Radius 2 given Moment of Inertia Calculator

✖Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.ⓘ Moment of Inertia [I]			+10% -10%
✖Mass 1 is the quantity of matter in a body 1 regardless of its volume or of any forces acting on it.ⓘ Mass 1 [m₁]			+10% -10%
✖Radius of mass 1 is a distance of mass 1 from the center of mass.ⓘ Radius of Mass 1 [R₁]			+10% -10%
✖Mass 2 is the quantity of matter in a body 2 regardless of its volume or of any forces acting on it.ⓘ Mass 2 [m₂]			+10% -10%

✖Radius 2 given Moment of Inertia is a distance of mass 1 from the center of mass.ⓘ Radius 2 given Moment of Inertia [R_i2]

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Radius 2 given Moment of Inertia Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius 2 given Moment of Inertia = sqrt((Moment of Inertia-(Mass 1*Radius of Mass 1^2))/Mass 2)
R_i2 = sqrt((I-(m₁*R₁^2))/m₂)
This formula uses 1 Functions, 5 Variables

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 2 given Moment of Inertia - (Measured in Meter) - Radius 2 given Moment of Inertia is a distance of mass 1 from the center of mass.
Moment of Inertia - (Measured in Kilogram Square Meter) - Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.
Mass 1 - (Measured in Kilogram) - Mass 1 is the quantity of matter in a body 1 regardless of its volume or of any forces acting on it.
Radius of Mass 1 - (Measured in Meter) - Radius of mass 1 is a distance of mass 1 from the center of mass.
Mass 2 - (Measured in Kilogram) - Mass 2 is the quantity of matter in a body 2 regardless of its volume or of any forces acting on it.

STEP 1: Convert Input(s) to Base Unit

Moment of Inertia: 1.125 Kilogram Square Meter --> 1.125 Kilogram Square Meter No Conversion Required
Mass 1: 14 Kilogram --> 14 Kilogram No Conversion Required
Radius of Mass 1: 1.5 Centimeter --> 0.015 Meter (Check conversion here)
Mass 2: 16 Kilogram --> 16 Kilogram No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_i2 = sqrt((I-(m₁*R₁^2))/m₂) --> sqrt((1.125-(14*0.015^2))/16)

Evaluating ... ...

R_i2 = 0.264793551658646

STEP 3: Convert Result to Output's Unit

0.264793551658646 Meter -->26.4793551658646 Centimeter (Check conversion here)

FINAL ANSWER

26.4793551658646 ≈ 26.47936 Centimeter <-- Radius 2 given Moment of Inertia

(Calculation completed in 00.004 seconds)

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Home » Chemistry » Analytical chemistry » Molecular Spectroscopy » Rotational Spectroscopy » Reduced Mass and Radius of Diatomic Molecule » Radius 2 given Moment of Inertia

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Created by Nishant Sihag

Indian Institute of Technology (IIT), Delhi

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National Institute of Information Technology (NIIT), Neemrana

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< Reduced Mass and Radius of Diatomic Molecule Calculators

Mass 1 of Diatomic Molecule

LaTeX Go Mass 1 of Diatomic Molecule = Mass 2*Radius of Mass 2/Radius of Mass 1

Mass 2 of Diatomic Molecule

LaTeX Go Mass 2 of Diatomic Molecule = Mass 1*Radius of Mass 1/Radius of Mass 2

Radius 2 of Rotation

LaTeX Go Radius 1 given Rotational Frequency = Mass 1*Radius of Mass 1/Mass 2

Radius 1 of Rotation

LaTeX Go Radius 1 of Rotation = Mass 2*Radius of Mass 2/Mass 1

< Reduced Mass and Radius of Diatomic Molecule Calculators

Mass 2 given Moment of Inertia

LaTeX Go Mass 2 given Moment of Inertia = (Moment of Inertia-(Mass 1*Radius of Mass 1^2))/Radius of Mass 2^2

