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Angular Velocity of Driven Shaft Formula

GoAngular Velocity of Driving Shaft given Angular Acceleration of Driven Shaft Formula

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Angular Velocity of Driven Shaft is the angular displacement of the driven shaft in a given unit of time. Check FAQs

ω B = (\frac{\cos (α)}{1 - {(\cos (θ))}^{2} \cdot {(\sin (α))}^{2}}) \cdot ω A

ω_B - Angular Velocity of Driven Shaft?α - Angle Between Driving And Driven Shafts?θ - Angle Rotated By Driving Shaft?ω_A - Angular Velocity of Driving Shaft?

Angular Velocity of Driven Shaft Example

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Here is how the Angular Velocity of Driven Shaft equation looks like with Values.

Here is how the Angular Velocity of Driven Shaft equation looks like with Units.

Here is how the Angular Velocity of Driven Shaft equation looks like.

62.3806 = (\frac{\cos (5)}{1 - {(\cos (60))}^{2} \cdot {(\sin (5))}^{2}}) \cdot 62.5

62.3806rad/s = (\frac{\cos (5°)}{1 - {(\cos (60°))}^{2} \cdot {(\sin (5°))}^{2}}) \cdot 62.5rad/s

62.3806 = (\frac{\cos (5)}{1 - {(\cos (60))}^{2} \cdot {(\sin (5))}^{2}}) \cdot 62.5

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Angular Velocity of Driven Shaft Solution

Follow our step by step solution on how to calculate Angular Velocity of Driven Shaft?

FIRST Step Consider the formula

ω B = (\frac{\cos (α)}{1 - {(\cos (θ))}^{2} \cdot {(\sin (α))}^{2}}) \cdot ω A

Next Step Substitute values of Variables

∴

ω B = (\frac{\cos (5°)}{1 - {(\cos (60°))}^{2} \cdot {(\sin (5°))}^{2}}) \cdot 62.5rad/s

Next Step Convert Units

∴

ω B = (\frac{\cos (0.0873rad)}{1 - {(\cos (1.0472rad))}^{2} \cdot {(\sin (0.0873rad))}^{2}}) \cdot 62.5rad/s

Next Step Prepare to Evaluate

∴

ω B = (\frac{\cos (0.0873)}{1 - {(\cos (1.0472))}^{2} \cdot {(\sin (0.0873))}^{2}}) \cdot 62.5

Next Step Evaluate

∴

ω B = 62.3806313756233rad/s

LAST Step Rounding Answer

∴

ω B = 62.3806rad/s

Angular Velocity of Driven Shaft Formula Elements

Variables

Functions

Angular Velocity of Driven Shaft

Angular Velocity of Driven Shaft is the angular displacement of the driven shaft in a given unit of time.

Symbol: ω_B

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Angular Velocity of Driven Shaft

Angle Between Driving And Driven Shafts

Angle Between Driving And Driven Shafts is the inclination of the driven shaft with respect to the driving shaft.

Symbol: α

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle Between Driving And Driven Shafts

Angle Rotated By Driving Shaft

Angle Rotated By Driving Shaft is the angular displacement of the the driving shaft.

Symbol: θ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle Rotated By Driving Shaft

Angular Velocity of Driving Shaft

Angular Velocity of Driving Shaft is the angular displacement of the driving shaft in a given unit of time.

Symbol: ω_A

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Angular Velocity of Driving Shaft

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other Formulas to find Angular Velocity of Driven Shaft

Go Angular Velocity of Driving Shaft given Angular Acceleration of Driven Shaft

ω B = \sqrt{\frac{α B \cdot {(1 - {\cos (Φ)}^{2} \cdot {\sin (α)}^{2})}^{2}}{\cos (α) \cdot {\sin (α)}^{2} \cdot \sin (2 \cdot Φ)}}

Other formulas in Driveline category

Go Velocity Ratio of Hooke's Joint

V = \frac{\cos (α)}{1 - {\cos (θ)}^{2} \cdot {\sin (α)}^{2}}

Go Angular Acceleration of Driven Shaft

α B = - {ω B}^{2} \cdot \cos (α) \cdot {\sin (α)}^{2} \cdot \frac{\sin (2 \cdot Φ)}{{(1 - {\cos (Φ)}^{2} \cdot {\sin (α)}^{2})}^{2}}

Go Axial Force of Multiplate Clutch using Uniform Wear Theory

F a = π \cdot p \cdot D i \cdot (D o - D i) \cdot 0.5

Go Gear Step

φ = \frac{i n-1}{i n}

How to Evaluate Angular Velocity of Driven Shaft?

