figuring out why Bessler ’s little Atavar looks so much like a spiral spring and why MT18 “tells more than shows� .

[Tarsier79]

You can't be sure that was a negative, or positive comment. I have built a similar design to MT18 before with only 2 arms. Below shows the problem, with the red arrow the intended direction of rotation.

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

The only thing that isn't immediately noticeable from B's drawing, is that the spring needs to taper to the weight, as there is noticeably more force on the spring the nearer the axis.

[Tarsier79]

Oops, its only just clicked.

A mass at double the radius rotating at the same rotational speed has 4x the inertia. The same mass has also 4x the KE due to mvv/2.

[broli]

I=mr^2 is not enough to prove peq's stuff. You still have conservation of angular momentum to deal with which he assumed to be invalid. I=mr^2 can hold but CoAM cannot while CoM can and you'd still be able to produce energy.

[pequaide]

I have been using the small 18 inch wheel to place about 1178 grams at about 18 inches and 1767 grams at 12 inches. The masses used are nuts bolts and big washers so the numbers are rough.

When using the same drive mass ; the distance traveled at the circumference is 36 inches in 3.06 second for the 1178 g at 18 inches, and 2.90 seconds for the 1767 g at 12 inches.

These are not great numbers but they much more strongly support mr and they do mr².

Your experiment '79' is moving to fast for mr².