Moment of Inertia using Kinetic Energy Calculator

✖Kinetic Energy is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.ⓘ Kinetic Energy [KE]			+10% -10%
✖Angular Velocity Spectroscopy refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.ⓘ Angular Velocity Spectroscopy [ω]			+10% -10%

✖Moment of Inertia using Angular Momentum is the measure of the resistance of a body to angular acceleration about a given axis.ⓘ Moment of Inertia using Kinetic Energy [I2]

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Formula

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Moment of Inertia using Kinetic Energy

Formula

`"I2" = 2*"KE"/("ω"^2)`

Example

`"0.2kg·m²"=2*"40J"/(("20rad/s")^2)`

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Moment of Inertia using Kinetic Energy Solution

STEP 0: Pre-Calculation Summary

Formula Used

Moment of Inertia using Angular Momentum = 2*Kinetic Energy/(Angular Velocity Spectroscopy^2)
I2 = 2*KE/(ω^2)
This formula uses 3 Variables

Variables Used

Moment of Inertia using Angular Momentum - (Measured in Kilogram Square Meter) - Moment of Inertia using Angular Momentum is the measure of the resistance of a body to angular acceleration about a given axis.
Kinetic Energy - (Measured in Joule) - Kinetic Energy is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.
Angular Velocity Spectroscopy - (Measured in Radian per Second) - Angular Velocity Spectroscopy refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.

STEP 1: Convert Input(s) to Base Unit

Kinetic Energy: 40 Joule --> 40 Joule No Conversion Required
Angular Velocity Spectroscopy: 20 Radian per Second --> 20 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I2 = 2*KE/(ω^2) --> 2*40/(20^2)

Evaluating ... ...

I2 = 0.2

STEP 3: Convert Result to Output's Unit

0.2 Kilogram Square Meter --> No Conversion Required

FINAL ANSWER

0.2 Kilogram Square Meter <-- Moment of Inertia using Angular Momentum

(Calculation completed in 00.004 seconds)

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Indian Institute of Technology (IIT), Delhi

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< 9 Moment of Inertia Calculators

Moment of Inertia using Masses of Diatomic Molecule and Bond Length

Go Moment of Inertia of Diatomic Molecule = ((Mass 1*Mass 2)/(Mass 1+Mass 2))*(Bond Length^2)

Moment of Inertia of Diatomic Molecule

Go Moment of Inertia of Diatomic Molecule = (Mass 1*Radius of Mass 1^2)+(Mass 2*Radius of Mass 2^2)

Moment of Inertia using Rotational Constant

Go Moment of Inertia given RC = [hP]/(8*(pi^2)*[c]*Rotational Constant)

Moment of Inertia using Kinetic Energy

Go Moment of Inertia using Angular Momentum = 2*Kinetic Energy/(Angular Velocity Spectroscopy^2)

Moment of Inertia using Angular Momentum

Go Moment of Inertia using Angular Momentum = Angular Momentum/Angular Velocity Spectroscopy

Moment of Inertia using Rotational Energy

Go Moment of Inertia given RE = (2*Rotational Energy)/(Angular Velocity Spectroscopy^2)

Moment of Inertia using Reduced Mass

Go Moment of Inertia of Diatomic Molecule = Reduced Mass*(Bond Length^2)

Moment of Inertia using Kinetic Energy and Angular Momentum

Go Moment of Inertia = (Angular Momentum^2)/(2*Kinetic Energy)

Reduced Mass using Moment of Inertia

Go Reduced Mass1 = Moment of Inertia/(Bond Length^2)

< 9 Moment of inertia Calculators

Moment of Inertia using Masses of Diatomic Molecule and Bond Length

Go Moment of Inertia of Diatomic Molecule = ((Mass 1*Mass 2)/(Mass 1+Mass 2))*(Bond Length^2)

Moment of Inertia of Diatomic Molecule

Go Moment of Inertia of Diatomic Molecule = (Mass 1*Radius of Mass 1^2)+(Mass 2*Radius of Mass 2^2)

Moment of Inertia using Rotational Constant

Go Moment of Inertia given RC = [hP]/(8*(pi^2)*[c]*Rotational Constant)

Moment of Inertia using Kinetic Energy

Go Moment of Inertia using Angular Momentum = 2*Kinetic Energy/(Angular Velocity Spectroscopy^2)

