## Calculating Rotational Kinetic Energy?

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EddieJ
Posts: 81
Joined: Sun Apr 08, 2018 2:11 pm
Location: Dorset

### Calculating Rotational Kinetic Energy?

How do we go about it? My maths is a bit basic, but I remember linear kinetic energy is

KE= 1/2 M x V ^2
M=Mass
V=Velocity

But I was trying to calculate better numbers for a spinning bar using rotational kinetic energy.
Does any numbers guru have advice on this?
Thanks!
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GeorgeR
Posts: 258
Joined: Sun Aug 28, 2016 9:53 pm
Location: Bath, Somerset

### Re: Calculating Rotational Kinetic Energy?

It's the same formula, but with mass replaced by "moment of inertia", and speed replaced by angular velocity....

Rotational KE = 1/2 * I * w^2
I = moment of inertia
w = angular velocity

Angular velocity is measured in radians per second. To convert from rpm, you need to divide by 60 (giving revs per second) and multiply by 6.28 (there are 2*Pi radians in a full revolution).

The moment of inertia is dependent on the size, shape, and weight of the rotating part, to calculate it you'll need a formula;
https://en.m.wikipedia.org/wiki/List_of ... of_inertia

As an example, for a uniform bar rotating around its centre, the moi is = 1/12 m*L^2
m = mass (weight) in kg
L = length (of the bar) in meters

Plug your numbers in and you should get a value in joules. For comparison my overhead bar spinner Vampire is roughly 90J, so if you're orders of magnitude away from that then you might want to check your calculations.
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EddieJ
Posts: 81
Joined: Sun Apr 08, 2018 2:11 pm
Location: Dorset

### Re: Calculating Rotational Kinetic Energy?

Thanks George, you are a robotics saint A bit of an estimate, but here is what i think is correct.

Motor KV is 2700KV on 11.1V - rounding down because that is no load values. So 2500 x 11 = 27500 RPM
27500 / 60 = 458 (rounding down) x 6.28 = 2876
so W = 2876

MOI is bringing tears to my eyes >.< going to call the bar one solid mass as well. Until i figure out how to work out a composite bar. The bar i have has 30g of the 46g weight on the tips, with the middle being light nylon. Mass is 0.046kg L is 0.146m
so
1/12 x 0.046 x 0.146 ^2
0.000980536‬ / 12 = I

1/2*I *W^2
8,271,376‬ * 0.000980536‬ /24 = 337.93 J

Seems a bit high, perhaps I messed up. To work out the composite bar, if i calculated each elements J using the fusion360 MOI calculations (...not sure what all these values it gives are) then added them together, it should give a more accurate KE result? Bots:
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GeorgeR
Posts: 258
Joined: Sun Aug 28, 2016 9:53 pm
Location: Bath, Somerset

### Re: Calculating Rotational Kinetic Energy?

Looks like you've run the numbers correctly - Vampire's only running a 2300kv motor on a 2s lipo, and the bar is less than half the weight of yours, so the total energy is going to be a fair bit less.

I do suspect the real energy will turn out to be less than you've currently calculated though, for two reasons. Firstly, the bar is quite thick, so drag might cut the rpm a fair bit. Secondly, the bar is heavily asymmetric - this reduces the relative moi because the heavy counterweight is close to the pivot.

As you suggested, you'll need to use fusion to get accurate results with a composite bar, but to make life easier I think you should be able to get it to calculate the moi of the whole bar as one assembly, rather than doing it all as separate parts. (But I'm no cad expert, so that might be wrong)

Whatever the final number turns out to be, there's no way it's going to be anything other than extremely powerful, I don't think many people will be too keen to face it!
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EddieJ
Posts: 81
Joined: Sun Apr 08, 2018 2:11 pm
Location: Dorset

### Re: Calculating Rotational Kinetic Energy?

Yea I think you are right, Im going to try and work out a better value for taking into account the multiple materials. Since some of the 9mm handguns are around that kind of J rating. Not sure if it's going to be a competition bot yet, or just something for whiteboards. Will have something more rugged for competing later on Thanks for the help George! Bots:
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