# What is moment of inertia?

1. Nov 8, 2012

### benoconnell22

What is "moment of inertia?"

Just curious and I use it a lot but I am not entirely sure what it is. Call me an idiot but I need to know before my physics endeavors proceed.

2. Nov 8, 2012

### aralbrec

Re: What is "moment of inertia?"

It is resistance of a rigid body to angular acceleration (M=Iα), just like mass is resistance to linear acceleration (F=ma).

It is derived from F=ma. If you look at a rigid body rotating around its center of gravity, you can say each piece of the body has mass dm and experiences a force dF=Ap dm, where Ap = the total acceleration of that piece of the body. Because it is a rigid body, Ap = Ag + rω2apg + rα aT where Ag is the total acceleration of the center of gravity and the other components are angular acceleration and centripetal force since the only acceleration a piece of the rigid body can experience wrt to another piece is a rotation. If you then sum the moment of all those dF in the body around the centre of gravity, you end up with M=Iα. I can be a complicated thing so I've left out some inconvenient details.

Last edited: Nov 8, 2012
3. Nov 8, 2012

### tiny-tim

yes

moment of inertia is just the ratio between angular momentum and angular velocity (L = Iω), and between torque and angular acceleration (τ = Iα)

4. Nov 8, 2012

### Basic_Physics

Re: What is "moment of inertia?"

A torque, $\tau$, is needed to change the angular velocity of a rotating or stationary object. The effect of the torque on the body is measured by the rate of change of its angular velocity, $\alpha$, or its angular acceleration. These two are directly propotional:
$\alpha\propto\tau$ just like its linear equivalent a$\propto$F, but this is hindered by its rotational inertia, I, or moment of inertia. So $\alpha\propto\frac{1}{I}$ just like a$\propto\frac{1}{m}$. The moment of inertia quantifies rotational inertia in rotational motion - similar to how mass quantifies inertia in linear motion.

5. Nov 8, 2012

### D H

Staff Emeritus
Re: What is "moment of inertia?"

Correct.
This is incorrect in general. It is valid only in very special cases. High school and freshman physics classes typically address just those special cases where τ = Iα is valid, but they steer clear of the general case where this equation is invalid.