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Radius of gyration given moment of inertia and area Formula

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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. Check FAQs

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

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

Radius of gyration given moment of inertia and area Example

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Here is how the Radius of gyration given moment of inertia and area equation looks like with Values.

Here is how the Radius of gyration given moment of inertia and area equation looks like with Units.

Here is how the Radius of gyration given moment of inertia and area equation looks like.

4.4294 = \sqrt{\frac{981}{50}}

4.4294m = \sqrt{\frac{981m⁴}{50m²}}

4.4294 = \sqrt{\frac{981}{50}}

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Radius of gyration given moment of inertia and area Solution

Follow our step by step solution on how to calculate Radius of gyration given moment of inertia and area?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

k G = \sqrt{\frac{981m⁴}{50m²}}

Next Step Prepare to Evaluate

∴

k G = \sqrt{\frac{981}{50}}

Next Step Evaluate

∴

k G = 4.42944691807002m

LAST Step Rounding Answer

∴

k G = 4.4294m

Radius of gyration given moment of inertia and area Formula Elements

Variables

Functions

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

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

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Mechanics and Statistics of Materials category

Go Moment of inertia given radius of gyration

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

Go Moment of inertia of circle about diametrical axis

I r = \frac{π \cdot d^{4}}{64}

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)})

How to Evaluate Radius of gyration given moment of inertia and area?

Radius of gyration given moment of inertia and area evaluator uses Radius of Gyration = sqrt(Rotational Inertia/Area of Cross-Section) to evaluate the Radius of Gyration, The Radius of gyration given moment of inertia and area formula is defined as the square root of ratio of moment of inertia to area. Radius of Gyration is denoted by k_G symbol.

How to evaluate Radius of gyration given moment of inertia and area using this online evaluator? To use this online evaluator for Radius of gyration given moment of inertia and area, enter Rotational Inertia (I_r) & Area of Cross-Section (A) and hit the calculate button.

FAQs on Radius of gyration given moment of inertia and area

What is the formula to find Radius of gyration given moment of inertia and area?

The formula of Radius of gyration given moment of inertia and area is expressed as Radius of Gyration = sqrt(Rotational Inertia/Area of Cross-Section). Here is an example- 0.43589 = sqrt(981/50).

How to calculate Radius of gyration given moment of inertia and area?

With Rotational Inertia (I_r) & Area of Cross-Section (A) we can find Radius of gyration given moment of inertia and area using the formula - Radius of Gyration = sqrt(Rotational Inertia/Area of Cross-Section). This formula also uses Square Root (sqrt) function(s).

Can the Radius of gyration given moment of inertia and area be negative?

Yes, the Radius of gyration given moment of inertia and area, measured in Length can be negative.

Which unit is used to measure Radius of gyration given moment of inertia and area?

Radius of gyration given moment of inertia and area is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Radius of gyration given moment of inertia and area can be measured.

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