We dispay the speed of rotation of the wheels on the brick screen. We use the math blocks to do a proper calculations from rotation to radians per second. Knowing the speed, the radiuses and the mass of the wheels we find energy in Joules accumulated in the construction.

**# 117**- 29 Nov 2015
- 10:35

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### English

We did number of calculations and we went through the theoretical part of conserving energy into the construction that we built. Last we built an EV3 program that was showing on the display the speed of rotation of our motor. If I now start the program

what you can see is that the speed of rotation of our motor is about 960 degrees. Previously it was 800 but I suppose that the battery was not that charged and now because of the battery we can see that it is rotating faster. This is the speed of rotation of our motor in degrees per second . so it's about 960 degrees per second. Because we did a calculation we need actually the speed of rotation

in radians per second. Now I'll show you how to improve the program so that you can show the speed of rotation in radians per second.

This here is the program developed previously. It was a motor, we reset the rotation sensor, we start with the large motor, we waited for a second and we measure the number of degrees that it rotated and we displayed this value on the display of the brick.

and we are doing this in a loop for 20 times, so actually 20 seconds and this will show the speed of rotation for 1 second, the speed of rotation in degrees, the angular velocity. But we want to show this in radians per second. How can we do this? We must convert this value of degrees to radians. We'll take 1 mathematical block

and we can choose advanced and in the advanced tab we need the following.

These are the degrees per second, so we must delete these degrees per second on 360. So we divide,

a is divided by 360 degrees and the result from this is multiplied by 2 pi and pi is 3,14. So that's the formula for converting degrees per second to radians per second.

We take the result and we display it on our brick.

This here is the brick, let's start the program, we start the program, it starts rotating and the result is actually the radians per second. It's about 16,7 radians per second, that's the speed of rotation of our motor. Now I'll stop this and let's try to connect this motor to our construction. In our construction we have 3 wheels. We have the first, the second and the third wheels. Let's try to rotate them with the motor.

We have here the axle for rotation. What will happen now is that the motor will input some power to the system. Because of the motor the wheels will start rotating and they'll start rotating faster and faster and more energy will be accumulated. Let's transfer the brick right here so that you can also see it and I'll now start the program.

You can see that the construction is rotating faster and faster.

The maximum speed that we reach is about 8 radians per second. So when we have the 3 wheels and we are trying to rotate these 3 wheels with the motor. The maximum speed that we reached was about 8 radians and this is the speed of the whole system. The motor is inputting a speed with 8 radians and we can calculate 8 by 25 it's about 200 radians per second, the speed of rotating of the 3 wheels. The conclusion here is that this motor has a finite power.

When there are no wheels attached to it, it rotates with 16 rad/s but when there are wheels attached to it, it rotates with about 8 rad/s. How much energy is accumulated here, in this construction when it is rotating with 8 radians per second? Let's do the calculation. Now let's do the calculations again. We have the mass of the 3 wheels and it's about 0,12 kg, we also have the angular velocity of our motor and it was about 8 rad/s. From there we can derive the speed, the angular velocity of the wheels, because there is gear system that increases the speed and actually the angular velocity is 25 times larger than the one on the motor. So it's 25 times 8, so the wheels are turning with 200 rad/s. From there we know the radii, I made a mistake in the previous videos. I was referring to the radii but I was using the values of the diameters. I'll fix this mistake now, we have the diameter of the wheel, the outer diameter that is 0,07 meters, we have the inner diameter that is 0,049 m.

From there we can get the radii, so the outer radii is 0,07 divided by 2 and the inner radius is 0,049 divided by 2

So we have the 2 radii, now the inertia moment from the previous video you know it was one half of the mass multiplied by the sum of the square of the 2 radii.

That's the moment of inertia. Then for the energy it is pretty straight forward. The formula is from the previous video. We get one half of the inertia moment multiplied by the square of the angular velocity. And we get about 2,2 joules. This is actually the energy that we have accumulated in our construction 2,19 J. Approximately of course, we've done many assumptions here but the principle is the same. Now what can we do with this energy? Can we use it, for example, to lift something or to power a light bulb or to drive a car. These are questions that we would answer in some of the next videos and we'll add a small task on this video for converting and finding different accumulated energy in different constructions. Just to give you a hint for now. If we have a light bulb that is, let's say, 30 W then you can power this light bulb for about 80 milliseconds. This energy will be enough to power this light bulb for 80 milliseconds. Check out the next videos, leave a comment below and we welcome you to build other resources on how the physics in the LEGO constructions work. I hope that the formulas were not that difficult. We tried to keep them minimal with only the formula for the energy and then deriving the rest from there.