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## Credits

National Institute Of Technology (NIT), Hamirpur
Anshika Arya has created this Calculator and 1000+ more calculators!
Birsa Institute of Technology (BIT), Sindri
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## Angular velocity of disc in terms of radial stress in a solid disc and outer radius of disc Solution

STEP 0: Pre-Calculation Summary
Formula Used
angular_velocity_1 = sqrt((8*Radial Stress)/(Density*(3+Poisson's ratio)*((Outer Radius^2)-(Radius of element^2))))
ω = sqrt((8*fr)/(ρ*(3+𝛎)*((R^2)-(r^2))))
This formula uses 1 Functions, 5 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Radial Stress - Radial Stress induced by a bending moment in a member of constant cross section. (Measured in Pascal)
Density - The density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object. (Measured in Kilogram per Meter³)
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
Density: 997 Kilogram per Meter³ --> 997 Kilogram per Meter³ 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
ω = sqrt((8*fr)/(ρ*(3+𝛎)*((R^2)-(r^2)))) --> sqrt((8*100)/(997*(3+0.3)*((0.1^2)-(0.005^2))))
Evaluating ... ...
ω = 4.93723719617692
STEP 3: Convert Result to Output's Unit
4.93723719617692 --> No Conversion Required
FINAL ANSWER
4.93723719617692 <-- Angular velocity
(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

### Angular velocity of disc in terms of radial stress in a solid disc and outer radius of disc Formula

angular_velocity_1 = sqrt((8*Radial Stress)/(Density*(3+Poisson's ratio)*((Outer Radius^2)-(Radius of element^2))))
ω = sqrt((8*fr)/(ρ*(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 Angular velocity of disc in terms of radial stress in a solid disc and outer radius of disc?

Angular velocity of disc in terms of radial stress in a solid disc and outer radius of disc calculator uses angular_velocity_1 = sqrt((8*Radial Stress)/(Density*(3+Poisson's ratio)*((Outer Radius^2)-(Radius of element^2)))) to calculate the Angular velocity, The Angular velocity of disc in terms of radial stress in a solid disc and outer radius of disc formula is defined as a pseudovector, with its magnitude measuring the angular speed, the rate at which an object rotates or revolves. Angular velocity and is denoted by ω symbol.

How to calculate Angular velocity of disc in terms of radial stress in a solid disc and outer radius of disc using this online calculator? To use this online calculator for Angular velocity of disc in terms of radial stress in a solid disc and outer radius of disc, enter Radial Stress (fr), Density (ρ), Poisson's ratio (𝛎), Outer Radius (R) and Radius of element (r) and hit the calculate button. Here is how the Angular velocity of disc in terms of radial stress in a solid disc and outer radius of disc calculation can be explained with given input values -> 4.937237 = sqrt((8*100)/(997*(3+0.3)*((0.1^2)-(0.005^2)))).

### FAQ

What is Angular velocity of disc in terms of radial stress in a solid disc and outer radius of disc?
The Angular velocity of disc in terms of radial stress in a solid disc and outer radius of disc 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*fr)/(ρ*(3+𝛎)*((R^2)-(r^2)))) or angular_velocity_1 = sqrt((8*Radial Stress)/(Density*(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 density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object, 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 Angular velocity of disc in terms of radial stress in a solid disc and outer radius of disc?
The Angular velocity of disc in terms of radial stress in a solid disc and outer radius of disc 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_1 = sqrt((8*Radial Stress)/(Density*(3+Poisson's ratio)*((Outer Radius^2)-(Radius of element^2)))). To calculate Angular velocity of disc in terms of radial stress in a solid disc and outer radius of disc, you need Radial Stress (fr), Density (ρ), 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, Density, 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 Angular velocity?
In this formula, Angular velocity uses Radial Stress, Density, 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)))
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