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Density of disc material in terms of radial stress in a solid disc and outer radius of disc Solution

STEP 0: Pre-Calculation Summary
Formula Used
density = ((8*Radial Stress)/((Angular Velocity^2)*(3+Poisson's ratio)*((Outer Radius^2)-(Radius of element^2))))
ρ = ((8*fr)/((ω^2)*(3+𝛎)*((R^2)-(r^2))))
This formula uses 5 Variables
Variables Used
Radial Stress - Radial Stress induced by a bending moment in a member of constant cross section. (Measured in Pascal)
Angular Velocity - 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. (Measured in Radian per Second)
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 0.25 and 0.35.
Outer Radius - Outer Radius is the radius of the larger of the two concentric circles that form its boundary. (Measured in Centimeter)
Radius of element - Radius of element is the radius of the element considered in the disc at radius r from the center. (Measured in Millimeter)
STEP 1: Convert Input(s) to Base Unit
Radial Stress: 100 Pascal --> 100 Pascal No Conversion Required
Angular Velocity: 20 Radian per Second --> 20 Radian per Second No Conversion Required
Poisson's ratio: 0.3 --> No Conversion Required
Outer Radius: 10 Centimeter --> 0.1 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*fr)/((ω^2)*(3+𝛎)*((R^2)-(r^2)))) --> ((8*100)/((20^2)*(3+0.3)*((0.1^2)-(0.005^2))))
Evaluating ... ...
ρ = 60.7579554947976
STEP 3: Convert Result to Output's Unit
60.7579554947976 Kilogram per Meter³ --> No Conversion Required
FINAL ANSWER
60.7579554947976 Kilogram per Meter³ <-- Density
(Calculation completed in 00.015 seconds)

10+ Expression For Stresses In A Solid Disc Calculators

Angular velocity of disc in terms of circumferential stress in a solid disc
angular_velocity_1 = sqrt((((Constant at boundary condition/2)-Circumferential stress)*8)/(Density*(Radius^2)*((3*Poisson's ratio)+1))) Go
Angular velocity of the disc in terms of radial stress in a solid disc
angular_velocity_1 = sqrt((((Constant at boundary condition/2)-Radial Stress)*8)/(Density*(Radius^2)*(3+Poisson's ratio))) Go
Radius of the disc in terms of radial stress in a solid disc
radius = sqrt((((Constant at boundary condition/2)-Radial Stress)*8)/(Density*(Angular velocity^2)*(3+Poisson's ratio))) Go
Density of material in terms of circumferential stress in a solid disc
density = (((Constant at boundary condition/2)-Circumferential stress)*8)/((Angular velocity^2)*(Radius^2)*((3*Poisson's ratio)+1)) Go
Constant at boundary condition in terms of circumferential stress in a solid disc
constant_at_boundary_condition = 2*(Circumferential stress+((Density*(Angular velocity^2)*(Radius^2)*((3*Poisson's ratio)+1))/8)) Go
Circumferential stress in a solid disc
circumferential_stress = (Constant at boundary condition/2)-((Density*(Angular velocity^2)*(Radius^2)*((3*Poisson's ratio)+1))/8) Go
Density of material in terms of radial stress in a solid disc
density = (((Constant at boundary condition/2)-Radial Stress)*8)/((Angular velocity^2)*(Radius^2)*(3+Poisson's ratio)) Go
Poisson's ratio in terms of radial stress in a solid disc
poissons_ratio = ((((Constant at boundary condition/2)-Radial Stress)*8)/(Density*(Angular velocity^2)*(Radius^2)))-3 Go
Constant at boundary condition in terms of radial stress in a solid disc
constant_at_boundary_condition = 2*(Radial Stress+((Density*(Angular velocity^2)*(Radius^2)*(3+Poisson's ratio))/8)) Go
Radial stress in a solid disc
radial_stress = (Constant at boundary condition/2)-((Density*(Angular velocity^2)*(Radius^2)*(3+Poisson's ratio))/8) Go

Density of disc material in terms of radial stress in a solid disc and outer radius of disc Formula

density = ((8*Radial Stress)/((Angular Velocity^2)*(3+Poisson's ratio)*((Outer Radius^2)-(Radius of element^2))))
ρ = ((8*fr)/((ω^2)*(3+𝛎)*((R^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 Density of disc material in terms of radial stress in a solid disc and outer radius of disc?

