Density of material 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%
✖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.ⓘ Angular Velocity [ω]			+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%

✖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 material given Circumferential stress and Outer radius [ρ]

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Density of material given Circumferential stress and Outer radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Density Of Disc = ((8*Circumferential Stress)/(((Angular Velocity^2))*(((3+Poisson's Ratio)*Outer Radius Disc^2)-(1+(3*Poisson's Ratio)*Radius of Element^2))))
ρ = ((8*σ_c)/(((ω^2))*(((3+𝛎)*r_outer^2)-(1+(3*𝛎)*R^2))))
This formula uses 6 Variables

Variables Used

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.
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.
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.
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)
Angular Velocity: 11.2 Radian per Second --> 11.2 Radian per Second 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

ρ = ((8*σ_c)/(((ω^2))*(((3+𝛎)*r_outer^2)-(1+(3*𝛎)*R^2)))) --> ((8*100)/(((11.2^2))*(((3+0.3)*0.9^2)-(1+(3*0.3)*0.005^2))))

Evaluating ... ...

ρ = 3.81209611032316

STEP 3: Convert Result to Output's Unit

3.81209611032316 Kilogram per Cubic Meter --> No Conversion Required

FINAL ANSWER

3.81209611032316 ≈ 3.812096 Kilogram per Cubic Meter <-- Density Of Disc

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Rotating Disc And Cylinder » Expression for Stresses in Solid Disc » Mechanical » Density of Disc » Density of material given Circumferential stress and Outer radius

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< Density of Disc Calculators

Density of material given Circumferential stress in solid disc

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

Density of disc material given Radial stress in solid disc and outer radius

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

Density of material given constant at boundary condition for circular disc

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

Density of material given Circumferential stress at center of solid disc

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

Density of material given Circumferential stress and Outer radius Formula

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 Density of material given Circumferential stress and Outer radius?

Density of material given Circumferential stress and Outer radius calculator uses Density Of Disc = ((8*Circumferential Stress)/(((Angular Velocity^2))*(((3+Poisson's Ratio)*Outer Radius Disc^2)-(1+(3*Poisson's Ratio)*Radius of Element^2)))) to calculate the Density Of Disc, The Density of material given Circumferential stress and Outer radius formula is defined as a measure of mass per volume. An object made from a comparatively dense material (such as iron) will have less volume than an object of equal mass made from some less dense substance (such as water). Density Of Disc is denoted by ρ symbol.

How to calculate Density of material given Circumferential stress and Outer radius using this online calculator? To use this online calculator for Density of material given Circumferential stress and Outer radius, enter Circumferential Stress (σ_c), Angular Velocity (ω), Poisson's Ratio (𝛎), Outer Radius Disc (r_outer) & Radius of Element (R) and hit the calculate button. Here is how the Density of material given Circumferential stress and Outer radius calculation can be explained with given input values -> 3.812096 = ((8*100)/(((11.2^2))*(((3+0.3)*0.9^2)-(1+(3*0.3)*0.005^2)))).

FAQ

What is Density of material given Circumferential stress and Outer radius?

The Density of material given Circumferential stress and Outer radius formula is defined as a measure of mass per volume. An object made from a comparatively dense material (such as iron) will have less volume than an object of equal mass made from some less dense substance (such as water) and is represented as ρ = ((8*σ_c)/(((ω^2))*(((3+𝛎)*r_outer^2)-(1+(3*𝛎)*R^2)))) or Density Of Disc = ((8*Circumferential Stress)/(((Angular Velocity^2))*(((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, 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, 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 Density of material given Circumferential stress and Outer radius?

The Density of material given Circumferential stress and Outer radius formula is defined as a measure of mass per volume. An object made from a comparatively dense material (such as iron) will have less volume than an object of equal mass made from some less dense substance (such as water) is calculated using Density Of Disc = ((8*Circumferential Stress)/(((Angular Velocity^2))*(((3+Poisson's Ratio)*Outer Radius Disc^2)-(1+(3*Poisson's Ratio)*Radius of Element^2)))). To calculate Density of material given Circumferential stress and Outer radius, you need Circumferential Stress (σ_c), Angular Velocity (ω), 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, Angular Velocity, 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 Density Of Disc?

In this formula, Density Of Disc uses Circumferential Stress, Angular Velocity, 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 -

Density Of Disc = ((8*Radial Stress)/((Angular Velocity^2)*(3+Poisson's Ratio)*((Outer Radius Disc^2)-(Radius of Element^2))))
Density Of Disc = ((8*Circumferential Stress)/((Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2)))
Density Of Disc = (8*Constant at Boundary Condition)/((Angular Velocity^2)*(Outer Radius Disc^2)*(3+Poisson's Ratio))

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