We got the speed of rotations of the motor in Radians per second. Let's calculate the value for the speed of the whole system. We calculate that the wheels are rotating with 375 radians per second. Which is impressive and quite fast for this system. From this speed, knowing the inertia mass we can calculate how much energy is the system accumulating.
- # 116
- 22 Nov 2015
The shown problem is very valuable for different STEM classes. On the stand we have three wheels that contribute to the mass of the system. We calculate the energy for one of the wheels and then for two and for four. We can conduct different experiments with different masses and get the different energies.
More about gears you can learn at:
Previous video tutorials:
So previously we stopped here and we got the speed of rotation of our EV3 Lego Mindstorms Model in radians per second, so it's approximately 15 radians per second is the speed of rotation of the model. What's important to notice is that in our system in the construction, if you check out the instructions for building our experimental construction, you can see that there is a gear system. This gear system involves a large gear and a small gear. Then we have one more large gear wheel and a small gear wheel. These two gear wheels are connected on the same axle. We have the wheel that is actually accumulating energy here, and we have the motor...so this here is the motor.
Now the motor is rotating the gear wheel one, which is rotating gear wheel two, which is rotating gear wheel three, which is rotating gear wheel four which is rotating the wheel. This here is the wheel.
The ratios between this gear wheel allows us to increase the speed of rotation because this large gear wheel one, it has 40 teeth, and gear wheel two has 8 teeth. So 40 divided by 8 is actually 5. The ratio between the larger gear wheel and the smaller gear wheel is five. This means that for every rotation of this gear wheel one, the small one will rotate five times.
Below the video you can find a link to another video where we explain the rations between the different gear wheels with some experiments. But continuing in this video, we have the gear wheel. It is rotating one time, so this small gear wheel is rotating five times, which means that these gear wheels are rotating five times because they are on the same axle. This gear wheel is rotating 25 times. So for one rotation of the motor, we get 25 rotations of the wheel that is circulating energy. So it's 25 by 1.
Here we can calculate this now.
This means that if the omega of our motor is 15 radians per second, then omega of the wheel is actually equal to 15 multiplied by 25 which is 375. So the speed of rotation in radians per second for our wheel, Lego wheel, is 375 radians per second. Now let's calculate the energy. We know the speed, the angle of velocity, we know the mass, we know the two radiuses, and we know the inertia moment. So we can can calculate the energy of our system.
Let's do this.
So mass is equal to, again, 0.04 kilograms. This is in kilograms. And radius outer is equal to 0.07 meters, radius inner is is equal to 0.049 meters, and omega is equal 375 radians per second. From there, we know that the inertia moment is equal to one half of the mass multiplied by radius outer squared, plus radius inner squared. We get the inertia moment and we get the value of the inertia moment. Then we know that energy is actually one half of the inertia moment, multiplied by the square of the angular velocity. We get the energy of our wheel. The energy of accumulated within our wheel if this wheel is starting with 375 radians per second. And this here is in joules.
We have this for one wheel. For two wheels, it will basically be the same... I'll just copy this, and for two wheels, we will just double the mass. The mass will be 0.08 grams, and as you can see, the energy is about twice as much so it's about 20 joules. The first one was about 10. The second one was about 20. And we can continue this with adding more wheels and more wheels and we can accumulate more energy in our system. Now let's do a few experiments and see how much exactly is the theoretical part, and let's check if we can do some experiments to see the practical part and whether we can find a way to use this energy that's accumulated.