Angular velocity of disc given maximum radial stress Calculator

✖Radial Stress induced by a bending moment in a member of constant cross section.ⓘ Radial Stress [σ_r]			+10% -10%
✖Density Of Disc shows the denseness of disc in a specific given area. This is taken as mass per unit volume of a given disc.ⓘ Density Of Disc [ρ]			+10% -10%
✖Poisson's Ratio is defined as the ratio of the lateral and axial strain. For many metals and alloys, values of Poisson’s ratio range between 0.1 and 0.5.ⓘ Poisson's Ratio [𝛎]			+10% -10%
✖Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary.ⓘ Outer Radius Disc [r_outer]			+10% -10%

✖The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.ⓘ Angular velocity of disc given maximum radial stress [ω]

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Angular velocity of disc given maximum radial stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angular Velocity = sqrt((8*Radial Stress)/(Density Of Disc*(3+Poisson's Ratio)*(Outer Radius Disc^2)))
ω = sqrt((8*σ_r)/(ρ*(3+𝛎)*(r_outer^2)))
This formula uses 1 Functions, 5 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Angular Velocity - (Measured in Radian per Second) - The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.
Radial Stress - (Measured in Pascal) - Radial Stress induced by a bending moment in a member of constant cross section.
Density Of Disc - (Measured in Kilogram per Cubic Meter) - Density Of Disc shows the denseness of disc in a specific given area. This is taken as mass per unit volume of a given disc.
Poisson's Ratio - Poisson's Ratio is defined as the ratio of the lateral and axial strain. For many metals and alloys, values of Poisson’s ratio range between 0.1 and 0.5.
Outer Radius Disc - (Measured in Meter) - Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary.

STEP 1: Convert Input(s) to Base Unit

Radial Stress: 100 Newton per Square Meter --> 100 Pascal (Check conversion here)
Density Of Disc: 2 Kilogram per Cubic Meter --> 2 Kilogram per Cubic Meter No Conversion Required
Poisson's Ratio: 0.3 --> No Conversion Required
Outer Radius Disc: 900 Millimeter --> 0.9 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ω = sqrt((8*σ_r)/(ρ*(3+𝛎)*(r_outer^2))) --> sqrt((8*100)/(2*(3+0.3)*(0.9^2)))

Evaluating ... ...

ω = 12.2329307236262

STEP 3: Convert Result to Output's Unit

12.2329307236262 Radian per Second --> No Conversion Required

FINAL ANSWER

12.2329307236262 ≈ 12.23293 Radian per Second <-- Angular Velocity

(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur

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< Angular Velocity of Disc Calculators

Angular velocity of disc given Circumferential stress in solid disc

LaTeX Go Angular Velocity = sqrt((((Constant at boundary condition/2)-Circumferential Stress)*8)/(Density Of Disc*(Disc Radius^2)*((3*Poisson's Ratio)+1)))

Angular velocity of disc given Constant at boundary condition for circular disc

LaTeX Go Angular Velocity = sqrt((8*Constant at boundary condition)/(Density Of Disc*(Outer Radius Disc^2)*(3+Poisson's Ratio)))

Angular Velocity of disc given Circumferential stress at center of solid disc

LaTeX Go Angular Velocity = sqrt((8*Circumferential Stress)/(Density Of Disc*(3+Poisson's Ratio)*(Outer Radius Disc^2)))

Angular velocity of disc given maximum radial stress

LaTeX Go Angular Velocity = sqrt((8*Radial Stress)/(Density Of Disc*(3+Poisson's Ratio)*(Outer Radius Disc^2)))

Angular velocity of disc given maximum radial stress Formula

LaTeX Go

Angular Velocity = sqrt((8*Radial Stress)/(Density Of Disc*(3+Poisson's Ratio)*(Outer Radius Disc^2)))
ω = sqrt((8*σ_r)/(ρ*(3+𝛎)*(r_outer^2)))

What is radial and tangential stress?

The “Hoop Stress” or “Tangential Stress” acts on a line perpendicular to the “longitudinal “and the “radial stress;” this stress attempts to separate the pipe wall in the circumferential direction. This stress is caused by internal pressure.

How to Calculate Angular velocity of disc given maximum radial stress?

Angular velocity of disc given maximum radial stress calculator uses Angular Velocity = sqrt((8*Radial Stress)/(Density Of Disc*(3+Poisson's Ratio)*(Outer Radius Disc^2))) to calculate the Angular Velocity, The Angular velocity of disc given maximum radial stress formula is defined as a pseudovector, with its magnitude measuring the angular speed, the rate at which an object rotates or revolves. Angular Velocity is denoted by ω symbol.

How to calculate Angular velocity of disc given maximum radial stress using this online calculator? To use this online calculator for Angular velocity of disc given maximum radial stress, enter Radial Stress (σ_r), Density Of Disc (ρ), Poisson's Ratio (𝛎) & Outer Radius Disc (r_outer) and hit the calculate button. Here is how the Angular velocity of disc given maximum radial stress calculation can be explained with given input values -> 12.23293 = sqrt((8*100)/(2*(3+0.3)*(0.9^2))).

FAQ

What is Angular velocity of disc given maximum radial stress?

The Angular velocity of disc given maximum radial stress formula is defined as a pseudovector, with its magnitude measuring the angular speed, the rate at which an object rotates or revolves and is represented as ω = sqrt((8*σ_r)/(ρ*(3+𝛎)*(r_outer^2))) or Angular Velocity = sqrt((8*Radial Stress)/(Density Of Disc*(3+Poisson's Ratio)*(Outer Radius Disc^2))). Radial Stress induced by a bending moment in a member of constant cross section, Density Of Disc shows the denseness of disc in a specific given area. This is taken as mass per unit volume of a given disc, Poisson's Ratio is defined as the ratio of the lateral and axial strain. For many metals and alloys, values of Poisson’s ratio range between 0.1 and 0.5 & Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary.

How to calculate Angular velocity of disc given maximum radial stress?

The Angular velocity of disc given maximum radial stress formula is defined as a pseudovector, with its magnitude measuring the angular speed, the rate at which an object rotates or revolves is calculated using Angular Velocity = sqrt((8*Radial Stress)/(Density Of Disc*(3+Poisson's Ratio)*(Outer Radius Disc^2))). To calculate Angular velocity of disc given maximum radial stress, you need Radial Stress (σ_r), Density Of Disc (ρ), Poisson's Ratio (𝛎) & Outer Radius Disc (r_outer). With our tool, you need to enter the respective value for Radial Stress, Density Of Disc, Poisson's Ratio & Outer Radius Disc 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 Angular Velocity?

In this formula, Angular Velocity uses Radial Stress, Density Of Disc, Poisson's Ratio & Outer Radius Disc. We can use 3 other way(s) to calculate the same, which is/are as follows -

Angular Velocity = sqrt((8*Circumferential Stress)/(Density Of Disc*(3+Poisson's Ratio)*(Outer Radius Disc^2)))
Angular Velocity = sqrt((((Constant at boundary condition/2)-Circumferential Stress)*8)/(Density Of Disc*(Disc Radius^2)*((3*Poisson's Ratio)+1)))
Angular Velocity = sqrt((8*Constant at boundary condition)/(Density Of Disc*(Outer Radius Disc^2)*(3+Poisson's Ratio)))

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