Radius of Gyration given Time Period of Rolling Calculator

✖Metacentric Height is defined as the vertical distance between the center of gravity of a body and metacenter of that body.ⓘ Metacentric Height [G_m]			+10% -10%
✖Time Period of Rolling is the time taken by an object to return to its upright position while it is rolling.ⓘ Time Period of Rolling [T]			+10% -10%

✖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.ⓘ Radius of Gyration given Time Period of Rolling [K_g]

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Radius of Gyration given Time Period of Rolling Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Gyration = sqrt([g]*Metacentric Height*(Time Period of Rolling/2*pi)^2)
K_g = sqrt([g]*G_m*(T/2*pi)^2)
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 - (Measured in Meter) - 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.
Metacentric Height - (Measured in Meter) - Metacentric Height is defined as the vertical distance between the center of gravity of a body and metacenter of that body.
Time Period of Rolling - (Measured in Second) - Time Period of Rolling is the time taken by an object to return to its upright position while it is rolling.

STEP 1: Convert Input(s) to Base Unit

Metacentric Height: 330 Millimeter --> 0.33 Meter (Check conversion here)
Time Period of Rolling: 10.4 Second --> 10.4 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

K_g = sqrt([g]*G_m*(T/2*pi)^2) --> sqrt([g]*0.33*(10.4/2*pi)^2)

Evaluating ... ...

K_g = 29.3880333526878

STEP 3: Convert Result to Output's Unit

29.3880333526878 Meter -->29388.0333526878 Millimeter (Check conversion here)

FINAL ANSWER

29388.0333526878 ≈ 29388.03 Millimeter <-- Radius of Gyration

(Calculation completed in 00.012 seconds)

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Center of Gravity

LaTeX Go Centre of Gravity = Moment of Inertia/(Volume of Object*(Centre of Buoyancy+Metacenter))

Radius of Gyration given Time Period of Rolling Formula

LaTeX Go

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

What is Timeperiod?

The time period is the time taken by a complete cycle of the wave to pass a point, Frequency is the number of complete cycle of waves passing a point in unit time. Frequency and time period are in a reciprocal relationship that can be expressed mathematically as T = 1/f or as f = 1/T.

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

Radius of Gyration given Time Period of Rolling calculator uses Radius of Gyration = sqrt([g]*Metacentric Height*(Time Period of Rolling/2*pi)^2) to calculate the Radius of Gyration, Radius of Gyration given Time Period of Rolling formula is defined as a measure of the distribution of the mass of an object or a system of objects rotating about a fixed axis, providing a way to describe the spread of the object's mass around its axis of rotation. Radius of Gyration is denoted by K_g symbol.

How to calculate Radius of Gyration given Time Period of Rolling using this online calculator? To use this online calculator for Radius of Gyration given Time Period of Rolling, enter Metacentric Height (G_m) & Time Period of Rolling (T) and hit the calculate button. Here is how the Radius of Gyration given Time Period of Rolling calculation can be explained with given input values -> 2.9E+7 = sqrt([g]*0.33*(10.4/2*pi)^2).

FAQ

What is Radius of Gyration given Time Period of Rolling?

Radius of Gyration given Time Period of Rolling formula is defined as a measure of the distribution of the mass of an object or a system of objects rotating about a fixed axis, providing a way to describe the spread of the object's mass around its axis of rotation and is represented as K_g = sqrt([g]*G_m*(T/2*pi)^2) or Radius of Gyration = sqrt([g]*Metacentric Height*(Time Period of Rolling/2*pi)^2). Metacentric Height is defined as the vertical distance between the center of gravity of a body and metacenter of that body & Time Period of Rolling is the time taken by an object to return to its upright position while it is rolling.

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

Radius of Gyration given Time Period of Rolling formula is defined as a measure of the distribution of the mass of an object or a system of objects rotating about a fixed axis, providing a way to describe the spread of the object's mass around its axis of rotation is calculated using Radius of Gyration = sqrt([g]*Metacentric Height*(Time Period of Rolling/2*pi)^2). To calculate Radius of Gyration given Time Period of Rolling, you need Metacentric Height (G_m) & Time Period of Rolling (T). With our tool, you need to enter the respective value for Metacentric Height & Time Period of Rolling 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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