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Radius of Gyration given Time Period of Rolling 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{[g] \cdot G m \cdot {(\frac{T}{2} \cdot π)}^{2}}

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

Radius of Gyration given Time Period of Rolling Example

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

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

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

29388.0334 = \sqrt{9.8066 \cdot 330 \cdot {(\frac{10.4}{2} \cdot 3.1416)}^{2}}

29388.0334mm = \sqrt{9.8066m/s² \cdot 330mm \cdot {(\frac{10.4s}{2} \cdot 3.1416)}^{2}}

29388.0334 = \sqrt{9.8066 \cdot 330 \cdot {(\frac{10.4}{2} \cdot 3.1416)}^{2}}

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Radius of Gyration given Time Period of Rolling Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

K g = \sqrt{[g] \cdot 330mm \cdot {(\frac{10.4s}{2} \cdot π)}^{2}}

Next Step Substitute values of Constants

∴

K g = \sqrt{9.8066m/s² \cdot 330mm \cdot {(\frac{10.4s}{2} \cdot 3.1416)}^{2}}

Next Step Convert Units

∴

K g = \sqrt{9.8066m/s² \cdot 0.33m \cdot {(\frac{10.4s}{2} \cdot 3.1416)}^{2}}

Next Step Prepare to Evaluate

∴

K g = \sqrt{9.8066 \cdot 0.33 \cdot {(\frac{10.4}{2} \cdot 3.1416)}^{2}}

Next Step Evaluate

∴

K g = 29.3880333526878m

Next Step Convert to Output's Unit

∴

K g = 29388.0333526878mm

LAST Step Rounding Answer

∴

K g = 29388.0334mm

Radius of Gyration given Time Period of Rolling Formula Elements

Variables

Constants

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: mm

Note: Value should be greater than 0.

Formulas to find Radius of Gyration

Metacentric Height

Metacentric Height is defined as the vertical distance between the center of gravity of a body and metacenter of that body.

Symbol: G_m

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Metacentric Height

Time Period of Rolling

Time Period of Rolling is the time taken by an object to return to its upright position while it is rolling.

Symbol: T

Measurement: TimeUnit: s

Note: Value can be positive or negative.

Formulas to find Time Period of Rolling

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 Hydrostatic Fluid category

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F y = ρ l \cdot Q \cdot (- V 2 \cdot \sin (θ) - P 2 \cdot A 2 \cdot \sin (θ))

Go Force Acting in x Direction in Momentum Equation

F x = ρ l \cdot Q \cdot (V 1 - V 2 \cdot \cos (θ)) + P 1 \cdot A 1 - (P 2 \cdot A 2 \cdot \cos (θ))

Go Fluid Dynamic or Shear Viscosity Formula

μ = \frac{F a \cdot r}{A \cdot P s}

Go Center of Gravity

G = \frac{I}{V o \cdot (B + M)}

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

Radius of Gyration given Time Period of Rolling evaluator uses Radius of Gyration = sqrt([g]*Metacentric Height*(Time Period of Rolling/2*pi)^2) to evaluate 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 evaluate Radius of Gyration given Time Period of Rolling using this online evaluator? To use this online evaluator for Radius of Gyration given Time Period of Rolling, enter Metacentric Height (G_m) & Time Period of Rolling (T) and hit the calculate button.

FAQs on Radius of Gyration given Time Period of Rolling

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

The formula of Radius of Gyration given Time Period of Rolling is expressed as Radius of Gyration = sqrt([g]*Metacentric Height*(Time Period of Rolling/2*pi)^2). Here is an example- 2.9E+7 = sqrt([g]*0.33*(10.4/2*pi)^2).

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

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

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

No, the Radius of Gyration given Time Period of Rolling, measured in Length cannot be negative.

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

Radius of Gyration given Time Period of Rolling is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Radius of Gyration given Time Period of Rolling can be measured.

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