Moment of Inertia of Disc given Time Period of Vibration Calculator

✖Time Period is the time taken by the shaft to complete one oscillation or vibration about its axis in a torsional vibration system.ⓘ Time Period [t_p]			+10% -10%
✖torsional stiffness is the ability of an object to resist twisting when acted upon by an external force, torque.ⓘ Torsional Stiffness [q]			+10% -10%

✖Mass Moment of Inertia of Disc is the rotational inertia of a disc that resists changes in its rotational motion, used in torsional vibration analysis.ⓘ Moment of Inertia of Disc given Time Period of Vibration [I_d]

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Moment of Inertia of Disc given Time Period of Vibration Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mass Moment of Inertia of Disc = (Time Period^2*Torsional Stiffness)/((2*pi)^2)
I_d = (t_p^2*q)/((2*pi)^2)
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Mass Moment of Inertia of Disc - (Measured in Kilogram Square Meter) - Mass Moment of Inertia of Disc is the rotational inertia of a disc that resists changes in its rotational motion, used in torsional vibration analysis.
Time Period - (Measured in Second) - Time Period is the time taken by the shaft to complete one oscillation or vibration about its axis in a torsional vibration system.
Torsional Stiffness - (Measured in Newton per Meter) - torsional stiffness is the ability of an object to resist twisting when acted upon by an external force, torque.

STEP 1: Convert Input(s) to Base Unit

Time Period: 6.7325383 Second --> 6.7325383 Second No Conversion Required
Torsional Stiffness: 5.4 Newton per Meter --> 5.4 Newton per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I_d = (t_p^2*q)/((2*pi)^2) --> (6.7325383^2*5.4)/((2*pi)^2)

Evaluating ... ...

I_d = 6.19999998587089

STEP 3: Convert Result to Output's Unit

6.19999998587089 Kilogram Square Meter --> No Conversion Required

FINAL ANSWER

6.19999998587089 ≈ 6.2 Kilogram Square Meter <-- Mass Moment of Inertia of Disc

(Calculation completed in 00.073 seconds)

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Home » Physics » Theory of Machine » Vibrations » Torsional Vibrations » Mechanical » Natural Frequency of Free Torsional Vibrations » Moment of Inertia of Disc given Time Period of Vibration

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< Natural Frequency of Free Torsional Vibrations Calculators

Moment of Inertia of Disc using Natural Frequency of Vibration

LaTeX Go Mass Moment of Inertia of Disc = Torsional Stiffness/((2*pi*Natural Frequency)^2)

Torsional Stiffness of Shaft given Natural Frequency of Vibration

LaTeX Go Torsional Stiffness = (2*pi*Natural Frequency)^2*Mass Moment of Inertia of Disc

Torsional Stiffness of Shaft given Time Period of Vibration

LaTeX Go Torsional Stiffness = ((2*pi)^2*Mass Moment of Inertia of Disc)/(Time Period)^2

Moment of Inertia of Disc given Time Period of Vibration

LaTeX Go Mass Moment of Inertia of Disc = (Time Period^2*Torsional Stiffness)/((2*pi)^2)

Moment of Inertia of Disc given Time Period of Vibration Formula

LaTeX Go

Mass Moment of Inertia of Disc = (Time Period^2*Torsional Stiffness)/((2*pi)^2)
I_d = (t_p^2*q)/((2*pi)^2)

What causes torsional vibration?

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 Moment of Inertia of Disc given Time Period of Vibration?

Moment of Inertia of Disc given Time Period of Vibration calculator uses Mass Moment of Inertia of Disc = (Time Period^2*Torsional Stiffness)/((2*pi)^2) to calculate the Mass Moment of Inertia of Disc, Moment of Inertia of Disc given Time Period of Vibration formula is defined as a measure of the tendency of an object to resist changes in its rotational motion, calculated based on the time period of vibration and other parameters, providing valuable insights into the torsional vibrations of a disc. Mass Moment of Inertia of Disc is denoted by I_d symbol.

How to calculate Moment of Inertia of Disc given Time Period of Vibration using this online calculator? To use this online calculator for Moment of Inertia of Disc given Time Period of Vibration, enter Time Period (t_p) & Torsional Stiffness (q) and hit the calculate button. Here is how the Moment of Inertia of Disc given Time Period of Vibration calculation can be explained with given input values -> 6.2 = (6.7325383^2*5.4)/((2*pi)^2).

FAQ

What is Moment of Inertia of Disc given Time Period of Vibration?

Moment of Inertia of Disc given Time Period of Vibration formula is defined as a measure of the tendency of an object to resist changes in its rotational motion, calculated based on the time period of vibration and other parameters, providing valuable insights into the torsional vibrations of a disc and is represented as I_d = (t_p^2*q)/((2*pi)^2) or Mass Moment of Inertia of Disc = (Time Period^2*Torsional Stiffness)/((2*pi)^2). Time Period is the time taken by the shaft to complete one oscillation or vibration about its axis in a torsional vibration system & torsional stiffness is the ability of an object to resist twisting when acted upon by an external force, torque.

How to calculate Moment of Inertia of Disc given Time Period of Vibration?

Moment of Inertia of Disc given Time Period of Vibration formula is defined as a measure of the tendency of an object to resist changes in its rotational motion, calculated based on the time period of vibration and other parameters, providing valuable insights into the torsional vibrations of a disc is calculated using Mass Moment of Inertia of Disc = (Time Period^2*Torsional Stiffness)/((2*pi)^2). To calculate Moment of Inertia of Disc given Time Period of Vibration, you need Time Period (t_p) & Torsional Stiffness (q). With our tool, you need to enter the respective value for Time Period & Torsional Stiffness 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 Mass Moment of Inertia of Disc?

In this formula, Mass Moment of Inertia of Disc uses Time Period & Torsional Stiffness. We can use 2 other way(s) to calculate the same, which is/are as follows -

Mass Moment of Inertia of Disc = Torsional Stiffness/((2*pi*Natural Frequency)^2)
Mass Moment of Inertia of Disc = Resistance Torsional Stiffness/(Angular Velocity^2)

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