Radius of Gyration of Body given Time Period Calculator

✖Time Period of Rolling is the time taken by a wave to complete one oscillation.ⓘ Time Period of Rolling [T]			+10% -10%
✖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.ⓘ Metacentric Height [GM]			+10% -10%

✖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.ⓘ Radius of Gyration of Body given Time Period [k_G]

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Formula

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Radius of Gyration of Body given Time Period

Formula

`"k"_{"G"} = sqrt((("T"/(2*pi))^2)*("[g]"*"GM"))`

Example

`"0.10385m"=sqrt((("5.38s"/(2*pi))^2)*("[g]"*"0.0015m"))`

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Radius of Gyration of Body given Time Period Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Gyration of Body = sqrt(((Time Period of Rolling/(2*pi))^2)*([g]*Metacentric Height))
k_G = sqrt(((T/(2*pi))^2)*([g]*GM))
This formula uses 2 Constants, 1 Functions, 3 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sqrt(Number)

Variables Used

Radius of Gyration of Body - (Measured in Meter) - 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.
Time Period of Rolling - (Measured in Second) - Time Period of Rolling is the time taken by a wave to complete one oscillation.
Metacentric Height - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Time Period of Rolling: 5.38 Second --> 5.38 Second No Conversion Required
Metacentric Height: 0.0015 Meter --> 0.0015 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

k_G = sqrt(((T/(2*pi))^2)*([g]*GM)) --> sqrt(((5.38/(2*pi))^2)*([g]*0.0015))

Evaluating ... ...

k_G = 0.103850448059422

STEP 3: Convert Result to Output's Unit

0.103850448059422 Meter --> No Conversion Required

FINAL ANSWER

0.103850448059422 ≈ 0.10385 Meter <-- Radius of Gyration of Body

(Calculation completed in 00.004 seconds)

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Created by M Naveen

National Institute of Technology (NIT), Warangal

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National Institute of Technology Karnataka (NITK), Surathkal

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< 2 Time Period of Transverse Oscillation of a Floating Body Calculators

Radius of Gyration of Body given Time Period

Go Radius of Gyration of Body = sqrt(((Time Period of Rolling/(2*pi))^2)*([g]*Metacentric Height))

Time Period of One Complete Oscillations

Go Time Period of Rolling = 2*pi*(Radius of Gyration of Body^2/([g]*Metacentric Height))^(1/2)

Radius of Gyration of Body given Time Period Formula

Radius of Gyration of Body = sqrt(((Time Period of Rolling/(2*pi))^2)*([g]*Metacentric Height))
k_G = sqrt(((T/(2*pi))^2)*([g]*GM))

What is Acceleration due to Gravity?

Acceleration due to gravity is the acceleration gained by an object due to gravitational force. Its SI unit is m/s2. It has both magnitude and direction.

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

Radius of Gyration of Body given Time Period calculator uses Radius of Gyration of Body = sqrt(((Time Period of Rolling/(2*pi))^2)*([g]*Metacentric Height)) to calculate 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 calculate Radius of Gyration of Body given Time Period using this online calculator? To use this online calculator for Radius of Gyration of Body given Time Period, enter Time Period of Rolling (T) & Metacentric Height (GM) and hit the calculate button. Here is how the Radius of Gyration of Body given Time Period calculation can be explained with given input values -> 0.10385 = sqrt(((5.38/(2*pi))^2)*([g]*0.0015)).

FAQ

What is Radius of Gyration of Body given Time Period?

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 and is represented as k_G = sqrt(((T/(2*pi))^2)*([g]*GM)) or Radius of Gyration of Body = sqrt(((Time Period of Rolling/(2*pi))^2)*([g]*Metacentric Height)). Time Period of Rolling is the time taken by a wave to complete one oscillation & 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.

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

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 is calculated using Radius of Gyration of Body = sqrt(((Time Period of Rolling/(2*pi))^2)*([g]*Metacentric Height)). To calculate Radius of Gyration of Body given Time Period, you need Time Period of Rolling (T) & Metacentric Height (GM). With our tool, you need to enter the respective value for Time Period of Rolling & Metacentric Height and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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