# What exactly is r in inertial equation I=mr^2?

Discussion in 'MCAT Study Question Q&A' started by m25, Sep 4, 2014.

1. ### m25

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So the general equation for inertia is I=mr^2

So the distance r represent the distance from the center of rotating axis to exactly what? Center of mass?

2. ### Cawolf 5+ Year Member

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The point particle of mass m.

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### m25

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So what if the mass has a ring-like shape? Would r be from the center of axis to just inside, outside, or right in the middle of the ring?

4. ### mehc012 Big Damn Hero 5+ Year Member

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In that case, technically, the moment of inertia for the entire object would be the sum of the moments of inertia for each point mass which composes the entire ring
∑ I1+I2+I3... = ∑ m1r1²+m2r2²+m3r3²...

Most physics books have a list of equations, somewhere in the rotational motion chapter, which detail the specific equations for finding the overall I of any given shape (assuming uniform density of the material the shape is made of).

These equations describe the sum of the moments of inertia for all point masses contained in the object.

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5. ### Cawolf 5+ Year Member

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That formula is specifically for a point mass rotating some distance r from the axis of rotation.

As @mehc012 said, continuous objects are a whole different beast - with integration required to solve for their moment of inertia. I would imagine any continuous object would have it's moment of inertia given on the MCAT.

6. ### mehc012 Big Damn Hero 5+ Year Member

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Or at the very least, an equation similar to those in the above images. My physics prof used to do this to us all the time!

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7. ### Cawolf 5+ Year Member

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Yah we had to solve a lot of those problems in physics also - crazy shapes with off center axis that required summing multiple integrals.

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### m25

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Ah, I see. So in the case of point mass, would the distance r be from the axis of rotation to the center of mass of the point mass? Or just outside of the point mass?

9. ### Cawolf 5+ Year Member

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Center of mass.

10. ### mehc012 Big Damn Hero 5+ Year Member

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The center of mass of a point mass...but by definition, a 'point mass' takes up only a single point in space, so r would be the distance to that point.

You can treat a larger mass as if it is a point mass existing at the center of mass of the larger object.

I know, it's nitpicky, but it is an important distinction.

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