Angular Displacement of Shaft from Mean Position Calculator

✖Restoring Force is a force which acts to bring a body to its equilibrium position.ⓘ Restoring Force [F_restoring]			+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%

✖Angular Displacement of Shaft is movement around an axis, such as the angular motion of the shaft of a motor.ⓘ Angular Displacement of Shaft from Mean Position [θ]

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Formula

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Angular Displacement of Shaft from Mean Position

Formula

`"θ" = "F"_{"restoring"}/"q"`

Example

`"12.03704rad"="65N"/"5.4N/m"`

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Angular Displacement of Shaft from Mean Position Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angular Displacement of Shaft = Restoring Force/Torsional Stiffness
θ = F_restoring/q
This formula uses 3 Variables

Variables Used

Angular Displacement of Shaft - (Measured in Radian) - Angular Displacement of Shaft is movement around an axis, such as the angular motion of the shaft of a motor.
Restoring Force - (Measured in Newton) - Restoring Force is a force which acts to bring a body to its equilibrium position.
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

Restoring Force: 65 Newton --> 65 Newton 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

θ = F_restoring/q --> 65/5.4

Evaluating ... ...

θ = 12.037037037037

STEP 3: Convert Result to Output's Unit

12.037037037037 Radian --> No Conversion Required

FINAL ANSWER

12.037037037037 ≈ 12.03704 Radian <-- Angular Displacement of Shaft

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Vibrations » Torsional Vibrations » Natural Frequency of Free Torsional Vibrations » Angular Displacement of Shaft from Mean Position

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< 13 Natural Frequency of Free Torsional Vibrations Calculators

Natural Frequency of Vibration

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

Time Period for Vibrations

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

Angular Velocity of Shaft

Go Angular Velocity = sqrt(Torsional Stiffness of Shaft/Mass Moment of Inertia of Disc)

Torsional Stiffness of Shaft given Time Period of Vibration

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

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

Moment of Inertia of Disc using Natural Frequency of Vibration

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

Torsional Stiffness of Shaft given Natural Frequency of Vibration

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

Moment of Inertia of Disc given Angular Velocity

Go Mass Moment of Inertia of Disc = Torsional Stiffness of Shaft/(Angular Velocity^2)

Torsional Stiffness of Shaft given Angular Velocity

Go Torsional Stiffness of Shaft = Angular Velocity^2*Mass Moment of Inertia of Disc

Angular Displacement of Shaft from Mean Position

Go Angular Displacement of Shaft = Restoring Force/Torsional Stiffness

Restoring Force for Free Torsional Vibrations

Go Restoring Force = Torsional Stiffness*Angular Displacement of Shaft

Torsional Stiffness of Shaft

Go Torsional Stiffness = Restoring Force/Angular Displacement of Shaft

Accelerating Force

Go Force = Mass Moment of Inertia of Disc*Angular Acceleration

Angular Displacement of Shaft from Mean Position Formula

Angular Displacement of Shaft = Restoring Force/Torsional Stiffness
θ = F_restoring/q

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 Angular Displacement of Shaft from Mean Position?

Angular Displacement of Shaft from Mean Position calculator uses Angular Displacement of Shaft = Restoring Force/Torsional Stiffness to calculate the Angular Displacement of Shaft, The Angular displacement of shaft from mean position formula is defined as movement around an axis, such as the angular motion of the shaft of a motor. Angular Displacement of Shaft is denoted by θ symbol.

How to calculate Angular Displacement of Shaft from Mean Position using this online calculator? To use this online calculator for Angular Displacement of Shaft from Mean Position, enter Restoring Force (F_restoring) & Torsional Stiffness (q) and hit the calculate button. Here is how the Angular Displacement of Shaft from Mean Position calculation can be explained with given input values -> 12.03704 = 65/5.4.

FAQ

What is Angular Displacement of Shaft from Mean Position?

The Angular displacement of shaft from mean position formula is defined as movement around an axis, such as the angular motion of the shaft of a motor and is represented as θ = F_restoring/q or Angular Displacement of Shaft = Restoring Force/Torsional Stiffness. Restoring Force is a force which acts to bring a body to its equilibrium position & torsional stiffness is the ability of an object to resist twisting when acted upon by an external force, torque.

How to calculate Angular Displacement of Shaft from Mean Position?

The Angular displacement of shaft from mean position formula is defined as movement around an axis, such as the angular motion of the shaft of a motor is calculated using Angular Displacement of Shaft = Restoring Force/Torsional Stiffness. To calculate Angular Displacement of Shaft from Mean Position, you need Restoring Force (F_restoring) & Torsional Stiffness (q). With our tool, you need to enter the respective value for Restoring Force & Torsional Stiffness 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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