Angular velocity of disc given Radial stress in solid disc and Outer radius 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 Radius of Element is the radius of the element considered in the disc at radius r from the centre.ⓘ Radius of Element [r]			+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 Radial stress in solid disc and Outer radius [ω]

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Angular velocity of disc given Radial stress in solid disc and Outer radius 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)-(Radius of Element^2))))
ω = sqrt((8*σ_r)/(ρ*(3+𝛎)*((r_outer^2)-(r^2))))
This formula uses 1 Functions, 6 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.
Radius of Element - (Measured in Meter) - The Radius of Element is the radius of the element considered in the disc at radius r from the centre.

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)
Radius of Element: 5 Millimeter --> 0.005 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ω = sqrt((8*σ_r)/(ρ*(3+𝛎)*((r_outer^2)-(r^2)))) --> sqrt((8*100)/(2*(3+0.3)*((0.9^2)-(0.005^2))))

Evaluating ... ...

ω = 12.2331195077914

STEP 3: Convert Result to Output's Unit

12.2331195077914 Radian per Second --> No Conversion Required

FINAL ANSWER

12.2331195077914 ≈ 12.23312 Radian per Second <-- Angular Velocity

(Calculation completed in 00.020 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 Radial stress in solid disc and Outer radius Formula

LaTeX Go

Angular Velocity = sqrt((8*Radial Stress)/(Density Of Disc*(3+Poisson's Ratio)*((Outer Radius Disc^2)-(Radius of Element^2))))
ω = sqrt((8*σ_r)/(ρ*(3+𝛎)*((r_outer^2)-(r^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 Radial stress in solid disc and Outer radius?

Angular velocity of disc given Radial stress in solid disc and Outer radius calculator uses Angular Velocity = sqrt((8*Radial Stress)/(Density Of Disc*(3+Poisson's Ratio)*((Outer Radius Disc^2)-(Radius of Element^2)))) to calculate the Angular Velocity, The Angular velocity of disc given Radial stress in solid disc and Outer radius 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 Radial stress in solid disc and Outer radius using this online calculator? To use this online calculator for Angular velocity of disc given Radial stress in solid disc and Outer radius, enter Radial Stress (σ_r), Density Of Disc (ρ), Poisson's Ratio (𝛎), Outer Radius Disc (r_outer) & Radius of Element (r) and hit the calculate button. Here is how the Angular velocity of disc given Radial stress in solid disc and Outer radius calculation can be explained with given input values -> 12.23312 = sqrt((8*100)/(2*(3+0.3)*((0.9^2)-(0.005^2)))).

FAQ

What is Angular velocity of disc given Radial stress in solid disc and Outer radius?

The Angular velocity of disc given Radial stress in solid disc and Outer radius 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)-(r^2)))) or Angular Velocity = sqrt((8*Radial Stress)/(Density Of Disc*(3+Poisson's Ratio)*((Outer Radius Disc^2)-(Radius of Element^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 & The Radius of Element is the radius of the element considered in the disc at radius r from the centre.

How to calculate Angular velocity of disc given Radial stress in solid disc and Outer radius?

The Angular velocity of disc given Radial stress in solid disc and Outer radius 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)-(Radius of Element^2)))). To calculate Angular velocity of disc given Radial stress in solid disc and Outer radius, you need Radial Stress (σ_r), Density Of Disc (ρ), Poisson's Ratio (𝛎), Outer Radius Disc (r_outer) & Radius of Element (r). With our tool, you need to enter the respective value for Radial Stress, Density Of Disc, Poisson's Ratio, Outer Radius Disc & Radius of Element 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 & Radius of Element. 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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