Moment of inertia from a Physics point of view is basically a quantitative measure of the rotational inertia or the angular mass of a body. In simple terms, it is the opposition that the body exhibits to the change in rotation about an axis which may further be internal or external.
The moment of inertia (I) is mostly specified based on the distribution of mass in the body with respect to the axis of rotation.
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Moment of Inertia Units
Following are the types of moment of inertia units along with their formula:
- Area moment of inertia: mm4 or in4
- Mass moment of inertia: kg.m2 or ft.lb.s2
What is the SI Unit of Moment of Inertia?
The SI unit of moment of inertia is: kg.m2
To know about units of other quantities, click the link below:
Moment Of Inertia Of Rigid Body
Following are the moment of inertia for rigid objects:
| Rigid object | Moment of inertia |
| Solid cylinder | \(\begin{array}{l}I=\frac{1}{2}MR^{2}\end{array} \) |
| Solid cylinder central diameter | \(\begin{array}{l}I=\frac{1}{4}MR^{2}+\frac{1}{12}ML^{2}\end{array} \) |
| Rod about centre | \(\begin{array}{l}I=\frac{1}{12}ML^{2}\end{array} \) |
| Hoop about the symmetry axis | \(\begin{array}{l}I=MR\end{array} \) |
| Hoop about diameter | \(\begin{array}{l}I=\frac{1}{2}MR^{2}\end{array} \) |
| Thin spherical shell | \(\begin{array}{l}I=\frac{2}{3}MR^{2}\end{array} \) |
| Rod about end | \(\begin{array}{l}I=\frac{1}{3}ML^{2}\end{array} \) |
Conversion Between Moment of Inertia Units
Following is the table with the moment of inertia unit conversion:
| Unit | kg. m2 | g.cm2 | lbmft2 | lbmin2 |
| kg. m2 | 1 | 1×107 | 2.37×10 | 3.42×103 |
| g.cm2 | 1×10-7 | 1 | 2.37×10-6 | 3.42×10-4 |
| lbmft2 | 4.21×10-2 | 4.21×105 | 1 | 1.44×102 |
| lbmin2 | 2.93×10-4 | 2.93×103 | 6.94×10-3 | 1 |
Example of Moment of Inertia
Consider a wheel and a uniform disc, both having the same mass rotating about the same axis. If you may have observed, it is difficult to start or stop the wheel than it is to start or stop the uniform disc.
Why is this so, in spite of both the objects having the same mass?
This is because the force required to stop a rotating object is directly proportional to the product of the mass and the square of the distance from the axis of rotation to the particles that make up the body.
Mathematically, it is represented as F = mr2
In this case, the mr2 of the wheel > mr2 of the disc.
This explains why it is difficult to rotate a wheel compared to a uniform disc.
Frequently Asked Questions – FAQs
State true or false: The moment of inertia is primarily specified based on the distribution of mass in the body with respect to the axis of rotation.
What is the moment of inertia unit (SI)?
What is the moment of inertia of a thin spherical shell
What are the factors on which moment of inertia depends?
What are the types of moment of inertia units?
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