Unit of Moment of Inertia - Definition, Unit, FAQs
Moment of inertia is a key concept in rotational motion that explains how objects resist changes in their rotation. It depends not only on the mass of a body but also on how that mass is distributed from the axis of rotation. The SI unit of moment of inertia is kg·m², also known as the moment of inertia unit or unit of inertia. Understanding these moment of inertia units and different inertia units is important for solving numerical problems accurately. A common example is a wheel and a solid disc of the same mass. The wheel is harder to start or stop because its mass lies farther from the axis. In this article, students will learn the SI unit of inertia, units for inertia, and real-life applications.
What is the SI Unit of Moment of Inertia?
The SI unit of moment of inertia is: $\mathrm{kg} \cdot \mathrm{~m}^2$
Moment of inertia is defined as the product of mass and the square of the distance from the axis of rotation. Since mass is measured in kilogram ( kg ) and distance in metre ( m ), its unit becomes $\mathbf{~} \mathbf{kg} \cdot \mathbf{m}^{\mathbf{2}}$.
The dimensional formula of moment of inertia is: $\left[M L^2\right]$
Thus, moment of inertia is expressed in kilogram metre squared $\mathbf{(} \mathbf{k g} \cdot \mathbf{m}^{\mathbf{2}}$ ) in the SI system.
Also read -
Moment of Inertia Units
The moment of inertia is of two types depending on its application in physics and engineering.
1. Area Moment of Inertia
The area moment of inertia is used in structural engineering to study bending of beams. It depends only on the geometry of the cross-section.
Its units are mm⁴ or in⁴.
2. Mass Moment of Inertia
The mass moment of inertia is used in rotational motion. It depends on the mass of the body and its distribution about the axis of rotation.
Its SI unit is kilogram metre squared (kg · m²), while in the FPS system it is ft · lb · s².
Moment of Inertia Explanation
Consider a wheel (ring) and a uniform disc, both having the same mass $M$ and rotating about the same axis.
It is observed that it is more difficult to start or stop the wheel than the disc. This is because the resistance to rotational motion depends on the moment of inertia, which is defined as:
$I=\sum m r^2$
where $m$ is the mass of each particle and $r$ is its distance from the axis of rotation.
Moment of Inertia of Rigid Body
| Rigid Body | Axis of Rotation | Moment of Inertia (I) |
| Thin Rod | About centre ( ⟂ to length) | $\frac{1}{12} M L^2$ |
| Thin Rod | About one end ( ⟂ to length) | $\frac{1}{3} M L^2$ |
| Ring | About centre ( ⟂ to plane) | $M R^2$ |
| Ring | About diameter | $\frac{1}{2} M R^2$ |
| Disc | About centre ( ⟂ to plane) | $\frac{1}{2} M R^2$ |
| Disc | About diameter | $\frac{1}{4} M R^2$ |
| Solid Cylinder | About its axis | $\frac{1}{2} M R^2$ |
| Hollow Cylinder | About its axis | $M R^2$ |
| Solid Sphere | About diameter | $\frac{2}{5} M R^2$ |
| Hollow Sphere | About diameter | $\frac{2}{3} M R^2$ |
Applications of Moment of Inertia
Moment of inertia is important in rotational motion as it determines the resistance of a body to changes in its rotation.
- Flywheels: Used in engines to maintain uniform speed.
- Vehicle Wheels: Lower moment of inertia helps in quick acceleration and braking.
- Sports: Athletes control speed by changing their moment of inertia (e.g., skaters).
- Doors: Require more effort to rotate due to mass being away from the axis.
- Engineering: Used in designing strong beams and structures.
- Machines: Helps in smooth operation of motors and turbines.
Also read :
- NCERT notes Class 11 Physics Chapter 7 System of Particles and Rotational motion
- NCERT Solutions for Class 11 Physics Chapter 7 System of Particles and Rotational motion
- NCERT Exemplar Class 11 Physics Solutions Chapter 7 System of Particles and Rotational motion
Also check-
- NCERT Exemplar Class 11th Physics Solutions
- NCERT Exemplar Class 12th Physics Solutions
- NCERT Exemplar Solutions for All Subjects
NCERT Physics Notes:
Frequently Asked Questions (FAQs)
The Unit of mass moment of inertia is given as kgm2
The moment of inertia is the product of sectional mass and the square of the distance between the centroid of the section and the reference axis. The SI unit of moment of inertia is kg m2 whereas the unit of moment of force is Nm, where N is the unit of force, m is the unit of length.
The moment of inertia is represented by the symbol or letter ‘I’.
The SI unit of moment of inertia and unit of moment of inertia in the MKS system is quite the same. The moment of inertia in the MKS system is given as k gm2 .
Many confusions occur between the unit of moment of inertia and unit of moment of force. The SI unit of moment of inertia is given as kg m2 whereas the unit of moment of force is Nm, where N is the unit of force, m is the unit of length.
The dimensional formula for the unit of moment of inertia is given as M1L2T0.
The moment of inertia for continuous mass distribution is given by the integral form. The system is considered to be divided into an infinitesimal element with mass dm and x will be the distance between the mass element and the axis of rotation. The moment of inertia for rigid bodies is given as
I=∫ r2 dm
1mm=10-3m
mm4=10-12m4
1cm=10mm
cm4=104mm4
