Credits

National Institute Of Technology (NIT), Hamirpur
Anshika Arya has created this Calculator and 1000+ more calculators!
Birsa Institute of Technology (BIT), Sindri
Payal Priya has verified this Calculator and 1000+ more calculators!

Angular velocity of disc in terms of maximum radial stress in solid disc Solution

STEP 0: Pre-Calculation Summary
Formula Used
angular_velocity_1 = sqrt((8*Radial Stress)/(Density*(3+Poisson's ratio)*(Outer Radius^2)))
ω = sqrt((8*fr)/(ρ*(3+𝛎)*(R^2)))
This formula uses 1 Functions, 4 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)
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)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ω = sqrt((8*fr)/(ρ*(3+𝛎)*(R^2))) --> sqrt((8*100)/(997*(3+0.3)*(0.1^2)))
Evaluating ... ...
ω = 4.93106178763608
STEP 3: Convert Result to Output's Unit
4.93106178763608 --> No Conversion Required
FINAL ANSWER
4.93106178763608 <-- Angular velocity
(Calculation completed in 00.053 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 maximum radial stress in solid disc Formula

angular_velocity_1 = sqrt((8*Radial Stress)/(Density*(3+Poisson's ratio)*(Outer Radius^2)))
ω = sqrt((8*fr)/(ρ*(3+𝛎)*(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 maximum radial stress in solid disc?

Angular velocity of disc in terms of maximum radial stress in solid disc calculator uses angular_velocity_1 = sqrt((8*Radial Stress)/(Density*(3+Poisson's ratio)*(Outer Radius^2))) to calculate the Angular velocity, The Angular velocity of disc in terms of maximum radial stress in solid 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 maximum radial stress in solid disc using this online calculator? To use this online calculator for Angular velocity of disc in terms of maximum radial stress in solid disc, enter Radial Stress (fr), Density (ρ), Poisson's ratio (𝛎) and Outer Radius (R) and hit the calculate button. Here is how the Angular velocity of disc in terms of maximum radial stress in solid disc calculation can be explained with given input values -> 4.931062 = sqrt((8*100)/(997*(3+0.3)*(0.1^2))).

FAQ

What is Angular velocity of disc in terms of maximum radial stress in solid disc?
The Angular velocity of disc in terms of maximum radial stress in solid 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))) or angular_velocity_1 = sqrt((8*Radial Stress)/(Density*(3+Poisson's ratio)*(Outer Radius^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 and Outer Radius is the radius of the larger of the two concentric circles that form its boundary.
How to calculate Angular velocity of disc in terms of maximum radial stress in solid disc?
The Angular velocity of disc in terms of maximum radial stress in solid 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))). To calculate Angular velocity of disc in terms of maximum radial stress in solid disc, you need Radial Stress (fr), Density (ρ), Poisson's ratio (𝛎) and Outer Radius (R). With our tool, you need to enter the respective value for Radial Stress, Density, Poisson's ratio and Outer Radius 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 and Outer Radius. 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 Angular velocity of disc in terms of maximum radial stress in solid disc calculator used?
Among many, Angular velocity of disc in terms of maximum radial stress in solid disc calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
{FormulaExamplesList}
Share Image
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!