Angular velocity of disc given Radial stress in solid disc and Outer radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Angular Velocity = sqrt((8*Radial Stress)/(Density Of Disc*(3+Poisson's Ratio)*((Outer Radius Disc^2)-(Radius of Element^2))))
ω = sqrt((8*σr)/(ρ*(3+𝛎)*((router^2)-(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) - 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.
Radial Stress - (Measured in Pascal) - Radial Stress induced by a bending moment in a member of constant cross section.
Density Of Disc - (Measured in Kilogram per Cubic Meter) - Density Of Disc shows the denseness of disc in a specific given area. This is taken as mass per unit volume of a given disc.
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 0.1 and 0.5.
Outer Radius Disc - (Measured in Meter) - Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary.
Radius of Element - (Measured in Meter) - The Radius of Element is the radius of the element considered in the disc at radius r from the centre.
STEP 1: Convert Input(s) to Base Unit
Radial 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*σr)/(ρ*(3+𝛎)*((router^2)-(r^2)))) --> sqrt((8*100)/(2*(3+0.3)*((0.9^2)-(0.005^2))))
Evaluating ... ...
ω = 12.2331195077914
STEP 3: Convert Result to Output's Unit
12.2331195077914 Radian per Second --> No Conversion Required
FINAL ANSWER
12.2331195077914 12.23312 Radian per Second <-- Angular Velocity
(Calculation completed in 00.004 seconds)

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9 Angular Velocity of Disc Calculators

Disc's Angular velocity given Circumferential stress and Outer radius
Go 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))))
Angular velocity of disc given Circumferential stress in solid disc
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 Radial stress in solid disc
Go Angular Velocity = sqrt((((Constant at boundary condition/2)-Radial Stress)*8)/(Density Of Disc*(Disc Radius^2)*(3+Poisson's Ratio)))
Angular velocity of disc given Radial stress in solid disc and Outer radius
Go Angular Velocity = sqrt((8*Radial Stress)/(Density Of Disc*(3+Poisson's Ratio)*((Outer Radius Disc^2)-(Radius of Element^2))))
Angular velocity of disc given Constant at boundary condition for circular disc
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
Go Angular Velocity = sqrt((8*Circumferential Stress)/(Density Of Disc*(3+Poisson's Ratio)*(Outer Radius Disc^2)))
Disc's angular velocity given maximum circumferential stress in solid disc
Go Angular Velocity = sqrt((8*Circumferential Stress)/(Density Of Disc*(3+Poisson's Ratio)*(Outer Radius Disc^2)))
Angular velocity of disc given Radial stress at center of solid disc
Go Angular Velocity = sqrt((8*Radial Stress)/(Density Of Disc*(3+Poisson's Ratio)*(Outer Radius Disc^2)))
Angular velocity of disc given maximum radial stress
Go Angular Velocity = sqrt((8*Radial Stress)/(Density Of Disc*(3+Poisson's Ratio)*(Outer Radius Disc^2)))

Angular velocity of disc given Radial stress in solid disc and Outer radius Formula

Angular Velocity = sqrt((8*Radial Stress)/(Density Of Disc*(3+Poisson's Ratio)*((Outer Radius Disc^2)-(Radius of Element^2))))
ω = sqrt((8*σr)/(ρ*(3+𝛎)*((router^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 given Radial stress in solid disc and Outer radius?

Angular velocity of disc given Radial stress in solid disc and Outer radius calculator uses Angular Velocity = sqrt((8*Radial Stress)/(Density Of Disc*(3+Poisson's Ratio)*((Outer Radius Disc^2)-(Radius of Element^2)))) to calculate the Angular Velocity, The Angular velocity of disc given Radial stress in solid disc 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 Angular velocity of disc given Radial stress in solid disc and Outer radius using this online calculator? To use this online calculator for Angular velocity of disc given Radial stress in solid disc and Outer radius, enter Radial Stress r), Density Of Disc (ρ), Poisson's Ratio (𝛎), Outer Radius Disc (router) & Radius of Element (r) and hit the calculate button. Here is how the Angular velocity of disc given Radial stress in solid disc and Outer radius calculation can be explained with given input values -> 12.23312 = sqrt((8*100)/(2*(3+0.3)*((0.9^2)-(0.005^2)))).

FAQ

What is Angular velocity of disc given Radial stress in solid disc and Outer radius?
The Angular velocity of disc given Radial stress in solid disc 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*σr)/(ρ*(3+𝛎)*((router^2)-(r^2)))) or Angular Velocity = sqrt((8*Radial Stress)/(Density Of Disc*(3+Poisson's Ratio)*((Outer Radius Disc^2)-(Radius of Element^2)))). Radial Stress induced by a bending moment in a member of constant cross section, Density Of Disc shows the denseness of disc in a specific given area. This is taken as mass per unit volume of a given disc, 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 0.1 and 0.5, Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary & The Radius of Element is the radius of the element considered in the disc at radius r from the centre.
How to calculate Angular velocity of disc given Radial stress in solid disc and Outer radius?
The Angular velocity of disc given Radial stress in solid disc 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*Radial Stress)/(Density Of Disc*(3+Poisson's Ratio)*((Outer Radius Disc^2)-(Radius of Element^2)))). To calculate Angular velocity of disc given Radial stress in solid disc and Outer radius, you need Radial Stress r), Density Of Disc (ρ), Poisson's Ratio (𝛎), Outer Radius Disc (router) & Radius of Element (r). With our tool, you need to enter the respective value for Radial 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 Radial Stress, Density Of Disc, Poisson's Ratio, Outer Radius Disc & Radius of Element. We can use 8 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)))
  • Angular Velocity = sqrt((8*Radial Stress)/(Density Of Disc*(3+Poisson's Ratio)*(Outer Radius Disc^2)))
  • Angular Velocity = sqrt((8*Radial Stress)/(Density Of Disc*(3+Poisson's Ratio)*(Outer Radius Disc^2)))
  • Angular Velocity = sqrt((((Constant at boundary condition/2)-Radial Stress)*8)/(Density Of Disc*(Disc Radius^2)*(3+Poisson's Ratio)))
  • 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))))
  • Angular Velocity = sqrt((8*Circumferential Stress)/(Density Of Disc*(3+Poisson's Ratio)*(Outer Radius Disc^2)))
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