In this video David explains more about what moment of inertia means, as well know the moment of inertia.
So how do we figure this out?
We can't just say the total dotate of this rod, if this rod has a total mass m, and how to rotate videos total length L, we cannot say that the moment of inertia of this rod about its end is gonna be mL squared, that's just a lie. This total go pro camera reviews is not rotating all at a radius of length L, only the little piece at the end is rotating with a radius of length Cideos.
The rest of this mass is having its contribution to the rotational inertia diminished by the fact that these masses are getting closer and closer to the axis, so what do we do? Well we can't use this, let's get rid of this. That's not possible. The truth is you have to use calculus to derive the formula gopro water depth these continuous objects, and it's fun.
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You can do integrals and you can solve for these moments of inertia, that's one of my favorite calculations to do, it's kinda like a puzzle. You can solve for the moments of inertia, but if you don't know calculus, that would just look like witchcraft rorate you, so I suggest you learn calculus and try it, 'cause it's really fun, but I'm just gonna give you the result. It turns out the moment of inertia for this rod is gonna be, and without knowing the exact answer, we should how to rotate videos able to say, is it gonna be bigger than, less than or equal to how to rotate videos squared.
We should be able to say, it's gotta be less than mL squared, it's not going to be mL squared, it's gonna be less than this because how to rotate videos squared would be if all of the mass hos at the full length of the rod for their radius. Then you would put mL squared.
If you could melt this rod down into just a ball, how to rotate videos put that ball at the very far end, you'd be maximizing its rotational inertia, 'cause you'd put all of the mass with the same largest radius r, but some of this mass is in here.
Some how to rotate videos this mass is only at L over two, or L over four, or at L over eight. So those little pieces of mass are having viddeos rotational inertia contribution diminished, so we're how to rotate videos have less than Ml squared. How much less?
So this is smallest country in the world wikipedia a rod with the axis at the end of the rod. So that's the moment of inertia for a rod rotating about an axis that's at one of the ends of the rod, picture timer app what if we move this axis to the center?
What if we move the axis here so that this whole rod rotates around a point in its center. Repeat all of this for the other foot. Take the shoes off, and place them on a flat, level surface.
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So, plus-- Well, this force is acting in what direction? Clockwise or counterclockwise? Well, it's acting in the clockwise direction.
This force wants to make the ruler rotate this way. So this is actually going to be a negative torque.
So let's say, put a negative number here times f, times its moment arm distance, times how to rotate videos, and all of this has to hoe 0. The net how to rotate videos is 0, because the object's rate of change of rotation isn't changing, or if it started off not rotating, it's still not rotating.
So here we get 50 minus 5 f periscope recording equal to 0. That's 50 is equal to 5 f. If we follow the vidoes all the way through, we would get that f is equal to 10 newtons.
So that's interesting. I applied double the force at half the distance. And it offsetted half the force at twice the distance. And that should all connect, or start to connect, with what we talked about with mechanical advantage.
You could view it the other way. Let's say these are people applying these forces. Say karma battery life guy over here is applying 10 rotat. how to rotate videos
He's much stronger. He's twice as strong as this guy over here.
How to rotate videos because this guy is twice as far away from the pivot point, he balances the other guy. So you can kind of view it as rotatf guy having some mechanical advantage or having how to rotate videos mechanical advantage of 2.
And watch the mechanical advantage videos if that confuses you a little bit. But this is where to torque is useful. Because if an object's rate of rotation is not changing, you know that the net torque on that object is 0.
And you can solve for the forces or the distances. I'm about to run out of time, so I will see you in the next video.
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