Pendulum calculation

[Fletcher]

Ta ...

Unfortunately they show that when Cf's are generated & then the forces allowed to do WORK thru a ratchet & pawl or one-way clutch like analogue to accelerate the pendulum that still CoE is not violated.

That makes sense because a perfect pendulum could almost restore Pe & if the Cf's were additional Work Done Joules then CoE would be violated - instead the changing radius adversely effects the angular momentum [& speed] etc & the sums are balanced by the Work Done Potential of the Cf's equaling the Pe loss from that change in radius.

IMO, gravity & inertia are proven conservative in sim world.

P.S. Clay, what are the linear bearings you are using & where did you get them - I was looking for something like them a while back ?

[clay973]

Fletcher, I made the linear bearings from 12mm square aluminium tubing, 8 x skateboard bearings per unit, and some bolts. I was pretty happy with the way they worked out as you can adjust the play on them using the bolts. They also act as a weight as they each weigh 480g.

The rod is the same 12mm aluminium tubing I used to construct the linear bearings.

[Fletcher]

Can you post up a close up photo ?

[clay973]

Homemade linear bearings pics attached. Made from 12mm aluminium square tubing and 8 x skateboard bearings.

Amazing what you can build with a hacksaw, hand drill and a spanner :)

[Fletcher]

Nice - I built a linear bogie system similar to yours a few years ago except to run on round steel rod - I couldn't locate good free running small bearings so I used small plastic bushes with a flange end as wheels & spacers - worked a treat & were free moving.

[clay973]

Skateboard bearings are cool. They are cheap, easy to obtain and run well out of the box.

I've tried things like door rollers in the past but they are normally 'sticky" when you buy them and need to be run in.

[justsomeone]

Clay, Thanks for posting the pic. !!!! Very nice and might be just what I need. Greeny sent.

[pequaide]

Does the period of the pendulum remain the same as the bob masses move away from each other?

If the two bob masses move equal distances from the center of mass then the center of mass should remain in the same location. If the center of mass remains in the same location does the period remain constant?

[jim_mich]

Does the period of the pendulum remain the same as the bob masses move away from each other?

No, it does not. Though the center of mass remains the same the radius of gyration changes. Most formulas for pendulum swing rate assume a point-mass where all the mass is located in a tiny point, which in reality is impossible. In the real world some of the mass of the pendulum weight is farther from the pivot and some is closer. In the case being discussed where you have two weights that move apart this becomes extreme with some mass very close to the pivot and some mass very far away.

To calculate the swing period one needs to calculate the radius of gyration. Their are many formulas for this calculation, each based upon the shape of the object that is swinging/rotating around the pivot. In essence, the distance of each molecule of mass is squared. Then all the squared values are added together. Then the square root of the sum is found.

In the case of the two weights that move apart, square the radius distance of each weight, add the two together, and find the square root. This assumes the weights are equal. If they are not equal then you must multiply the mass of each weight by its squared distance, then sum the values, find the square root, then divide that by the sum of the two masses.

To get even more complex, to get a real accurate radius of gyration you should first calculate the radius of gyration of each weight and then use those two radii in the calculations of the combined two weight pendulum rather than the actual pendulum length.

Now, the reason why this all works... when a weight mass is farther from its pivot point then it must move faster to keep up with a weight that is closer to the same pivot point. The KE of a moving weight is 1/2 × M × V^2. If the weight is twice as far out from the pivot then its KE must be four times as much. It is the KE of the moving/swinging weight that determines its swing period.

Machinery's Handbook has an extensive listing of the different formulas for radius of gyration. But the book is rather expensive when new. Used books are just as good. I'm sure these formulas are on the internet somewhere.

See this thread which discusses this subject.

Formula for Radius of Gyration of a Sphere from my Machinery's Handbook...


Formula for Radius of Gyration of a parallelepiped from my Machinery's Handbook...


Maybe this post will make it clearer?

[Fletcher]

Jim_mich is correct - the sims show a longer period for the system where the bob masses are allowed to move apart as compared to the locked in place version - their CoM is the same but their Moment of Inertia & Center of Gyration is different.

He has explained it rather well as he usually does when it arises.

[justsomeone]

Fletcher, could you post a pic. of your linear bogie system? Thanks

[Fletcher]

Don't have one 'justsomeone' - it was about 7 or 8 years ago - I made it out of flange ended bushes butted together with an axle thru them, one set top & bottom - the flange wheels acted like a V pulley wheel top & bottom of rod [worked upside down as well], the flanges like a train wheel but on round rod track.

At the time, IIRC, I sort of used the ski gondola or flying fox as inspiration.

To stop it twisting you need two parallel rods or do as Clay did & use square rod with guide wheels each side - I made a smaller version like this as well.

Today you can get good linear bearings from the net or scavenged out of printers etc - anything that has a carriage component - for more robust uses you need to build your own though you can also buy heavy load ones - they are very free moving i.e. low rolling resistance.

[justsomeone]

How well do bronze bushings work on a threaded bolt or rod?

[Fletcher]

Fine if there is not to much load or friction - use oil or lithium grease rather than run them dry - I used plastic bushes from an engineering supplier because they are made of teflon like material that doesn't need lubricating & has low friction coefficient.

P.S. no bushes work well on the threaded portion - I assumed you meant the threaded part for a nut - use the zinc bolts & not galvanized or hard steel.

[rlortie]

Fletcher,

I believe there is a good chance that the plastic with Teflon type material is called 'UHMW' We used a lot of it when I was working for USACE.

And yes it makes for great bearing material, radial or liniear, easy to machine and drill using low speed so as not to overheat it.

Ultra High Molecular Weight Polyethylene is an extremely high abrasion resistant material. The molecular weights range between 3.1 to 5.67 million.

UHMW sheet and rod resembles other polyethylene's in superficial characteristics such as texture, color, stiffness, weight and general appearance, but
UHMW is superior in physical and mechanical strength.

UHMW will not encourage growth of bacteria or fungus, is self-lubricating, and it meets FDA requirements for direct food contact. It also
meets USDA requirements in specific applications.

EDIT: here is a good link comparing UHMW to metals when used for moving parts.

http://en.wikipedia.org/wiki/Ultra-high ... lyethylene