0
$\begingroup$

I have undertaken a project where I need to design a brake system for a miniature locomotive. To test the effective of the brakes I have decided to create a rig where the brake system is attached to a flywheel which is spun to a certain angular speed in order to simulate the momentum of the locomotive as if it was on a track. I don't have a track available which is why I am doing this.

The mass of the locomotive is 800KG and assumed to be travelling at a const velocity of 4.2 m/s therefore will possess a linear momentum of 3,360 kg.m/s and a linear kinetic energy of 7065J.

I would like to simulate this momentum in the form of a flywheel, in order to determine its dimensions I need to know how much angular momentum the flywheel needs.

I am not sure how I can correctly mathematically/physically be able to "convert" linear momentum into angular momentum. I know that these two quantities are independent which is why I am asking this question.

Where I have ended up so far:

The energy in an object has two components: linear K.E. (El) and rotation K.E.(Er) Et = El + Er

El = 0.5*m*(v^2) , Er = 0.5*I*w^2, Et = total energy where, 'v' is linear velocity, 'w' is angular speed and 'I' is moment if inertia.

If I assume the locomotive only has linear component: 7065J and I assume that the flywheel only has rotation component - can I assume it to have 7065J of energy.

I question myself whether a linear joule is the same as rotational joule.

Any comment is helpful - i can work on from a hint

$\endgroup$
  • $\begingroup$ This sounds like you need to apply dimensional analysis : dynamic similarity, kinematic similarity etc. $\endgroup$ – Solar Mike Nov 8 '17 at 10:22
1
$\begingroup$

Your fundamental assumptions are correct, but I would question the practicality of the system that you are suggesting for testing.

Even with a heavy flywheel at a large diameter, you would need to spin it to a very high rotational speed in order to store the 7065J of energy that you are trying to mimic. Unfortunately brake-force is not independent of the surface speeds, and other important effects such as overheating/longevity of the system may not be accurately modeled in this case.

I would recommend dimensional analysis to allow you to model the system at a smaller scale (see https://en.wikipedia.org/wiki/Buckingham_%CF%80_theorem and https://en.wikipedia.org/wiki/Similitude_(model))

$\endgroup$
0
$\begingroup$

To answer your question "whether a linear joule is the same as rotational joule"

They are both forms of energy that are considered equal when using the conservation of energy methods - which I believe is what you're trying to do.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.