Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint Solution

STEP 0: Pre-Calculation Summary
Formula Used
Total Mass Moment of Inertia = (6*Kinetic Energy)/(Angular Velocity of Free End^2)
Ic = (6*KE)/(ωf^2)
This formula uses 3 Variables
Variables Used
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.
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 of Free End - (Measured in Radian per Second) - Angular Velocity of Free End is a vector measure of rotation rate, that refers to how fast an object rotates or revolves relative to another point.
STEP 1: Convert Input(s) to Base Unit
Kinetic Energy: 900 Joule --> 900 Joule No Conversion Required
Angular Velocity of Free End: 22.5 Radian per Second --> 22.5 Radian per Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Ic = (6*KE)/(ωf^2) --> (6*900)/(22.5^2)
Evaluating ... ...
Ic = 10.6666666666667
STEP 3: Convert Result to Output's Unit
10.6666666666667 Kilogram Square Meter --> No Conversion Required
FINAL ANSWER
10.6666666666667 10.66667 Kilogram Square Meter <-- Total Mass Moment of Inertia
(Calculation completed in 00.004 seconds)

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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

Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint Formula

Total Mass Moment of Inertia = (6*Kinetic Energy)/(Angular Velocity of Free End^2)
Ic = (6*KE)/(ωf^2)

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 Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint?

Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint calculator uses Total Mass Moment of Inertia = (6*Kinetic Energy)/(Angular Velocity of Free End^2) to calculate the Total Mass Moment of Inertia, The Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint 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. Total Mass Moment of Inertia is denoted by Ic symbol.

How to calculate Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint using this online calculator? To use this online calculator for Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint, enter Kinetic Energy (KE) & Angular Velocity of Free End f) and hit the calculate button. Here is how the Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint calculation can be explained with given input values -> 10.66667 = (6*900)/(22.5^2).

FAQ

What is Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint?
The Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint 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 Ic = (6*KE)/(ωf^2) or Total Mass Moment of Inertia = (6*Kinetic Energy)/(Angular Velocity of Free End^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 of Free End is a vector measure of rotation rate, that refers to how fast an object rotates or revolves relative to another point.
How to calculate Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint?
The Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint 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 Total Mass Moment of Inertia = (6*Kinetic Energy)/(Angular Velocity of Free End^2). To calculate Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint, you need Kinetic Energy (KE) & Angular Velocity of Free End f). With our tool, you need to enter the respective value for Kinetic Energy & Angular Velocity of Free End 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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