Moment of Inertia: A Fundamental Property of Rotating Objects

[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.

 

[aralbrec]

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.

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 + rω²a_pg + rα a_T 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.

 

[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)

 

[Basic_Physics]

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.

 

[D H]

moment of inertia is just the ratio between angular momentum and angular velocity (L = Iω)

Correct.

and between torque and angular acceleration (τ = Iα)

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.