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Angular Velocity of disc given Radial stress in solid disc Formula

GoAngular Velocity of disc given Circumferential stress at center of solid disc Formula

GoAngular velocity of disc given Circumferential stress in solid disc Formula

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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. Check FAQs

ω = \sqrt{\frac{((\frac{C 1}{2}) - σ r) \cdot 8}{ρ \cdot ({r disc}^{2}) \cdot (3 + 𝛎)}}

ω - Angular Velocity?C₁ - Constant at boundary condition?σ_r - Radial Stress?ρ - Density Of Disc?r_disc - Disc Radius?𝛎 - Poisson's Ratio?

Angular Velocity of disc given Radial stress in solid disc Example

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Here is how the Angular Velocity of disc given Radial stress in solid disc equation looks like with Values.

Here is how the Angular Velocity of disc given Radial stress in solid disc equation looks like with Units.

Here is how the Angular Velocity of disc given Radial stress in solid disc equation looks like.

7.785 = \sqrt{\frac{((\frac{300}{2}) - 100) \cdot 8}{2 \cdot (1000^{2}) \cdot (3 + 0.3)}}

7.785rad/s = \sqrt{\frac{((\frac{300}{2}) - 100N/m²) \cdot 8}{2kg/m³ \cdot ({1000mm}^{2}) \cdot (3 + 0.3)}}

7.785 = \sqrt{\frac{((\frac{300}{2}) - 100) \cdot 8}{2 \cdot (1000^{2}) \cdot (3 + 0.3)}}

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Angular Velocity of disc given Radial stress in solid disc Solution

Follow our step by step solution on how to calculate Angular Velocity of disc given Radial stress in solid disc?

FIRST Step Consider the formula

ω = \sqrt{\frac{((\frac{C 1}{2}) - σ r) \cdot 8}{ρ \cdot ({r disc}^{2}) \cdot (3 + 𝛎)}}

Next Step Substitute values of Variables

∴

ω = \sqrt{\frac{((\frac{300}{2}) - 100N/m²) \cdot 8}{2kg/m³ \cdot ({1000mm}^{2}) \cdot (3 + 0.3)}}

Next Step Convert Units

∴

ω = \sqrt{\frac{((\frac{300}{2}) - 100Pa) \cdot 8}{2kg/m³ \cdot ({1m}^{2}) \cdot (3 + 0.3)}}

Next Step Prepare to Evaluate

∴

ω = \sqrt{\frac{((\frac{300}{2}) - 100) \cdot 8}{2 \cdot (1^{2}) \cdot (3 + 0.3)}}

Next Step Evaluate

∴

ω = 7.78498944161523rad/s

LAST Step Rounding Answer

∴

ω = 7.785rad/s

Angular Velocity of disc given Radial stress in solid disc Formula Elements

Variables

Functions

Angular Velocity

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.

Symbol: ω

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Angular Velocity

Constant at boundary condition

Constant at boundary condition is value obtained for stress in solid disc.

Symbol: C₁

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Constant at boundary condition

Radial Stress

Radial Stress induced by a bending moment in a member of constant cross section.

Symbol: σ_r

Measurement: PressureUnit: N/m²

Note: Value should be greater than 0.

Formulas to find Radial Stress

Density Of Disc

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.

Symbol: ρ

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Density Of Disc

Disc Radius

Disc Radius is a radial line from the focus to any point of a curve.

Symbol: r_disc

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Disc Radius

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.

Symbol: 𝛎

Measurement: NAUnit: Unitless

Note: Value should be between -1 to 10.

Formulas to find Poisson's Ratio

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.

Syntax: sqrt(Number)

Other Formulas to find Angular Velocity

Go Angular Velocity of disc given Circumferential stress at center of solid disc

ω = \sqrt{\frac{8 \cdot σ c}{ρ \cdot (3 + 𝛎) \cdot ({r outer}^{2})}}

Go Angular velocity of disc given Circumferential stress in solid disc

ω = \sqrt{\frac{((\frac{C 1}{2}) - σ c) \cdot 8}{ρ \cdot ({r disc}^{2}) \cdot ((3 \cdot 𝛎) + 1)}}

Go Angular velocity of disc given Constant at boundary condition for circular disc

ω = \sqrt{\frac{8 \cdot C 1}{ρ \cdot ({r outer}^{2}) \cdot (3 + 𝛎)}}

Go Angular velocity of disc given maximum radial stress

ω = \sqrt{\frac{8 \cdot σ r}{ρ \cdot (3 + 𝛎) \cdot ({r outer}^{2})}}

How to Evaluate Angular Velocity of disc given Radial stress in solid disc?

Angular Velocity of disc given Radial stress in solid disc evaluator uses Angular Velocity = sqrt((((Constant at boundary condition/2)-Radial Stress)*8)/(Density Of Disc*(Disc Radius^2)*(3+Poisson's Ratio))) to evaluate 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 evaluate Angular Velocity of disc given Radial stress in solid disc using this online evaluator? To use this online evaluator 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.

FAQs on Angular Velocity of disc given Radial stress in solid disc

What is the formula to find Angular Velocity of disc given Radial stress in solid disc?

The formula of Angular Velocity of disc given Radial stress in solid disc is expressed as Angular Velocity = sqrt((((Constant at boundary condition/2)-Radial Stress)*8)/(Density Of Disc*(Disc Radius^2)*(3+Poisson's Ratio))). Here is an example- 7.784989 = sqrt((((300/2)-100)*8)/(2*(1^2)*(3+0.3))).

How to calculate Angular Velocity of disc given Radial stress in solid disc?

With Constant at boundary condition (C₁), Radial Stress (σ_r), Density Of Disc (ρ), Disc Radius (r_disc) & Poisson's Ratio (𝛎) we can find Angular Velocity of disc given Radial stress in solid disc using the formula - Angular Velocity = sqrt((((Constant at boundary condition/2)-Radial Stress)*8)/(Density Of Disc*(Disc Radius^2)*(3+Poisson's Ratio))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Angular Velocity?

Here are the different ways to Calculate Angular Velocity-

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)))

Can the Angular Velocity of disc given Radial stress in solid disc be negative?

No, the Angular Velocity of disc given Radial stress in solid disc, measured in Angular Velocity cannot be negative.

Which unit is used to measure Angular Velocity of disc given Radial stress in solid disc?

Angular Velocity of disc given Radial stress in solid disc is usually measured using the Radian per Second[rad/s] for Angular Velocity. Radian per Day[rad/s], Radian per Hour[rad/s], Radian per Minute[rad/s] are the few other units in which Angular Velocity of disc given Radial stress in solid disc can be measured.

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Angular Velocity of disc given Radial stress in solid disc Formula

​GoAngular Velocity of disc given Circumferential stress at center of solid disc Formula

​GoAngular velocity of disc given Circumferential stress in solid disc Formula

Angular Velocity of disc given Radial stress in solid disc Example

Angular Velocity of disc given Radial stress in solid disc Solution

Angular Velocity of disc given Radial stress in solid disc Formula Elements

Other Formulas to find Angular Velocity

How to Evaluate Angular Velocity of disc given Radial stress in solid disc?

FAQs on Angular Velocity of disc given Radial stress in solid disc

Variable Name

GoAngular Velocity of disc given Circumferential stress at center of solid disc Formula

GoAngular velocity of disc given Circumferential stress in solid disc Formula