Angular Velocity of disc given Radial stress in solid disc Calculator

✖Constant at boundary condition is a type of boundary condition used in mathematical and physical problems where a specific variable is held constant along the boundary of the domain.ⓘ Constant at Boundary Condition [C₁]			+10% -10%
✖Radial stress refers to the stress that acts perpendicular to the longitudinal axis of a component, directed either towards or away from the central axis.ⓘ Radial Stress [σ_r]			+10% -10%
✖Density of disc typically refers to the mass per unit volume of the disc material. It is a measure of how much mass is contained in a given volume of the disc.ⓘ Density Of Disc [ρ]			+10% -10%
✖Disc radius is the distance from the center of the disc to any point on its circumference.ⓘ Disc Radius [r_disc]			+10% -10%
✖Poisson's ratio is a measure of the deformation of a material in directions perpendicular to the direction of loading. It is defined as the negative ratio of transverse strain to axial strain.ⓘ Poisson's Ratio [𝛎]			+10% -10%

✖Angular velocity is a measure of how quickly an object rotates or revolves around a central point or axis, describes the rate of change of the angular position of the object with respect to time.ⓘ Angular Velocity of disc given Radial stress in solid disc [ω]

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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)-σ_r)*8)/(ρ*(r_disc^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) - Angular velocity is a measure of how quickly an object rotates or revolves around a central point or axis, describes the rate of change of the angular position of the object with respect to time.
Constant at Boundary Condition - Constant at boundary condition is a type of boundary condition used in mathematical and physical problems where a specific variable is held constant along the boundary of the domain.
Radial Stress - (Measured in Pascal) - Radial stress refers to the stress that acts perpendicular to the longitudinal axis of a component, directed either towards or away from the central axis.
Density Of Disc - (Measured in Kilogram per Cubic Meter) - Density of disc typically refers to the mass per unit volume of the disc material. It is a measure of how much mass is contained in a given volume of the disc.
Disc Radius - (Measured in Meter) - Disc radius is the distance from the center of the disc to any point on its circumference.
Poisson's Ratio - Poisson's ratio is a measure of the deformation of a material in directions perpendicular to the direction of loading. It is defined as the negative ratio of transverse strain to axial strain.

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)-σ_r)*8)/(ρ*(r_disc^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 00.020 seconds)

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Home » Physics » Strength of Materials » Rotating Disc And Cylinder » Expression for Stresses in Solid Disc » Mechanical » Angular Velocity of Disc » Angular Velocity of disc given Radial stress in solid disc

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Birsa Institute of Technology (BIT), Sindri

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< Angular Velocity of Disc Calculators

Angular velocity of disc given Circumferential stress in solid disc

LaTeX 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 Constant at boundary condition for circular disc

LaTeX 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

LaTeX Go Angular Velocity = sqrt((8*Circumferential Stress)/(Density Of Disc*(3+Poisson's Ratio)*(Outer Radius Disc^2)))

Angular velocity of disc given maximum radial stress

LaTeX 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

LaTeX Go

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)-σ_r)*8)/(ρ*(r_disc^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 (σ_r), Density Of Disc (ρ), Disc Radius (r_disc) & 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)-σ_r)*8)/(ρ*(r_disc^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 a type of boundary condition used in mathematical and physical problems where a specific variable is held constant along the boundary of the domain, Radial stress refers to the stress that acts perpendicular to the longitudinal axis of a component, directed either towards or away from the central axis, Density of disc typically refers to the mass per unit volume of the disc material. It is a measure of how much mass is contained in a given volume of the disc, Disc radius is the distance from the center of the disc to any point on its circumference & Poisson's ratio is a measure of the deformation of a material in directions perpendicular to the direction of loading. It is defined as the negative ratio of transverse strain to axial strain.

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 (σ_r), Density Of Disc (ρ), Disc Radius (r_disc) & 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 3 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)))

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