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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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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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.
Factors that affect the moment of inertia:
The moment of inertia is dependent on some factors, they are
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=∑miri2
Where, ri represents the perpendicular distance between the axis and its particle which contains the mass of mi.
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 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 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 | lbmft2 | lbmin2 |
kgm2 | 1 | 1×107 | 2.37×10 | 3.42×103 |
gcm2 | 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 |
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:
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
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