Mass 1 given Moment of Inertia

LaTeX Go Mass2 of object1 = (Moment of Inertia-(Mass 2*Radius of Mass 2^2))/Radius of Mass 1^2

Mass 1 of Diatomic Molecule

LaTeX Go Mass 1 of Diatomic Molecule = Mass 2*Radius of Mass 2/Radius of Mass 1

Mass 2 of Diatomic Molecule

LaTeX Go Mass 2 of Diatomic Molecule = Mass 1*Radius of Mass 1/Radius of Mass 2

Radius 2 given Moment of Inertia Formula

LaTeX Go

Radius 2 given Moment of Inertia = sqrt((Moment of Inertia-(Mass 1*Radius of Mass 1^2))/Mass 2)
R_i2 = sqrt((I-(m₁*R₁^2))/m₂)

How do we get radius 2 when moment of inertia is given ?

The total moment of inertia is the sum of the moments of inertia of the mass elements in the body. So for moment of inertia of mass 2, total moment of inertia is reduced by moment of inertia of mass 1. And this moment of inertia of mass 2 is divided by mass 2 to get square of radius 2. And then by applying square root, we obtain radius 2.

How to Calculate Radius 2 given Moment of Inertia?

Radius 2 given Moment of Inertia calculator uses Radius 2 given Moment of Inertia = sqrt((Moment of Inertia-(Mass 1*Radius of Mass 1^2))/Mass 2) to calculate the Radius 2 given Moment of Inertia, The Radius 2 given moment of inertia is basically a method to get Radius 2 from the formula of the moment of inertia. The total moment of inertia is the sum of the moments of inertia of the mass elements in the body. So for moment of inertia of mass 2, total moment of inertia is reduced by moment of inertia of mass 1. And thus, by the formula, Radius 2 is obtained. Radius 2 given Moment of Inertia is denoted by R_i2 symbol.

How to calculate Radius 2 given Moment of Inertia using this online calculator? To use this online calculator for Radius 2 given Moment of Inertia, enter Moment of Inertia (I), Mass 1 (m₁), Radius of Mass 1 (R₁) & Mass 2 (m₂) and hit the calculate button. Here is how the Radius 2 given Moment of Inertia calculation can be explained with given input values -> 2647.936 = sqrt((1.125-(14*0.015^2))/16).

FAQ

What is Radius 2 given Moment of Inertia?

The Radius 2 given moment of inertia is basically a method to get Radius 2 from the formula of the moment of inertia. The total moment of inertia is the sum of the moments of inertia of the mass elements in the body. So for moment of inertia of mass 2, total moment of inertia is reduced by moment of inertia of mass 1. And thus, by the formula, Radius 2 is obtained and is represented as R_i2 = sqrt((I-(m₁*R₁^2))/m₂) or Radius 2 given Moment of Inertia = sqrt((Moment of Inertia-(Mass 1*Radius of Mass 1^2))/Mass 2). Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis, Mass 1 is the quantity of matter in a body 1 regardless of its volume or of any forces acting on it, Radius of mass 1 is a distance of mass 1 from the center of mass & Mass 2 is the quantity of matter in a body 2 regardless of its volume or of any forces acting on it.

How to calculate Radius 2 given Moment of Inertia?

The Radius 2 given moment of inertia is basically a method to get Radius 2 from the formula of the moment of inertia. The total moment of inertia is the sum of the moments of inertia of the mass elements in the body. So for moment of inertia of mass 2, total moment of inertia is reduced by moment of inertia of mass 1. And thus, by the formula, Radius 2 is obtained is calculated using Radius 2 given Moment of Inertia = sqrt((Moment of Inertia-(Mass 1*Radius of Mass 1^2))/Mass 2). To calculate Radius 2 given Moment of Inertia, you need Moment of Inertia (I), Mass 1 (m₁), Radius of Mass 1 (R₁) & Mass 2 (m₂). With our tool, you need to enter the respective value for Moment of Inertia, Mass 1, Radius of Mass 1 & Mass 2 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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