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

GoAngular Velocity 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 = \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)}}

ω_B - Angular Velocity of Driven Shaft?α_B - Angular Acceleration of Driven Shaft?Φ - Angle Rotated By Driven Shaft?α - Angle Between Driving And Driven Shafts?

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

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

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

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

61.9946 = \sqrt{\frac{14.75 \cdot {(1 - {\cos (15)}^{2} \cdot {\sin (5)}^{2})}^{2}}{\cos (5) \cdot {\sin (5)}^{2} \cdot \sin (2 \cdot 15)}}

61.9946rad/s = \sqrt{\frac{14.75rad/s² \cdot {(1 - {\cos (15°)}^{2} \cdot {\sin (5°)}^{2})}^{2}}{\cos (5°) \cdot {\sin (5°)}^{2} \cdot \sin (2 \cdot 15°)}}

61.9946 = \sqrt{\frac{14.75 \cdot {(1 - {\cos (15)}^{2} \cdot {\sin (5)}^{2})}^{2}}{\cos (5) \cdot {\sin (5)}^{2} \cdot \sin (2 \cdot 15)}}

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

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

FIRST Step Consider the formula

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)}}

Next Step Substitute values of Variables

∴

ω B = \sqrt{\frac{14.75rad/s² \cdot {(1 - {\cos (15°)}^{2} \cdot {\sin (5°)}^{2})}^{2}}{\cos (5°) \cdot {\sin (5°)}^{2} \cdot \sin (2 \cdot 15°)}}

Next Step Convert Units

∴

ω B = \sqrt{\frac{14.75rad/s² \cdot {(1 - {\cos (0.2618rad)}^{2} \cdot {\sin (0.0873rad)}^{2})}^{2}}{\cos (0.0873rad) \cdot {\sin (0.0873rad)}^{2} \cdot \sin (2 \cdot 0.2618rad)}}

Next Step Prepare to Evaluate

∴

ω B = \sqrt{\frac{14.75 \cdot {(1 - {\cos (0.2618)}^{2} \cdot {\sin (0.0873)}^{2})}^{2}}{\cos (0.0873) \cdot {\sin (0.0873)}^{2} \cdot \sin (2 \cdot 0.2618)}}

Next Step Evaluate

∴

ω B = 61.9946141270659rad/s

LAST Step Rounding Answer

∴

ω B = 61.9946rad/s

Angular Velocity of Driving Shaft given Angular Acceleration 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

Angular Acceleration of Driven Shaft

Angular Acceleration of Driven Shaft is the rate of the angular displacement of the driven shaft.

Symbol: α_B

Measurement: Angular AccelerationUnit: rad/s²

Note: Value should be greater than 0.

Formulas to find Angular Acceleration of Driven Shaft

Angle Rotated By Driven Shaft

Angle Rotated By Driven Shaft is the angular displacement of the driven shaft.

Symbol: Φ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle Rotated By 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

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)

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 of Driven Shaft

Go Angular Velocity of Driven Shaft

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

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 Driving Shaft given Angular Acceleration of Driven Shaft?

Angular Velocity of Driving Shaft given Angular Acceleration of Driven Shaft evaluator uses 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))) to evaluate the Angular Velocity of Driven Shaft, The Angular velocity of driving shaft given angular acceleration of driven shaft formula is used to find the angular displacement of the driven shaft in a given unit of time. Angular Velocity of Driven Shaft is denoted by ω_B symbol.

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

FAQs on Angular Velocity of Driving Shaft given Angular Acceleration of Driven Shaft

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

The formula of Angular Velocity of Driving Shaft given Angular Acceleration of Driven Shaft is expressed as 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))). Here is an example- 61.99461 = sqrt((14.75*(1-cos(0.2617993877991)^2*sin(0.0872664625997001)^2)^2)/(cos(0.0872664625997001)*sin(0.0872664625997001)^2*sin(2*0.2617993877991))).

How to calculate Angular Velocity of Driving Shaft given Angular Acceleration of Driven Shaft?

With Angular Acceleration of Driven Shaft (α_B), Angle Rotated By Driven Shaft (Φ) & Angle Between Driving And Driven Shafts (α) we can find Angular Velocity of Driving Shaft given Angular Acceleration of Driven Shaft using the formula - 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))). This formula also uses Sine (sin)Cosine (cos), Square Root (sqrt) 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=(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

Can the Angular Velocity of Driving Shaft given Angular Acceleration of Driven Shaft be negative?

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

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

Angular Velocity of Driving Shaft given Angular Acceleration 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 Driving Shaft given Angular Acceleration of Driven Shaft can be measured.

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

​GoAngular Velocity of Driven Shaft Formula

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

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

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

FAQs on Angular Velocity of Driving Shaft given Angular Acceleration of Driven Shaft

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GoAngular Velocity of Driven Shaft Formula