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Moment of inertia given radius of gyration Formula

GoMoment of inertia of circle about diametrical axis Formula

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Rotational Inertia is a physical property of an object that quantifies its resistance to rotational motion about a particular axis. Check FAQs

I r = A \cdot {k G}^{2}

I_r - Rotational Inertia?A - Area of Cross-Section?k_G - Radius of Gyration?

Moment of inertia given radius of gyration Example

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Here is how the Moment of inertia given radius of gyration equation looks like with Values.

Here is how the Moment of inertia given radius of gyration equation looks like with Units.

Here is how the Moment of inertia given radius of gyration equation looks like.

981.245 = 50 \cdot {4.43}^{2}

981.245m⁴ = 50m² \cdot {4.43m}^{2}

981.245 = 50 \cdot {4.43}^{2}

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Moment of inertia given radius of gyration Solution

Follow our step by step solution on how to calculate Moment of inertia given radius of gyration?

FIRST Step Consider the formula

I r = A \cdot {k G}^{2}

Next Step Substitute values of Variables

∴

I r = 50m² \cdot {4.43m}^{2}

Next Step Prepare to Evaluate

∴

I r = 50 \cdot {4.43}^{2}

LAST Step Evaluate

∴

I r = 981.245m⁴

Moment of inertia given radius of gyration Formula Elements

Variables

Rotational Inertia

Rotational Inertia is a physical property of an object that quantifies its resistance to rotational motion about a particular axis.

Symbol: I_r

Measurement: Second Moment of AreaUnit: m⁴

Note: Value can be positive or negative.

Formulas to find Rotational Inertia

Area of Cross-Section

The Area of Cross-Section is the enclosed surface area, product of length and breadth.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Cross-Section

Radius of Gyration

The Radius of Gyration or gyradius is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass.

Symbol: k_G

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Radius of Gyration

Other Formulas to find Rotational Inertia

Go Moment of inertia of circle about diametrical axis

I r = \frac{π \cdot d^{4}}{64}

Other formulas in Mechanics and Statistics of Materials category

Go Radius of gyration given moment of inertia and area

k G = \sqrt{\frac{I r}{A}}

Go Resultant of Two Forces acting on Particle with Angle

R par = \sqrt{{F 1}^{2} + 2 \cdot F 1 \cdot F 2 \cdot \cos (θ) + {F 2}^{2}}

Go Inclination of Resultant of Two Forces Acting on Particle

α = a \tan (\frac{F 2 \cdot \sin (θ)}{F 1 + F 2 \cdot \cos (θ)})

Go Resultant of Two Forces Acting on Particle at 90 Degrees

R = \sqrt{{F 1}^{2} + {F 2}^{2}}

How to Evaluate Moment of inertia given radius of gyration?

Moment of inertia given radius of gyration evaluator uses Rotational Inertia = Area of Cross-Section*Radius of Gyration^2 to evaluate the Rotational Inertia, The Moment of inertia given radius of gyration formula is defined as the product of the area of cross-section and the square of the radius of gyration. Rotational Inertia is denoted by I_r symbol.

How to evaluate Moment of inertia given radius of gyration using this online evaluator? To use this online evaluator for Moment of inertia given radius of gyration, enter Area of Cross-Section (A) & Radius of Gyration (k_G) and hit the calculate button.

FAQs on Moment of inertia given radius of gyration

What is the formula to find Moment of inertia given radius of gyration?

The formula of Moment of inertia given radius of gyration is expressed as Rotational Inertia = Area of Cross-Section*Radius of Gyration^2. Here is an example- 981.245 = 50*4.43^2.

How to calculate Moment of inertia given radius of gyration?

With Area of Cross-Section (A) & Radius of Gyration (k_G) we can find Moment of inertia given radius of gyration using the formula - Rotational Inertia = Area of Cross-Section*Radius of Gyration^2.

What are the other ways to Calculate Rotational Inertia?

Here are the different ways to Calculate Rotational Inertia-

Rotational Inertia=(pi*Diameter of Circle^4)/64

Can the Moment of inertia given radius of gyration be negative?

Yes, the Moment of inertia given radius of gyration, measured in Second Moment of Area can be negative.

Which unit is used to measure Moment of inertia given radius of gyration?

Moment of inertia given radius of gyration is usually measured using the Meter⁴[m⁴] for Second Moment of Area. Centimeter⁴[m⁴], Millimeter⁴[m⁴] are the few other units in which Moment of inertia given radius of gyration can be measured.

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