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Radius of Gyration of Body given Time Period Formula

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The Radius of Gyration of Body 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{T}{2 \cdot π})}^{2}) \cdot ([g] \cdot GM)}

k_G - Radius of Gyration of Body?T - Time Period of Rolling?GM - Metacentric Height?[g] - Gravitational acceleration on Earth?π - Archimedes' constant?

Radius of Gyration of Body given Time Period Example

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Here is how the Radius of Gyration of Body given Time Period equation looks like with Values.

Here is how the Radius of Gyration of Body given Time Period equation looks like with Units.

Here is how the Radius of Gyration of Body given Time Period equation looks like.

0.1039 = \sqrt{({(\frac{5.38}{2 \cdot 3.1416})}^{2}) \cdot (9.8066 \cdot 0.0015)}

0.1039m = \sqrt{({(\frac{5.38s}{2 \cdot 3.1416})}^{2}) \cdot (9.8066m/s² \cdot 0.0015m)}

0.1039 = \sqrt{({(\frac{5.38}{2 \cdot 3.1416})}^{2}) \cdot (9.8066 \cdot 0.0015)}

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Radius of Gyration of Body given Time Period Solution

Follow our step by step solution on how to calculate Radius of Gyration of Body given Time Period?

FIRST Step Consider the formula

k G = \sqrt{({(\frac{T}{2 \cdot π})}^{2}) \cdot ([g] \cdot GM)}

Next Step Substitute values of Variables

∴

k G = \sqrt{({(\frac{5.38s}{2 \cdot π})}^{2}) \cdot ([g] \cdot 0.0015m)}

Next Step Substitute values of Constants

∴

k G = \sqrt{({(\frac{5.38s}{2 \cdot 3.1416})}^{2}) \cdot (9.8066m/s² \cdot 0.0015m)}

Next Step Prepare to Evaluate

∴

k G = \sqrt{({(\frac{5.38}{2 \cdot 3.1416})}^{2}) \cdot (9.8066 \cdot 0.0015)}

Next Step Evaluate

∴

k G = 0.103850448059422m

LAST Step Rounding Answer

∴

k G = 0.1039m

Radius of Gyration of Body given Time Period Formula Elements

Variables

Constants

Functions

Radius of Gyration of Body

The Radius of Gyration of Body 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 of Body

Time Period of Rolling

Time Period of Rolling is the time taken by a wave to complete one oscillation.

Symbol: T

Measurement: TimeUnit: s

Note: Value can be positive or negative.

Formulas to find Time Period of Rolling

Metacentric Height

Metacentric Height is the vertical distance between the center of buoyance of the body and center of gravity.where B stands for center of buoyancy and G stands for center of gravity.

Symbol: GM

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Metacentric Height

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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 Time Period of Transverse Oscillation of a Floating Body category

Go Time Period of One Complete Oscillations

T = 2 \cdot π \cdot {(\frac{{k G}^{2}}{[g] \cdot GM})}^{\frac{1}{2}}

How to Evaluate Radius of Gyration of Body given Time Period?

Radius of Gyration of Body given Time Period evaluator uses Radius of Gyration of Body = sqrt(((Time Period of Rolling/(2*pi))^2)*([g]*Metacentric Height)) to evaluate the Radius of Gyration of Body, Radius of Gyration of Body given Time Period is body about axis of rotation is defined as radial distance to point which would have moment of inertia same as body's actual distribution of mass, if total mass of body were concentrated there. Radius of Gyration of Body is denoted by k_G symbol.

How to evaluate Radius of Gyration of Body given Time Period using this online evaluator? To use this online evaluator for Radius of Gyration of Body given Time Period, enter Time Period of Rolling (T) & Metacentric Height (GM) and hit the calculate button.

FAQs on Radius of Gyration of Body given Time Period

What is the formula to find Radius of Gyration of Body given Time Period?

The formula of Radius of Gyration of Body given Time Period is expressed as Radius of Gyration of Body = sqrt(((Time Period of Rolling/(2*pi))^2)*([g]*Metacentric Height)). Here is an example- 0.10385 = sqrt(((5.38/(2*pi))^2)*([g]*0.0015)).

How to calculate Radius of Gyration of Body given Time Period?

With Time Period of Rolling (T) & Metacentric Height (GM) we can find Radius of Gyration of Body given Time Period using the formula - Radius of Gyration of Body = sqrt(((Time Period of Rolling/(2*pi))^2)*([g]*Metacentric Height)). This formula also uses Gravitational acceleration on Earth, Archimedes' constant and Square Root (sqrt) function(s).

Can the Radius of Gyration of Body given Time Period be negative?

Yes, the Radius of Gyration of Body given Time Period, measured in Length can be negative.

Which unit is used to measure Radius of Gyration of Body given Time Period?

Radius of Gyration of Body given Time Period 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 of Body given Time Period can be measured.

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Radius of Gyration of Body given Time Period Formula

Radius of Gyration of Body given Time Period Example

Radius of Gyration of Body given Time Period Solution

Radius of Gyration of Body given Time Period Formula Elements

Other formulas in Time Period of Transverse Oscillation of a Floating Body category

How to Evaluate Radius of Gyration of Body given Time Period?

FAQs on Radius of Gyration of Body given Time Period

Variable Name