Length of Shaft given Circular Frequency Solution

STEP 0: Pre-Calculation Summary
Formula Used
Length of Shaft = ((pi^4)/(Natural Circular Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length))^(1/4)
Lshaft = ((pi^4)/(ωn^2)*(E*Ishaft*g)/(w))^(1/4)
This formula uses 1 Constants, 6 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Length of Shaft - (Measured in Meter) - Length of shaft is the distance between two ends of shaft.
Natural Circular Frequency - (Measured in Radian per Second) - Natural Circular Frequency is a scalar measure of rotation rate.
Young's Modulus - (Measured in Newton per Meter) - Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.
Moment of inertia of shaft - (Measured in Kilogram Square Meter) - Moment of inertia of shaft can be calculated by taking the distance of each particle from the axis of rotation.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration due to Gravity is acceleration gained by an object because of gravitational force.
Load per unit length - Load per unit length is the distributed load which is spread over a surface or line.
STEP 1: Convert Input(s) to Base Unit
Natural Circular Frequency: 13.1 Radian per Second --> 13.1 Radian per Second No Conversion Required
Young's Modulus: 15 Newton per Meter --> 15 Newton per Meter No Conversion Required
Moment of inertia of shaft: 1.085522 Kilogram Square Meter --> 1.085522 Kilogram Square Meter No Conversion Required
Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required
Load per unit length: 3 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Lshaft = ((pi^4)/(ωn^2)*(E*Ishaft*g)/(w))^(1/4) --> ((pi^4)/(13.1^2)*(15*1.085522*9.8)/(3))^(1/4)
Evaluating ... ...
Lshaft = 2.34408255216658
STEP 3: Convert Result to Output's Unit
2.34408255216658 Meter --> No Conversion Required
FINAL ANSWER
2.34408255216658 2.344083 Meter <-- Length of Shaft
(Calculation completed in 00.004 seconds)

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Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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Natural Frequency of Free Transverse Vibrations Calculators

Length of Shaft
​ Go Length of Shaft = ((Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Load Attached to Free End of Constraint))^(1/3)
Static Deflection given Moment of Inertia of Shaft
​ Go Static Deflection = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Moment of inertia of shaft)
Moment of Inertia of Shaft given Static Deflection
​ Go Moment of inertia of shaft = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Static Deflection)
Load at Free End in Free Transverse Vibrations
​ Go Load Attached to Free End of Constraint = (Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Length of Shaft^3)

Length of Shaft given Circular Frequency Formula

​Go
Length of Shaft = ((pi^4)/(Natural Circular Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length))^(1/4)
Lshaft = ((pi^4)/(ωn^2)*(E*Ishaft*g)/(w))^(1/4)

What is transverse and longitudinal vibration?

The difference between transverse and longitudinal waves is the direction in which the waves shake. If the wave shakes perpendicular to the movement direction, it's a transverse wave, if it shakes in the movement direction, then it's a longitudinal wave.

How to Calculate Length of Shaft given Circular Frequency?

Length of Shaft given Circular Frequency calculator uses Length of Shaft = ((pi^4)/(Natural Circular Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length))^(1/4) to calculate the Length of Shaft, Length of Shaft given Circular Frequency formula is defined as the measure of the length of a shaft in a mechanical system, which is influenced by the circular frequency, modulus of elasticity, moment of inertia, and weight per unit length of the shaft, and is crucial in determining the natural frequency of free transverse vibrations. Length of Shaft is denoted by Lshaft symbol.

How to calculate Length of Shaft given Circular Frequency using this online calculator? To use this online calculator for Length of Shaft given Circular Frequency, enter Natural Circular Frequency n), Young's Modulus (E), Moment of inertia of shaft (Ishaft), Acceleration due to Gravity (g) & Load per unit length (w) and hit the calculate button. Here is how the Length of Shaft given Circular Frequency calculation can be explained with given input values -> 3.59419 = ((pi^4)/(13.1^2)*(15*1.085522*9.8)/(3))^(1/4).

FAQ

What is Length of Shaft given Circular Frequency?
Length of Shaft given Circular Frequency formula is defined as the measure of the length of a shaft in a mechanical system, which is influenced by the circular frequency, modulus of elasticity, moment of inertia, and weight per unit length of the shaft, and is crucial in determining the natural frequency of free transverse vibrations and is represented as Lshaft = ((pi^4)/(ωn^2)*(E*Ishaft*g)/(w))^(1/4) or Length of Shaft = ((pi^4)/(Natural Circular Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length))^(1/4). Natural Circular Frequency is a scalar measure of rotation rate, Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain, Moment of inertia of shaft can be calculated by taking the distance of each particle from the axis of rotation, Acceleration due to Gravity is acceleration gained by an object because of gravitational force & Load per unit length is the distributed load which is spread over a surface or line.
How to calculate Length of Shaft given Circular Frequency?
Length of Shaft given Circular Frequency formula is defined as the measure of the length of a shaft in a mechanical system, which is influenced by the circular frequency, modulus of elasticity, moment of inertia, and weight per unit length of the shaft, and is crucial in determining the natural frequency of free transverse vibrations is calculated using Length of Shaft = ((pi^4)/(Natural Circular Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length))^(1/4). To calculate Length of Shaft given Circular Frequency, you need Natural Circular Frequency n), Young's Modulus (E), Moment of inertia of shaft (Ishaft), Acceleration due to Gravity (g) & Load per unit length (w). With our tool, you need to enter the respective value for Natural Circular Frequency, Young's Modulus, Moment of inertia of shaft, Acceleration due to Gravity & Load per unit length 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 Length of Shaft?
In this formula, Length of Shaft uses Natural Circular Frequency, Young's Modulus, Moment of inertia of shaft, Acceleration due to Gravity & Load per unit length. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Length of Shaft = ((Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Load Attached to Free End of Constraint))^(1/3)
  • Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(Load per unit length))^(1/4)
  • Length of Shaft = 3.573^2*((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Frequency^2))^(1/4)
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