Mass Moment of Inertia of Element Solution

STEP 0: Pre-Calculation Summary
Formula Used
Moment of Inertia = (Length of Small Element*Total Mass Moment of Inertia)/Length of Constraint
I = (δx*Ic)/l
This formula uses 4 Variables
Variables Used
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.
Length of Small Element - (Measured in Meter) - Length of Small Element is a measure of distance.
Total Mass Moment of Inertia - (Measured in Kilogram Square Meter) - Total Mass Moment of Inertia measures the extent to which an object resists rotational acceleration about an axis, and is the rotational analog to mass.
Length of Constraint - (Measured in Meter) - Length of Constraint is a measure of distance.
STEP 1: Convert Input(s) to Base Unit
Length of Small Element: 9.82 Millimeter --> 0.00982 Meter (Check conversion here)
Total Mass Moment of Inertia: 10.65 Kilogram Square Meter --> 10.65 Kilogram Square Meter No Conversion Required
Length of Constraint: 7.33 Millimeter --> 0.00733 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
I = (δx*Ic)/l --> (0.00982*10.65)/0.00733
Evaluating ... ...
I = 14.2678035470669
STEP 3: Convert Result to Output's Unit
14.2678035470669 Kilogram Square Meter --> No Conversion Required
FINAL ANSWER
14.2678035470669 14.2678 Kilogram Square Meter <-- Moment of Inertia
(Calculation completed in 00.004 seconds)

Credits

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National Institute Of Technology (NIT), Hamirpur
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8 Effect of Inertia of Constraint on Torsional Vibrations Calculators

Kinetic Energy Possessed by Element
Go Kinetic Energy = (Total Mass Moment of Inertia*(Angular Velocity of Free End*Distance between Small Element and Fixed End)^2*Length of Small Element)/(2*Length of Constraint^3)
Natural Frequency of Torsional Vibration due to Effect of Inertia of Constraint
Go Frequency = (sqrt(Torsional Stiffness/(Mass Moment of Inertia of Disc+Total Mass Moment of Inertia/3)))/(2*pi)
Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations
Go Torsional Stiffness = (2*pi*Frequency)^2*(Mass Moment of Inertia of Disc+Total Mass Moment of Inertia/3)
Angular Velocity of Element
Go Angular Velocity = (Angular Velocity of Free End*Distance between Small Element and Fixed End)/Length of Constraint
Mass Moment of Inertia of Element
Go Moment of Inertia = (Length of Small Element*Total Mass Moment of Inertia)/Length of Constraint
Angular Velocity of Free End using Kinetic Energy of Constraint
Go Angular Velocity of Free End = sqrt((6*Kinetic Energy)/Total Mass Moment of Inertia)
Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint
Go Total Mass Moment of Inertia = (6*Kinetic Energy)/(Angular Velocity of Free End^2)
Total Kinetic Energy of Constraint
Go Kinetic Energy = (Total Mass Moment of Inertia*Angular Velocity of Free End^2)/6

Mass Moment of Inertia of Element Formula

Moment of Inertia = (Length of Small Element*Total Mass Moment of Inertia)/Length of Constraint
I = (δx*Ic)/l

What causes torsional vibration on the shaft?

Torsional vibrations are an example of machinery vibrations and are caused by the superposition of angular oscillations along the whole propulsion shaft system including propeller shaft, engine crankshaft, engine, gearbox, flexible coupling and along the intermediate shafts.

How to Calculate Mass Moment of Inertia of Element?

Mass Moment of Inertia of Element calculator uses Moment of Inertia = (Length of Small Element*Total Mass Moment of Inertia)/Length of Constraint to calculate the Moment of Inertia, The Mass Moment of Inertia of Element formula is defined as a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for the desired acceleration. Moment of Inertia is denoted by I symbol.

How to calculate Mass Moment of Inertia of Element using this online calculator? To use this online calculator for Mass Moment of Inertia of Element, enter Length of Small Element (δx), Total Mass Moment of Inertia (Ic) & Length of Constraint (l) and hit the calculate button. Here is how the Mass Moment of Inertia of Element calculation can be explained with given input values -> 14.2678 = (0.00982*10.65)/0.00733.

FAQ

What is Mass Moment of Inertia of Element?
The Mass Moment of Inertia of Element formula is defined as a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for the desired acceleration and is represented as I = (δx*Ic)/l or Moment of Inertia = (Length of Small Element*Total Mass Moment of Inertia)/Length of Constraint. Length of Small Element is a measure of distance, Total Mass Moment of Inertia measures the extent to which an object resists rotational acceleration about an axis, and is the rotational analog to mass & Length of Constraint is a measure of distance.
How to calculate Mass Moment of Inertia of Element?
The Mass Moment of Inertia of Element formula is defined as a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for the desired acceleration is calculated using Moment of Inertia = (Length of Small Element*Total Mass Moment of Inertia)/Length of Constraint. To calculate Mass Moment of Inertia of Element, you need Length of Small Element (δx), Total Mass Moment of Inertia (Ic) & Length of Constraint (l). With our tool, you need to enter the respective value for Length of Small Element, Total Mass Moment of Inertia & Length of Constraint 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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