Units of Moment of Inertia

Last Updated: April 24, 2024

Units of Moment of Inertia

What is Moment of Inertia?

Moment of Inertia, often denoted as 饾惣, is a measure of an object’s resistance to changes in its rotational motion. It quantifies how the mass of an object is distributed around its axis of rotation. Objects with larger moments of inertia require more torque to change their rotational motion, while objects with smaller moments of inertia are easier to rotate. The moment of inertia depends not only on the mass of the object but also on its shape and distribution of mass relative to the axis of rotation. It plays a crucial role in various mechanical and engineering applications, such as designing rotating machinery, analyzing the stability of structures, and understanding the behavior of rotating bodies in physics.

Formula of Moment of Inertia

饾惣 = 饾惪/

The formula represents the moment of inertia (饾惣) of an object rotating about an axis, where 饾惪 is the angular momentum and 饾湐 is the angular velocity. This formula relates the rotational inertia of an object to its angular momentum and angular velocity, providing insight into the object’s resistance to changes in its rotational motion.

What are the units of Moment of Inertia?

The units of moment of inertia depend on the specific formula used to calculate it and the units of its components. In general, the moment of inertia is expressed in units of kilogram meters squared (kg路m虏) or gram centimeters squared (g路cm虏). These units arise from the combination of mass units (kilograms or grams) and distance units (meters or centimeters) squared. The moment of inertia quantifies the rotational inertia of an object and represents a measure of its resistance to changes in its rotational motion. It is a fundamental concept in physics and engineering, essential for understanding the behavior of rotating objects and designing mechanical systems.

SI Unit of Moment of Inertia

SI unit of moment of inertia : (kg路m虏).

The SI (International System of Units) unit of moment of inertia is kilogram meter squared (kg路m虏). This unit combines the SI units for mass (kilogram) and distance (meter) squared, reflecting the rotational inertia of an object relative to its axis of rotation.

CGS Unit of Moment of Inertia

CGS unit of moment of inertia : (g路cm虏)

The CGS (Centimeter-Gram-Second) unit of moment of inertia is gram centimeter squared (g路cm虏). This unit combines the CGS units for mass (gram) and distance (centimeter) squared, providing a measure of rotational inertia relative to the axis of rotation in CGS-based calculations and analyses.

Examples of Moment of Inertia

1.Solid Cylinder (Axis along the center): The moment of inertia for a solid cylinder about its central axis is given by the formula I = 1/2 饾憖饾憛 , where 饾憖 is the mass and 饾憛 is the radius of the cylinder.

2.Hollow Cylinder (Axis along the center): For a hollow cylinder (like a pipe), the moment of inertia is 饾惣 = 饾憖饾憛 , assuming the mass is concentrated at the radius 饾憛 from the central axis.

3.Solid Sphere (Axis through the center): The moment of inertia for a solid sphere about any axis through its center is 饾惣 = 2/5 饾憖饾憛

4.Hollow Sphere (Axis through the center): For a hollow sphere, the moment of inertia is 饾惣=2/3 饾憖饾憛

5.Thin Rod (Axis through one end, perpendicular to length): If the axis is through one end of the rod, perpendicular to its length, the moment of inertia is 饾惣=1/3 饾憖饾惪虏

List of Units of Moment of Inertia

Unit SystemUnitSymbolDescription
SIKilogram-square meterkg路m虏The SI unit of moment of inertia.
CGSGram-centimeter squaredg路cm虏The CGS unit of moment of inertia.
ImperialSlug-square footslug路ft虏Used in the imperial system, less common in engineering.
EngineeringPound-square footlb路ft虏Commonly used in the United States for engineering.

Kilogram-square meter (kg路m虏)

This is the standard SI unit for moment of inertia, where the mass is in kilograms and the distance squared is in meters. It is predominantly used in scientific and engineering applications worldwide due to its straightforward relation to other SI units.

Gram-centimeter squared (g路cm虏)

Used in the CGS system, this unit measures moment of inertia where mass is in grams and distance squared is in centimeters. It is less commonly used today but still appears in some academic contexts and older literature.

Slug-square foot (slug路ft虏)

In the imperial system, particularly used in the United States, the slug-square foot is occasionally used in engineering contexts. The slug is the unit of mass, and feet are the units of distance.

Pound-square foot (lb路ft虏)

Also from the imperial system, this unit is more commonly encountered in engineering practices within the United States. It is particularly used in situations where the pound and foot are the standard units for mass and distance, respectively.

Conversion of Units of Moment of Inertia

Conversion of Units of Moment of Inertia
From UnitTo UnitConversion Factor
Kilogram-square meter (kg路m虏)Gram-centimeter squared (g路cm虏)1 kg路m虏 = 10,000,000 g路cm虏
Gram-centimeter squared (g路cm虏)Kilogram-square meter (kg路m虏)1 g路cm虏 = 0.0000001 kg路m虏
Slug-square foot (slug路ft虏)Pound-square foot (lb路ft虏)1 slug路ft虏 = 32.174 lb路ft虏
Pound-square foot (lb路ft虏)Slug-square foot (slug路ft虏)1 lb路ft虏 = 0.031081 slug路ft虏
Kilogram-square meter (kg路m虏)Pound-square foot (lb路ft虏)1 kg路m虏 鈮 23.73036 lb路ft虏
Pound-square foot (lb路ft虏)Kilogram-square meter (kg路m虏)1 lb路ft虏 鈮 0.04214 kg路m虏

From Kilogram-square Meter (kg路m虏) to Gram-centimeter Squared (g路cm虏)

1 kg路m虏 = 10,000,000 g路cm虏

This conversion is based on converting kilograms to grams (1 kg = 1000 g) and meters to centimeters (1 m = 100 cm), then squaring the distance conversion.

From Gram-centimeter Squared (g路cm虏) to Kilogram-square Meter (kg路m虏)

1 g路cm虏 = 0.0000001 kg路m虏

This conversion inversely scales down the mass from grams to kilograms and the squared distance from centimeters to meters.

From Slug-square Foot (slug路ft虏) to Pound-square Foot (lb路ft虏)

1 slug路ft虏 = 32.174 lb路ft虏

Since one slug is equal to 32.174 pounds (the gravitational constant in ft/s虏), this conversion accounts for the difference in mass units while keeping the distance in feet.

From Pound-square Foot (lb路ft虏) to Slug-square Foot (slug路ft虏)

1 lb路ft虏 = 0.031081 slug路ft虏

This conversion utilizes the reciprocal value of the gravitational constant to convert pound-mass units back to slugs, maintaining the square of feet for the moment of inertia.

From Kilogram-square Meter (kg路m虏) to Pound-square Foot (lb路ft虏)

1 kg路m虏 鈮 23.73036 lb路ft虏

This conversion combines the mass conversion from kilograms to pounds (1 kg = 2.20462 lbs) and the distance conversion from meters to feet (1 m = 3.28084 ft), then squares the distance.

From Pound-square foot (lb路ft虏) to Kilogram-square meter (kg路m虏)

1 lb路ft虏 鈮 0.04214 kg路m虏

This conversion combines the mass conversion from Pound-square foot to Kilogram-square root (1 lb路ft虏 鈮 0.04214 kg路m虏).

FAQ’s

What are the units of section moment of inertia?

The units of section moment of inertia are typically expressed as length to the fourth power, such as
饾憪饾憵4 or 饾憱饾憶4 in engineering contexts.

What is the unit of first area moment of inertia?

The unit of the first area moment of inertia is typically length cubed, such as 饾憪饾憵3, reflecting the product of area and distance.

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