Calculating Moment of Inertia: What Does 'r' Refer To?

AI Thread Summary
In calculating the moment of inertia, 'r' refers to the distance from the axis of rotation to the specific point on the body being considered. For point masses, this distance is crucial as it directly affects the torque required to rotate the object. The confusion arises when considering rigid bodies, where the moment of inertia must account for all point masses within the body. To accurately compute this for a 2D game, one must consider the distribution of mass and potentially sum the contributions of individual points or pixels. Understanding this concept is essential for effective physics simulation in game development.
Eeduh
Messages
14
Reaction score
0
Hi,

I'm trying to teach myself some physics (dynamics in this case) and there's something I don't really get. It's how to calculate the moment of inertia.
I know the standard formula is I = m*r^2 for point masses, and I = (1/3)*m*r^2 for rigid bodies with equally divided mass, which is the case I'm interested in (I'm working on some 2d game, that's why).

Now can someone tell me what the 'r' is really referring to? Some lectures speak of the radius of the body, but I think that would be silly because then it would be the same for every point of rotation.

Is it then the distance from the point of rotation to the center of mass? This seems kind of logical, because the further away the point of rotation is from the center of mass, the more torque it'll require to rotate the object. But this would also mean that when the point of rotation is the same as the center of mass (which will be the case in many situations), moment of inertia would be 0 for r = 0, which would mean the object is infinitely easy to rotate. Makes no sense either.

Then what is r referring to? I hope someone can give me the answer.:rolleyes:
 
Last edited:
Physics news on Phys.org
In the equation you give, r refers to the distance from the axis of rotation.
 
Allright thanks, that's at least one step in the right direction. But the distance from the axis of rotation to what? CM? Because there's a problem with that which I've allready described in my first post..
 
The distance from the axis of rotation to the point on the body that you are considering.

If you're considering a point mass, as you say in the first part of your first post, then r will be the distance from the mass to the axis which you are rotating the mass about.
 
Hmm I still don't really get it.. perhaps I should read some more on the subject. Thanks anyway.
 
Yeah I get it now but there remains a problem. For a rigid body, you theoretically have to sum up all the point moments of inertia. But how am I going to approach this then? For a 2d rigid body in a game, this would mean dividing the mass by the amount of pixels the object is built from, calculation the point moment of inertia for each pixel and summing it up again? There must be a better and more accurate way. please help?:confused:
 
Thread 'Minimum mass of a block'
Here we know that if block B is going to move up or just be at the verge of moving up ##Mg \sin \theta ## will act downwards and maximum static friction will act downwards ## \mu Mg \cos \theta ## Now what im confused by is how will we know " how quickly" block B reaches its maximum static friction value without any numbers, the suggested solution says that when block A is at its maximum extension, then block B will start to move up but with a certain set of values couldn't block A reach...
TL;DR Summary: Find Electric field due to charges between 2 parallel infinite planes using Gauss law at any point Here's the diagram. We have a uniform p (rho) density of charges between 2 infinite planes in the cartesian coordinates system. I used a cube of thickness a that spans from z=-a/2 to z=a/2 as a Gaussian surface, each side of the cube has area A. I know that the field depends only on z since there is translational invariance in x and y directions because the planes are...
Thread 'Calculation of Tensile Forces in Piston-Type Water-Lifting Devices at Elevated Locations'
Figure 1 Overall Structure Diagram Figure 2: Top view of the piston when it is cylindrical A circular opening is created at a height of 5 meters above the water surface. Inside this opening is a sleeve-type piston with a cross-sectional area of 1 square meter. The piston is pulled to the right at a constant speed. The pulling force is(Figure 2): F = ρshg = 1000 × 1 × 5 × 10 = 50,000 N. Figure 3: Modifying the structure to incorporate a fixed internal piston When I modify the piston...
Back
Top