equation for polar moment of inertia circle

Larger angular acceleration 'cause you're now dividingīy a smaller number. You've got a big denominator, you're gonna have a small value, that means this alpha is gonna be small, it's gonna be a smallĪngular acceleration, but if this moment of inertia were small, then it's gonna be easier to rotate, and you'll get a relatively

Rotational inertia is big, look it, this is in the denominator. We're dividing by the moment of inertia, we're dividingīy the rotational inertia because that means if this Is gonna be equal to the net torque dividedīy the moment of inertia, or the rotational inertia, In the angular version of Newton's second law, that says that the angular acceleration Know the moment of inertia is 'cause it'll let you determine how difficult it'll be toĪngularly accelerate something, and remember it shows up So that's what this number is good for, the reason why you wanna To be very difficult to try to get this thing accelerating, but if the moment of inertia is small, it should be very easy, relatively easy to get this thing angularly accelerating. System has a large moment of inertia, it's going In other words, how much something's going to resist being angularly accelerated, so being sped up in its

This moment of inertia is really just the rotational inertia. 'cause this is something that people get confused about a lot. Talk some more about the moment of inertia, You can also check that it would not matter if the distance wasn't squared - then your method would produce correct results. The result is clearly different, and shows you cannot just consider the mass of an object to be concentrated in one point (like you did when you averaged the distance). The total moment of inertia is just their sum (as we could see in the video): I = i1 + i2 + i3 = 0 + mL^2/4 + mL^2 = 5mL^2/4 = 5ML^2/12. The moment of intertia of the first point is i1 = 0 (as the distance from the axis is 0).

However, let's now consider these points separately. One is at the axis of rotation (like the left end of the rod), the third is at the distance L from the axis, and the second point lies exactly between them.Įach has a mass m, so the total mass is obviously M=3m and m = 1/3 M.įollowing your way of thinking, the mean distance from the axis of rotation is L/2 (equal to (0 + L/2 + L)/3), so the moment of inertia would be I am sure you will understand this when you learn calculus, but let me give you an example.Ĭonsider just 3 point masses for simplicity. If there was just L (not-squared), you would be right.

Equation for polar moment of inertia circle