Radius of Gyration given Time Period of Rolling Solution

STEP 0: Pre-Calculation Summary
Formula Used
Radius of Gyration = sqrt(Acceleration Due to Gravity*Metacentric Height*(Time Period of Rolling/2*pi)^2)
kG = sqrt(g*GM*(T/2*pi)^2)
This formula uses 1 Constants, 1 Functions, 4 Variables
Constants Used
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.
Acceleration Due to Gravity - (Measured in Meter per Square Second) - Acceleration Due to Gravity is acceleration gained by an object because of gravitational force.
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
Acceleration Due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required
Metacentric Height: 33000 Millimeter --> 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
kG = sqrt(g*GM*(T/2*pi)^2) --> sqrt(9.8*33*(10.4/2*pi)^2)
Evaluating ... ...
kG = 293.780674844287
STEP 3: Convert Result to Output's Unit
293.780674844287 Meter -->293780.674844287 Millimeter (Check conversion here)
FINAL ANSWER
293780.674844287 293780.7 Millimeter <-- Radius of Gyration
(Calculation completed in 00.004 seconds)

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19 Hydrostatic Fluid Calculators

Force Acting in x Direction in Momentum Equation
Go Force in X-Direction = Density of Liquid*Discharge*(Velocity at Section 1-1-Velocity at Section 2-2*cos(Theta))+Pressure at Section 1*Cross-Sectional Area at Point 1-(Pressure at Section 2*Cross-Sectional Area at Point 2*cos(Theta))
Force Acting in y-Direction in Momentum Equation
Go Force in Y-Direction = Density of Liquid*Discharge*(-Velocity at Section 2-2*sin(Theta)-Pressure at Section 2*Cross-Sectional Area at Point 2*sin(Theta))
Experimental Determination of Metacentric height
Go Metacentric Height = (Movable Weight on Ship*Transverse Displacement)/((Movable Weight on Ship+Ship Weight)*tan(Angle of Tilt))
Radius of Gyration given Time Period of Rolling
Go Radius of Gyration = sqrt(Acceleration Due to Gravity*Metacentric Height*(Time Period of Rolling/2*pi)^2)
Fluid Dynamic or Shear Viscosity Formula
Go Dynamic Viscosity = (Applied Force*Distance between Two Masses)/(Area of Solid Plates*Peripheral Speed)
Moment of Inertia of Waterline Area using Metacentric Height
Go Moment of Inertia of Waterline Area = (Metacentric Height+Distance Between Point B and G)*Volume of Liquid Displaced by Body
Volume of Liquid Displaced given Metacentric Height
Go Volume of Liquid Displaced by Body = Moment of Inertia of Waterline Area/(Metacentric Height+Distance Between Point B and G)
Distance between Buoyancy Point and Center of Gravity given Metacenter Height
Go Distance Between Point B and G = Moment of Inertia of Waterline Area/Volume of Liquid Displaced by Body-Metacentric Height
Metacentric Height given Moment of Inertia
Go Metacentric Height = Moment of Inertia of Waterline Area/Volume of Liquid Displaced by Body-Distance Between Point B and G
Center of Gravity
Go Centre of Gravity = Moment of Inertia/(Volume of Object*(Centre of Buoyancy+Metacenter))
Center of Buoyancy
Go Centre of Buoyancy = Moment of Inertia/(Volume of Object*Centre of Gravity)-Metacenter
Metacenter
Go Metacenter = Moment of Inertia/(Volume of Object*Centre of Gravity)-Centre of Buoyancy
Theoretical Velocity for Pitot Tube
Go Theoretical Velocity = sqrt(2*Acceleration Due to Gravity*Dynamic Pressure Head)
Metacentric Height
Go Metacentric Height = Distance between Point B and M-Distance Between Point B and G
Volume of Submerged Object given Buoyancy Force
Go Volume of Object = Buoyancy Force/Specific Weight of Liquid
Buoyancy Force
Go Buoyancy Force = Specific Weight of Liquid*Volume of Object
Surface Tension given Surface Energy and Area
Go Surface Tension = (Surface Energy)/(Surface Area)
Surface Energy given Surface Tension
Go Surface Energy = Surface Tension*Surface Area
Surface Area given Surface Tension
Go Surface Area = Surface Energy/Surface Tension

Radius of Gyration given Time Period of Rolling Formula

Radius of Gyration = sqrt(Acceleration Due to Gravity*Metacentric Height*(Time Period of Rolling/2*pi)^2)
kG = sqrt(g*GM*(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(Acceleration Due to Gravity*Metacentric Height*(Time Period of Rolling/2*pi)^2) to calculate the Radius of Gyration, The Radius of Gyration given Time Period of Rolling formula is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass if the total mass of the body were concentrated there. Radius of Gyration is denoted by kG 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 Acceleration Due to Gravity (g), Metacentric Height (GM) & 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+8 = sqrt(9.8*33*(10.4/2*pi)^2).

FAQ

What is Radius of Gyration given Time Period of Rolling?
The Radius of Gyration given Time Period of Rolling formula is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass if the total mass of the body were concentrated there and is represented as kG = sqrt(g*GM*(T/2*pi)^2) or Radius of Gyration = sqrt(Acceleration Due to Gravity*Metacentric Height*(Time Period of Rolling/2*pi)^2). Acceleration Due to Gravity is acceleration gained by an object because of gravitational force, 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?
The Radius of Gyration given Time Period of Rolling formula is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass if the total mass of the body were concentrated there is calculated using Radius of Gyration = sqrt(Acceleration Due to Gravity*Metacentric Height*(Time Period of Rolling/2*pi)^2). To calculate Radius of Gyration given Time Period of Rolling, you need Acceleration Due to Gravity (g), Metacentric Height (GM) & Time Period of Rolling (T). With our tool, you need to enter the respective value for Acceleration Due to Gravity, 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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