Disc's Angular velocity given Circumferential stress and Outer radius Calculator

✖Circumferential stress, also known as hoop stress, is a type of normal stress that acts tangentially to the circumference of a cylindrical or spherical object.ⓘ Circumferential Stress [σ_c]			+10% -10%
✖Density of disc typically refers to the mass per unit volume of the disc material. It is a measure of how much mass is contained in a given volume of the disc.ⓘ Density Of Disc [ρ]			+10% -10%
✖Poisson's ratio is a measure of the deformation of a material in directions perpendicular to the direction of loading. It is defined as the negative ratio of transverse strain to axial strain.ⓘ Poisson's Ratio [𝛎]			+10% -10%
✖Outer radius disc is the distance from the center of the disc to its outer edge or boundary.ⓘ Outer Radius Disc [r_outer]			+10% -10%
✖Radius of element often referred to as the atomic radius, is a measure of the size of an atom, typically defined as the distance from the center of the nucleus to the outermost shell of electrons.ⓘ Radius of Element [R]			+10% -10%

✖Angular velocity is a measure of how quickly an object rotates or revolves around a central point or axis, describes the rate of change of the angular position of the object with respect to time.ⓘ Disc's Angular velocity given Circumferential stress and Outer radius [ω]

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Disc's Angular velocity given Circumferential stress and Outer radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angular Velocity = sqrt((8*Circumferential Stress)/((Density Of Disc)*(((3+Poisson's Ratio)*Outer Radius Disc^2)-(1+(3*Poisson's Ratio)*Radius of Element^2))))
ω = sqrt((8*σ_c)/((ρ)*(((3+𝛎)*r_outer^2)-(1+(3*𝛎)*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) - Angular velocity is a measure of how quickly an object rotates or revolves around a central point or axis, describes the rate of change of the angular position of the object with respect to time.
Circumferential Stress - (Measured in Pascal) - Circumferential stress, also known as hoop stress, is a type of normal stress that acts tangentially to the circumference of a cylindrical or spherical object.
Density Of Disc - (Measured in Kilogram per Cubic Meter) - Density of disc typically refers to the mass per unit volume of the disc material. It is a measure of how much mass is contained in a given volume of the disc.
Poisson's Ratio - Poisson's ratio is a measure of the deformation of a material in directions perpendicular to the direction of loading. It is defined as the negative ratio of transverse strain to axial strain.
Outer Radius Disc - (Measured in Meter) - Outer radius disc is the distance from the center of the disc to its outer edge or boundary.
Radius of Element - (Measured in Meter) - Radius of element often referred to as the atomic radius, is a measure of the size of an atom, typically defined as the distance from the center of the nucleus to the outermost shell of electrons.

STEP 1: Convert Input(s) to Base Unit

Circumferential 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_c)/((ρ)*(((3+𝛎)*r_outer^2)-(1+(3*𝛎)*R^2)))) --> sqrt((8*100)/((2)*(((3+0.3)*0.9^2)-(1+(3*0.3)*0.005^2))))

Evaluating ... ...

ω = 15.4626863138159

STEP 3: Convert Result to Output's Unit

15.4626863138159 Radian per Second --> No Conversion Required

FINAL ANSWER

15.4626863138159 ≈ 15.46269 Radian per Second <-- Angular Velocity

(Calculation completed in 00.020 seconds)

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Home » Physics » Strength of Materials » Rotating Disc And Cylinder » Expression for Stresses in Solid Disc » Mechanical » Angular Velocity of Disc » Disc's Angular velocity given Circumferential stress and Outer radius

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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)))

Disc's Angular velocity given Circumferential stress and Outer radius Formula

LaTeX Go

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 Disc's Angular velocity given Circumferential stress and Outer radius?

Disc's Angular velocity given Circumferential stress and Outer radius calculator uses Angular Velocity = sqrt((8*Circumferential Stress)/((Density Of Disc)*(((3+Poisson's Ratio)*Outer Radius Disc^2)-(1+(3*Poisson's Ratio)*Radius of Element^2)))) to calculate the Angular Velocity, The Disc's Angular velocity given Circumferential stress 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 Disc's Angular velocity given Circumferential stress and Outer radius using this online calculator? To use this online calculator for Disc's Angular velocity given Circumferential stress and Outer radius, enter Circumferential Stress (σ_c), 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 Disc's Angular velocity given Circumferential stress and Outer radius calculation can be explained with given input values -> 15.46269 = sqrt((8*100)/((2)*(((3+0.3)*0.9^2)-(1+(3*0.3)*0.005^2)))).

FAQ

What is Disc's Angular velocity given Circumferential stress and Outer radius?

The Disc's Angular velocity given Circumferential stress 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_c)/((ρ)*(((3+𝛎)*r_outer^2)-(1+(3*𝛎)*R^2)))) or Angular Velocity = sqrt((8*Circumferential Stress)/((Density Of Disc)*(((3+Poisson's Ratio)*Outer Radius Disc^2)-(1+(3*Poisson's Ratio)*Radius of Element^2)))). Circumferential stress, also known as hoop stress, is a type of normal stress that acts tangentially to the circumference of a cylindrical or spherical object, Density of disc typically refers to the mass per unit volume of the disc material. It is a measure of how much mass is contained in a given volume of the disc, Poisson's ratio is a measure of the deformation of a material in directions perpendicular to the direction of loading. It is defined as the negative ratio of transverse strain to axial strain, Outer radius disc is the distance from the center of the disc to its outer edge or boundary & Radius of element often referred to as the atomic radius, is a measure of the size of an atom, typically defined as the distance from the center of the nucleus to the outermost shell of electrons.

How to calculate Disc's Angular velocity given Circumferential stress and Outer radius?

The Disc's Angular velocity given Circumferential stress 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*Circumferential Stress)/((Density Of Disc)*(((3+Poisson's Ratio)*Outer Radius Disc^2)-(1+(3*Poisson's Ratio)*Radius of Element^2)))). To calculate Disc's Angular velocity given Circumferential stress and Outer radius, you need Circumferential Stress (σ_c), 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 Circumferential 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 Circumferential 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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