Density of disc material in terms of radial stress in a solid disc and outer radius of disc calculator uses density = ((8*Radial Stress)/((Angular Velocity^2)*(3+Poisson's ratio)*((Outer Radius^2)-(Radius of element^2)))) to calculate the Density, The Density of disc material in terms of radial stress in a solid disc and outer radius of disc 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 and is denoted by ρ symbol.

How to calculate Density of disc material in terms of radial stress in a solid disc and outer radius of disc using this online calculator? To use this online calculator for Density of disc material in terms of radial stress in a solid disc and outer radius of disc, enter Radial Stress (fr), Angular Velocity (ω), Poisson's ratio (𝛎), Outer Radius (R) and Radius of element (r) and hit the calculate button. Here is how the Density of disc material in terms of radial stress in a solid disc and outer radius of disc calculation can be explained with given input values -> 60.75796 = ((8*100)/((20^2)*(3+0.3)*((0.1^2)-(0.005^2)))).

FAQ

What is Density of disc material in terms of radial stress in a solid disc and outer radius of disc?
The Density of disc material in terms of radial stress in a solid disc and outer radius of disc 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*fr)/((ω^2)*(3+𝛎)*((R^2)-(r^2)))) or density = ((8*Radial Stress)/((Angular Velocity^2)*(3+Poisson's ratio)*((Outer Radius^2)-(Radius of element^2)))). Radial Stress induced by a bending moment in a member of constant cross section, 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, 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 0.25 and 0.35, Outer Radius is the radius of the larger of the two concentric circles that form its boundary and Radius of element is the radius of the element considered in the disc at radius r from the center.
How to calculate Density of disc material in terms of radial stress in a solid disc and outer radius of disc?
The Density of disc material in terms of radial stress in a solid disc and outer radius of disc 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 = ((8*Radial Stress)/((Angular Velocity^2)*(3+Poisson's ratio)*((Outer Radius^2)-(Radius of element^2)))). To calculate Density of disc material in terms of radial stress in a solid disc and outer radius of disc, you need Radial Stress (fr), Angular Velocity (ω), Poisson's ratio (𝛎), Outer Radius (R) and Radius of element (r). With our tool, you need to enter the respective value for Radial Stress, Angular Velocity, Poisson's ratio, Outer Radius and 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?
In this formula, Density uses Radial Stress, Angular Velocity, Poisson's ratio, Outer Radius and Radius of element. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • radial_stress = (Constant at boundary condition/2)-((Density*(Angular velocity^2)*(Radius^2)*(3+Poisson's ratio))/8)
  • constant_at_boundary_condition = 2*(Radial Stress+((Density*(Angular velocity^2)*(Radius^2)*(3+Poisson's ratio))/8))
  • density = (((Constant at boundary condition/2)-Radial Stress)*8)/((Angular velocity^2)*(Radius^2)*(3+Poisson's ratio))
  • angular_velocity_1 = sqrt((((Constant at boundary condition/2)-Radial Stress)*8)/(Density*(Radius^2)*(3+Poisson's ratio)))
  • radius = sqrt((((Constant at boundary condition/2)-Radial Stress)*8)/(Density*(Angular velocity^2)*(3+Poisson's ratio)))
  • poissons_ratio = ((((Constant at boundary condition/2)-Radial Stress)*8)/(Density*(Angular velocity^2)*(Radius^2)))-3
  • circumferential_stress = (Constant at boundary condition/2)-((Density*(Angular velocity^2)*(Radius^2)*((3*Poisson's ratio)+1))/8)
  • constant_at_boundary_condition = 2*(Circumferential stress+((Density*(Angular velocity^2)*(Radius^2)*((3*Poisson's ratio)+1))/8))
  • density = (((Constant at boundary condition/2)-Circumferential stress)*8)/((Angular velocity^2)*(Radius^2)*((3*Poisson's ratio)+1))
  • angular_velocity_1 = sqrt((((Constant at boundary condition/2)-Circumferential stress)*8)/(Density*(Radius^2)*((3*Poisson's ratio)+1)))
Where is the Density of disc material in terms of radial stress in a solid disc and outer radius of disc calculator used?
Among many, Density of disc material in terms of radial stress in a solid disc and outer radius of disc calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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