Moment of Inertia using Angular Momentum

Go Moment of Inertia using Angular Momentum = Angular Momentum/Angular Velocity Spectroscopy

Moment of Inertia using Rotational Energy

Go Moment of Inertia given RE = (2*Rotational Energy)/(Angular Velocity Spectroscopy^2)

Moment of Inertia using Reduced Mass

Go Moment of Inertia of Diatomic Molecule = Reduced Mass*(Bond Length^2)

Moment of Inertia using Kinetic Energy and Angular Momentum

Go Moment of Inertia = (Angular Momentum^2)/(2*Kinetic Energy)

Reduced Mass using Moment of Inertia

Go Reduced Mass1 = Moment of Inertia/(Bond Length^2)

Moment of Inertia using Kinetic Energy Formula

Moment of Inertia using Angular Momentum = 2*Kinetic Energy/(Angular Velocity Spectroscopy^2)
I2 = 2*KE/(ω^2)

How to get Moment of Inertia in terms of K.E and angular velocity?

Rotational kinetic energy (K.E.) of a rotating object can be expressed as half of the product of the angular velocity of the object and moment of inertia around the axis of rotation (0.5*I* ω^2). So we get moment of inertia as twice of K.E. divided by square of angular velocity (2*K.E./ω^2).

How to Calculate Moment of Inertia using Kinetic Energy?

Moment of Inertia using Kinetic Energy calculator uses Moment of Inertia using Angular Momentum = 2*Kinetic Energy/(Angular Velocity Spectroscopy^2) to calculate the Moment of Inertia using Angular Momentum, The Moment of Inertia using Kinetic Energy formula is a variation of K.E. formula. As kinetic energy is directly proportional to the rotational inertia and the square of the magnitude of the angular velocity. Kinetic energy of a rotating object can be expressed as half of the product of the angular velocity of the object and moment of inertia around the axis of rotation. So thus we get the relation between moment of inertia and K.E. Moment of Inertia using Angular Momentum is denoted by I2 symbol.

How to calculate Moment of Inertia using Kinetic Energy using this online calculator? To use this online calculator for Moment of Inertia using Kinetic Energy, enter Kinetic Energy (KE) & Angular Velocity Spectroscopy (ω) and hit the calculate button. Here is how the Moment of Inertia using Kinetic Energy calculation can be explained with given input values -> 0.2 = 2*40/(20^2).

FAQ

What is Moment of Inertia using Kinetic Energy?

The Moment of Inertia using Kinetic Energy formula is a variation of K.E. formula. As kinetic energy is directly proportional to the rotational inertia and the square of the magnitude of the angular velocity. Kinetic energy of a rotating object can be expressed as half of the product of the angular velocity of the object and moment of inertia around the axis of rotation. So thus we get the relation between moment of inertia and K.E and is represented as I2 = 2*KE/(ω^2) or Moment of Inertia using Angular Momentum = 2*Kinetic Energy/(Angular Velocity Spectroscopy^2). Kinetic Energy is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity & Angular Velocity Spectroscopy refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.

How to calculate Moment of Inertia using Kinetic Energy?

The Moment of Inertia using Kinetic Energy formula is a variation of K.E. formula. As kinetic energy is directly proportional to the rotational inertia and the square of the magnitude of the angular velocity. Kinetic energy of a rotating object can be expressed as half of the product of the angular velocity of the object and moment of inertia around the axis of rotation. So thus we get the relation between moment of inertia and K.E is calculated using Moment of Inertia using Angular Momentum = 2*Kinetic Energy/(Angular Velocity Spectroscopy^2). To calculate Moment of Inertia using Kinetic Energy, you need Kinetic Energy (KE) & Angular Velocity Spectroscopy (ω). With our tool, you need to enter the respective value for Kinetic Energy & Angular Velocity Spectroscopy and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Moment of Inertia using Angular Momentum?

In this formula, Moment of Inertia using Angular Momentum uses Kinetic Energy & Angular Velocity Spectroscopy. We can use 2 other way(s) to calculate the same, which is/are as follows -

Moment of Inertia using Angular Momentum = Angular Momentum/Angular Velocity Spectroscopy
Moment of Inertia using Angular Momentum = Angular Momentum/Angular Velocity Spectroscopy

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