Angular Velocity of Driven Shaft evaluator uses Angular Velocity of Driven Shaft = (cos(Angle Between Driving And Driven Shafts)/(1-(cos(Angle Rotated By Driving Shaft))^2*(sin(Angle Between Driving And Driven Shafts))^2))*Angular Velocity of Driving Shaft to evaluate the Angular Velocity of Driven Shaft, The Angular velocity of driven shaft formula is used to find the rate of angular displacement of the driven shaft. Angular Velocity of Driven Shaft is denoted by ω_B symbol.

How to evaluate Angular Velocity of Driven Shaft using this online evaluator? To use this online evaluator for Angular Velocity of Driven Shaft, enter Angle Between Driving And Driven Shafts (α), Angle Rotated By Driving Shaft (θ) & Angular Velocity of Driving Shaft (ω_A) and hit the calculate button.

FAQs on Angular Velocity of Driven Shaft

What is the formula to find Angular Velocity of Driven Shaft?

The formula of Angular Velocity of Driven Shaft is expressed as Angular Velocity of Driven Shaft = (cos(Angle Between Driving And Driven Shafts)/(1-(cos(Angle Rotated By Driving Shaft))^2*(sin(Angle Between Driving And Driven Shafts))^2))*Angular Velocity of Driving Shaft. Here is an example- 62.38063 = (cos(0.0872664625997001)/(1-(cos(1.0471975511964))^2*(sin(0.0872664625997001))^2))*62.5.

How to calculate Angular Velocity of Driven Shaft?

With Angle Between Driving And Driven Shafts (α), Angle Rotated By Driving Shaft (θ) & Angular Velocity of Driving Shaft (ω_A) we can find Angular Velocity of Driven Shaft using the formula - Angular Velocity of Driven Shaft = (cos(Angle Between Driving And Driven Shafts)/(1-(cos(Angle Rotated By Driving Shaft))^2*(sin(Angle Between Driving And Driven Shafts))^2))*Angular Velocity of Driving Shaft. This formula also uses Sine (sin), Cosine (cos) function(s).

What are the other ways to Calculate Angular Velocity of Driven Shaft?

Here are the different ways to Calculate Angular Velocity of Driven Shaft-

Angular Velocity of Driven Shaft=sqrt((Angular Acceleration of Driven Shaft*(1-cos(Angle Rotated By Driven Shaft)^2*sin(Angle Between Driving And Driven Shafts)^2)^2)/(cos(Angle Between Driving And Driven Shafts)*sin(Angle Between Driving And Driven Shafts)^2*sin(2*Angle Rotated By Driven Shaft)))

Can the Angular Velocity of Driven Shaft be negative?

No, the Angular Velocity of Driven Shaft, measured in Angular Velocity cannot be negative.

Which unit is used to measure Angular Velocity of Driven Shaft?

Angular Velocity of Driven Shaft 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 Driven Shaft can be measured.

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Angular Velocity of Driven Shaft Formula

​GoAngular Velocity of Driving Shaft given Angular Acceleration of Driven Shaft Formula

Angular Velocity of Driven Shaft Example

Angular Velocity of Driven Shaft Solution

Angular Velocity of Driven Shaft Formula Elements

Other Formulas to find Angular Velocity of Driven Shaft

Other formulas in Driveline category

How to Evaluate Angular Velocity of Driven Shaft?

FAQs on Angular Velocity of Driven Shaft

Variable Name

GoAngular Velocity of Driving Shaft given Angular Acceleration of Driven Shaft Formula