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Angular velocity of disc given Radial stress in solid disc and Outer radius 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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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. Check FAQs

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

ω - Angular Velocity?σ_r - Radial Stress?ρ - Density Of Disc?𝛎 - Poisson's Ratio?r_outer - Outer Radius Disc?R - Radius of Element?

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

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Here is how the Angular velocity of disc given Radial stress in solid disc and Outer radius equation looks like with Values.

Here is how the Angular velocity of disc given Radial stress in solid disc and Outer radius equation looks like with Units.

Here is how the Angular velocity of disc given Radial stress in solid disc and Outer radius equation looks like.

12.2331 = \sqrt{\frac{8 \cdot 100}{2 \cdot (3 + 0.3) \cdot ((900^{2}) - (5^{2}))}}

12.2331rad/s = \sqrt{\frac{8 \cdot 100N/m²}{2kg/m³ \cdot (3 + 0.3) \cdot (({900mm}^{2}) - ({5mm}^{2}))}}

12.2331 = \sqrt{\frac{8 \cdot 100}{2 \cdot (3 + 0.3) \cdot ((900^{2}) - (5^{2}))}}

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

Follow our step by step solution on how to calculate Angular velocity of disc given Radial stress in solid disc and Outer radius?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

ω = \sqrt{\frac{8 \cdot 100N/m²}{2kg/m³ \cdot (3 + 0.3) \cdot (({900mm}^{2}) - ({5mm}^{2}))}}

Next Step Convert Units

∴

ω = \sqrt{\frac{8 \cdot 100Pa}{2kg/m³ \cdot (3 + 0.3) \cdot (({0.9m}^{2}) - ({0.005m}^{2}))}}

Next Step Prepare to Evaluate

∴

ω = \sqrt{\frac{8 \cdot 100}{2 \cdot (3 + 0.3) \cdot (({0.9}^{2}) - ({0.005}^{2}))}}

Next Step Evaluate

∴

ω = 12.2331195077914rad/s

LAST Step Rounding Answer

∴

ω = 12.2331rad/s

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

Variables

Functions

Angular Velocity

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.

Symbol: ω

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Angular Velocity

Radial Stress

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.

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 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.

Symbol: ρ

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Density Of Disc

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.

Symbol: 𝛎

Measurement: NAUnit: Unitless

Note: Value should be between -1 to 10.

Formulas to find Poisson's Ratio

Outer Radius Disc

Outer radius disc is the distance from the center of the disc to its outer edge or boundary.

Symbol: r_outer

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Outer Radius Disc

Radius of Element

Radius of element often referred to as the atomic radius, is a measure of the size of an atom, typically defined as the distance from the center of the nucleus to the outermost shell of electrons.

Symbol: R

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Element

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 and Outer radius?

Angular velocity of disc given Radial stress in solid disc and Outer radius evaluator uses Angular Velocity = sqrt((8*Radial Stress)/(Density Of Disc*(3+Poisson's Ratio)*((Outer Radius Disc^2)-(Radius of Element^2)))) to evaluate 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 evaluate Angular velocity of disc given Radial stress in solid disc and Outer radius using this online evaluator? To use this online evaluator for Angular velocity of disc given Radial stress in solid disc and Outer radius, enter Radial Stress (σ_r), Density Of Disc (ρ), Poisson's Ratio (𝛎), Outer Radius Disc (r_outer) & Radius of Element (R) and hit the calculate button.

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

What is the formula to find Angular velocity of disc given Radial stress in solid disc and Outer radius?

The formula of Angular velocity of disc given Radial stress in solid disc and Outer radius is expressed as Angular Velocity = sqrt((8*Radial Stress)/(Density Of Disc*(3+Poisson's Ratio)*((Outer Radius Disc^2)-(Radius of Element^2)))). Here is an example- 12.23312 = sqrt((8*100)/(2*(3+0.3)*((0.9^2)-(0.005^2)))).

How to calculate Angular velocity of disc given Radial stress in solid disc and Outer radius?

With Radial Stress (σ_r), Density Of Disc (ρ), Poisson's Ratio (𝛎), Outer Radius Disc (r_outer) & Radius of Element (R) we can find Angular velocity of disc given Radial stress in solid disc and Outer radius using the formula - Angular Velocity = sqrt((8*Radial Stress)/(Density Of Disc*(3+Poisson's Ratio)*((Outer Radius Disc^2)-(Radius of Element^2)))). 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 and Outer radius be negative?

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

Which unit is used to measure 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 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 and Outer radius can be measured.

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

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

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

Other Formulas to find Angular Velocity

How to Evaluate Angular velocity of disc given Radial stress in solid disc and Outer radius?

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

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