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Disc's Angular velocity given Circumferential stress 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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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{8 \cdot σ c}{(ρ) \cdot (((3 + 𝛎) \cdot {r outer}^{2}) - (1 + (3 \cdot 𝛎) \cdot r^{2}))}}

ω - Angular Velocity?σ_c - Circumferential Stress?ρ - Density Of Disc?𝛎 - Poisson's Ratio?r_outer - Outer Radius Disc?r - Radius of Element?

Disc's Angular velocity given Circumferential stress and Outer radius Example

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Here is how the Disc's Angular velocity given Circumferential stress and Outer radius equation looks like with Values.

Here is how the Disc's Angular velocity given Circumferential stress and Outer radius equation looks like with Units.

Here is how the Disc's Angular velocity given Circumferential stress and Outer radius equation looks like.

15.4627 = \sqrt{\frac{8 \cdot 100}{(2) \cdot (((3 + 0.3) \cdot 900^{2}) - (1 + (3 \cdot 0.3) \cdot 5^{2}))}}

15.4627rad/s = \sqrt{\frac{8 \cdot 100N/m²}{(2kg/m³) \cdot (((3 + 0.3) \cdot {900mm}^{2}) - (1 + (3 \cdot 0.3) \cdot {5mm}^{2}))}}

15.4627 = \sqrt{\frac{8 \cdot 100}{(2) \cdot (((3 + 0.3) \cdot 900^{2}) - (1 + (3 \cdot 0.3) \cdot 5^{2}))}}

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Disc's Angular velocity given Circumferential stress and Outer radius Solution

Follow our step by step solution on how to calculate Disc's Angular velocity given Circumferential stress and Outer radius?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

ω = \sqrt{\frac{8 \cdot 100N/m²}{(2kg/m³) \cdot (((3 + 0.3) \cdot {900mm}^{2}) - (1 + (3 \cdot 0.3) \cdot {5mm}^{2}))}}

Next Step Convert Units

∴

ω = \sqrt{\frac{8 \cdot 100Pa}{(2kg/m³) \cdot (((3 + 0.3) \cdot {0.9m}^{2}) - (1 + (3 \cdot 0.3) \cdot {0.005m}^{2}))}}

Next Step Prepare to Evaluate

∴

ω = \sqrt{\frac{8 \cdot 100}{(2) \cdot (((3 + 0.3) \cdot {0.9}^{2}) - (1 + (3 \cdot 0.3) \cdot {0.005}^{2}))}}

Next Step Evaluate

∴

ω = 15.4626863138159rad/s

LAST Step Rounding Answer

∴

ω = 15.4627rad/s

Disc's Angular velocity given Circumferential stress and Outer radius 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

Circumferential Stress

Circumferential Stress is the force over area exerted circumferentially perpendicular to the axis and the radius.

Symbol: σ_c

Measurement: StressUnit: N/m²

Note: Value should be greater than 0.

Formulas to find Circumferential 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

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

Outer Radius Disc

Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary.

Symbol: r_outer

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Outer Radius Disc

Radius of Element

The Radius of Element is the radius of the element considered in the disc at radius r from the centre.

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 Disc's Angular velocity given Circumferential stress and Outer radius?

Disc's Angular velocity given Circumferential stress and Outer radius evaluator uses 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)))) to evaluate the Angular Velocity, The Disc's Angular velocity given Circumferential stress 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 Disc's Angular velocity given Circumferential stress and Outer radius using this online evaluator? To use this online evaluator for Disc's Angular velocity given Circumferential stress and Outer radius, enter Circumferential Stress (σ_c), Density Of Disc (ρ), Poisson's Ratio (𝛎), Outer Radius Disc (r_outer) & Radius of Element (r) and hit the calculate button.

FAQs on Disc's Angular velocity given Circumferential stress and Outer radius

What is the formula to find Disc's Angular velocity given Circumferential stress and Outer radius?

The formula of Disc's Angular velocity given Circumferential stress and Outer radius is expressed as 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)))). Here is an example- 15.46269 = sqrt((8*100)/((2)*(((3+0.3)*0.9^2)-(1+(3*0.3)*0.005^2)))).

How to calculate Disc's Angular velocity given Circumferential stress and Outer radius?

With Circumferential Stress (σ_c), Density Of Disc (ρ), Poisson's Ratio (𝛎), Outer Radius Disc (r_outer) & Radius of Element (r) we can find Disc's Angular velocity given Circumferential stress and Outer radius using the formula - 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)))). 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 Disc's Angular velocity given Circumferential stress and Outer radius be negative?

No, the Disc's Angular velocity given Circumferential stress and Outer radius, measured in Angular Velocity cannot be negative.

Which unit is used to measure Disc's Angular velocity given Circumferential stress and Outer radius?

Disc's Angular velocity given Circumferential stress 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 Disc's Angular velocity given Circumferential stress and Outer radius can be measured.

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Disc's Angular velocity given Circumferential stress 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

Disc's Angular velocity given Circumferential stress and Outer radius Example

Disc's Angular velocity given Circumferential stress and Outer radius Solution

Disc's Angular velocity given Circumferential stress and Outer radius Formula Elements

Other Formulas to find Angular Velocity

How to Evaluate Disc's Angular velocity given Circumferential stress and Outer radius?

FAQs on Disc's Angular velocity given Circumferential stress 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