Unit of Moment of Inertia - Definition, Unit, FAQs

Q: What is the Unit of mass moment of inertia?

The Unit of mass moment of inertia is given as kgm 2

Edited By Team Careers360 | Updated on Nov 12, 2024 11:22 PM IST

In physics, the moment of inertia is used to get the basic quantitative measurement of rotational inertia. The opposing act that is exhibited by a body against its rotational change about an axis, (this rotation might be caused internally or externally). It is also based on the mass distribution of the body with respect to the rotational axis specifically. Let us see about the moment of inertia units, the difference between the unit of moment of inertia of and SI unit of moment of force, different types of inertia units and learn about the SI unit of moment of inertia (SI unit of inertia).

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Unit of Moment of Inertia - Definition, Unit, FAQs

The SI unit of moment of inertia is given as kg m2 where kg is the unit of mass and m is the unit of length. Many confusions occur between the unit of moment of inertia and the 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.

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Moment of inertia Definition:

The moment of inertia of anybody or object is considered as the extensive property or an additive property of that body. The definition of the moment of inertia is given as the product of sectional mass and the square of the distance between the centroid of the section and the reference axis. It also gives the ratio of the total angular momentum of the object to its angular velocity with respect to its principle axis. I =L/ω , I represents the moment of inertia, L gives the angular momentum and ω gives the angular velocity. The other terms that describe the moment of inertia are rotational inertia, mass moment of inertia, second moment of mass, angular mass moment. It is known as the quantity that can determine the torque required for a desired angular acceleration about the axis of rotation. For a rigid composite system, the moment of inertia is taken as the sum of all the moments of inertia of the system. The value of torque required for the cause of angular acceleration has its proportionality with the moment of inertia of the body.

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Factors that affect the moment of inertia:

The moment of inertia is dependent on some factors, they are

The material density
Size and shape of the body
Rotational axis

Now, let us see how the moment of inertia works for the system of particles and rigid bodies.

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Moment of inertia for the system of particles:

For a system of particles, the moment of inertia can be written

I=∑m_ir_i²

Where, r_i represents the perpendicular distance between the axis and its particle which contains the mass of m_i.

Moment of inertia for rigid bodies:

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

moment of inertia of different objects is depicted

Moment of inertia for different objects:

Shapes	Moment of inertia
Solid cylinder or disc with the symmetric axis	I = 1/2 (MR²)
Hoop with the symmetric axis	I = MR²
Solid sphere	I = 2/5 (MR²)
Rod about centre	I = 1/12 (ML²)
Solid cylinder with central diameter	I = 1/2 (MR²) + 1/4 (MR²)
Hoop about diameter	I = 1/2 (MR²)
Thin spherical shell	I = 2/3 (MR²)
Rod about end	I = 1/3 (ML²)

What is the SI unit of moment of inertia?/ si unit of inertia class 9

SI unit of moment of inertia:

The SI unit of moment of inertia is given as kg m² where kg is the unit of mass and m is the unit of length.

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Other units of the moment of inertia:

There are some other units used to represent the moment of inertia in different formulae. They are listed below

The Unit of the moment of inertia of an area or area moment of inertia is given as mm⁴ or in⁴
The Unit of mass moment of inertia/mass moment of inertia units is given as kgm² or ft.ln.s²

The dimensional formula for the unit of moment of inertia is given as M¹L²T⁰

The value conversion between the different units of the moment of inertia:

Unit	kgm²	gcm²	lb_mft²	lb_min²
kgm²	1	1×10⁷	2.37×10	3.42×10³
gcm²	1×10^-7	1	2.37×10^-6	3.42×10^-4
lb_mft²	4.21×10^-2	4.21×10⁵	1	1.44×10²
lb_min²	2.93×10^-4	2.93×10³	6.94×10^-3	1

In this article, we read about Moment of inertia Definition, Factors that affect the moment of inertia, Moment of inertia for the system of particles, Moment of inertia for rigid bodies, Moment of inertia for different objects, SI unit of moment of inertia, Other units of the moment of inertia, The value conversion between the different units of the moment of inertia. Let us discuss some of the frequently asked questions and their answers related to the unit of moment of inertia from class 10, class 11 and class 12.

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NCERT Physics Notes:

Frequently Asked Questions (FAQs)

1. What is the Unit of mass moment of inertia?

The Unit of mass moment of inertia is given as kgm²

2. What is the unit of moment of inertia or what is the SI unit of inertia?

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.

3. Give the moment of inertia symbol:

The moment of inertia is represented by the symbol or letter ‘I’.

4. What is the unit of moment of inertia in the mks system?

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 .

5. State the SI unit of moment of force.

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.

6. Give the dimensional formula for the unit of moment of inertia.

The dimensional formula for the unit of moment of inertia is given as M¹L²T⁰.

7. What is the Moment of Inertia for rigid bodies?

I=∫ r² dm

8. Convert mm4 to m4?

1mm=10^-3m

mm⁴=10^-12m⁴

9. Convert cm4 to mm4?

1cm=10mm

cm⁴=10⁴mm⁴