Time Period of Rolling Calculator

✖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 [k_G]			+10% -10%
✖Acceleration due to Gravity is acceleration gained by an object because of gravitational force.ⓘ Acceleration due to Gravity [g]			+10% -10%
✖Metacentric height is defined as the vertical distance between the center of gravity of a body and metacenter of that body.ⓘ Metacentric Height [GM]			+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]

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Formula

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Time Period of Rolling

Formula

T = 2 \cdot π \cdot \sqrt{\frac{{k G}^{2}}{g \cdot GM}}

Example

4.916346 s = 2 \cdot π \cdot \sqrt{\frac{{3 m}^{2}}{9.8 m/s² \cdot 1.50 m}}

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Time Period of Rolling Solution

STEP 0: Pre-Calculation Summary

Formula Used

Time Period of Rolling = 2*pi*sqrt((Radius of Gyration^(2))/(Acceleration due to Gravity*Metacentric Height))
T = 2*pi*sqrt((k_G^(2))/(g*GM))
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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Radius of Gyration: 3 Meter --> 3 Meter No Conversion Required
Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required
Metacentric Height: 1.5 Meter --> 1.5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T = 2*pi*sqrt((k_G^(2))/(g*GM)) --> 2*pi*sqrt((3^(2))/(9.8*1.5))

Evaluating ... ...

T = 4.91634617961041

STEP 3: Convert Result to Output's Unit

4.91634617961041 Second --> No Conversion Required

FINAL ANSWER

4.91634617961041 ≈ 4.916346 Second <-- Time Period of Rolling

(Calculation completed in 00.004 seconds)

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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Time Period of Rolling Formula

Time Period of Rolling = 2*pi*sqrt((Radius of Gyration^(2))/(Acceleration due to Gravity*Metacentric Height))
T = 2*pi*sqrt((k_G^(2))/(g*GM))

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 Time Period of Rolling?

Time Period of Rolling calculator uses Time Period of Rolling = 2*pi*sqrt((Radius of Gyration^(2))/(Acceleration due to Gravity*Metacentric Height)) to calculate the Time Period of Rolling, Time period of Rolling is defined as the time taken by an object to return to its upright position while it is rolling. Time Period of Rolling is denoted by T symbol.

How to calculate Time Period of Rolling using this online calculator? To use this online calculator for Time Period of Rolling, enter Radius of Gyration (k_G), Acceleration due to Gravity (g) & Metacentric Height (GM) and hit the calculate button. Here is how the Time Period of Rolling calculation can be explained with given input values -> 4.916346 = 2*pi*sqrt((3^(2))/(9.8*1.5)).

FAQ

What is Time Period of Rolling?

Time period of Rolling is defined as the time taken by an object to return to its upright position while it is rolling and is represented as T = 2*pi*sqrt((k_G^(2))/(g*GM)) or Time Period of Rolling = 2*pi*sqrt((Radius of Gyration^(2))/(Acceleration due to Gravity*Metacentric Height)). 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 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.

How to calculate Time Period of Rolling?

Time period of Rolling is defined as the time taken by an object to return to its upright position while it is rolling is calculated using Time Period of Rolling = 2*pi*sqrt((Radius of Gyration^(2))/(Acceleration due to Gravity*Metacentric Height)). To calculate Time Period of Rolling, you need Radius of Gyration (k_G), Acceleration due to Gravity (g) & Metacentric Height (GM). With our tool, you need to enter the respective value for Radius of Gyration, Acceleration due to Gravity & 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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