Angular Velocity of disc given Radial stress in solid disc Solution

STEP 0: Pre-Calculation Summary
Formula Used
Angular Velocity = sqrt((((Constant at boundary condition/2)-Radial Stress)*8)/(Density Of Disc*(Disc Radius^2)*(3+Poisson's Ratio)))
ω = sqrt((((C1/2)-σr)*8)/(ρ*(rdisc^2)*(3+𝛎)))
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.
Constant at boundary condition - Constant at boundary condition is value obtained for stress in solid disc.
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.
Disc Radius - (Measured in Meter) - Disc Radius is a radial line from the focus to any point of a curve.
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.
STEP 1: Convert Input(s) to Base Unit
Constant at boundary condition: 300 --> No Conversion Required
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
Disc Radius: 1000 Millimeter --> 1 Meter (Check conversion here)
Poisson's Ratio: 0.3 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ω = sqrt((((C1/2)-σr)*8)/(ρ*(rdisc^2)*(3+𝛎))) --> sqrt((((300/2)-100)*8)/(2*(1^2)*(3+0.3)))
Evaluating ... ...
ω = 7.78498944161523
STEP 3: Convert Result to Output's Unit
7.78498944161523 Radian per Second --> No Conversion Required
FINAL ANSWER
7.78498944161523 7.784989 Radian per Second <-- Angular Velocity
(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur
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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 Formula

Angular Velocity = sqrt((((Constant at boundary condition/2)-Radial Stress)*8)/(Density Of Disc*(Disc Radius^2)*(3+Poisson's Ratio)))
ω = sqrt((((C1/2)-σr)*8)/(ρ*(rdisc^2)*(3+𝛎)))

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?

Angular Velocity of disc given Radial stress in solid disc calculator uses Angular Velocity = sqrt((((Constant at boundary condition/2)-Radial Stress)*8)/(Density Of Disc*(Disc Radius^2)*(3+Poisson's Ratio))) to calculate the Angular Velocity, The Angular Velocity of disc given 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 is denoted by ω symbol.

How to calculate Angular Velocity of disc given Radial stress in solid disc using this online calculator? To use this online calculator for Angular Velocity of disc given Radial stress in solid disc, enter Constant at boundary condition (C1), Radial Stress r), Density Of Disc (ρ), Disc Radius (rdisc) & Poisson's Ratio (𝛎) and hit the calculate button. Here is how the Angular Velocity of disc given Radial stress in solid disc calculation can be explained with given input values -> 7.784989 = sqrt((((300/2)-100)*8)/(2*(1^2)*(3+0.3))).

FAQ

What is Angular Velocity of disc given Radial stress in solid disc?
The Angular Velocity of disc given 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((((C1/2)-σr)*8)/(ρ*(rdisc^2)*(3+𝛎))) or Angular Velocity = sqrt((((Constant at boundary condition/2)-Radial Stress)*8)/(Density Of Disc*(Disc Radius^2)*(3+Poisson's Ratio))). Constant at boundary condition is value obtained for stress in solid disc, 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, Disc Radius is a radial line from the focus to any point of a curve & 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.
How to calculate Angular Velocity of disc given Radial stress in solid disc?
The Angular Velocity of disc given 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 = sqrt((((Constant at boundary condition/2)-Radial Stress)*8)/(Density Of Disc*(Disc Radius^2)*(3+Poisson's Ratio))). To calculate Angular Velocity of disc given Radial stress in solid disc, you need Constant at boundary condition (C1), Radial Stress r), Density Of Disc (ρ), Disc Radius (rdisc) & Poisson's Ratio (𝛎). With our tool, you need to enter the respective value for Constant at boundary condition, Radial Stress, Density Of Disc, Disc Radius & Poisson's Ratio 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 Constant at boundary condition, Radial Stress, Density Of Disc, Disc Radius & Poisson's Ratio. 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((8*Radial Stress)/(Density Of Disc*(3+Poisson's Ratio)*((Outer Radius Disc^2)-(Radius of Element^2))))
  • 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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