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Angular Acceleration of Driven Shaft Formula

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

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}}

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

Angular Acceleration of Driven Shaft Example

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

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

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

14.7526 = - 62^{2} \cdot \cos (5) \cdot {\sin (5)}^{2} \cdot \frac{\sin (2 \cdot 15)}{{(1 - {\cos (15)}^{2} \cdot {\sin (5)}^{2})}^{2}}

14.7526rad/s² = - {62rad/s}^{2} \cdot \cos (5°) \cdot {\sin (5°)}^{2} \cdot \frac{\sin (2 \cdot 15°)}{{(1 - {\cos (15°)}^{2} \cdot {\sin (5°)}^{2})}^{2}}

14.7526 = - 62^{2} \cdot \cos (5) \cdot {\sin (5)}^{2} \cdot \frac{\sin (2 \cdot 15)}{{(1 - {\cos (15)}^{2} \cdot {\sin (5)}^{2})}^{2}}

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Angular Acceleration of Driven Shaft Solution

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

FIRST Step Consider the formula

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}}

Next Step Substitute values of Variables

∴

α B = - {62rad/s}^{2} \cdot \cos (5°) \cdot {\sin (5°)}^{2} \cdot \frac{\sin (2 \cdot 15°)}{{(1 - {\cos (15°)}^{2} \cdot {\sin (5°)}^{2})}^{2}}

Next Step Convert Units

∴

α B = - {62rad/s}^{2} \cdot \cos (0.0873rad) \cdot {\sin (0.0873rad)}^{2} \cdot \frac{\sin (2 \cdot 0.2618rad)}{{(1 - {\cos (0.2618rad)}^{2} \cdot {\sin (0.0873rad)}^{2})}^{2}}

Next Step Prepare to Evaluate

∴

α B = - 62^{2} \cdot \cos (0.0873) \cdot {\sin (0.0873)}^{2} \cdot \frac{\sin (2 \cdot 0.2618)}{{(1 - {\cos (0.2618)}^{2} \cdot {\sin (0.0873)}^{2})}^{2}}

Next Step Evaluate

∴

α B = 14.7525629670481rad/s²

LAST Step Rounding Answer

∴

α B = 14.7526rad/s²

Angular Acceleration of Driven Shaft Formula Elements

Variables

Functions

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

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 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

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)

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P v = \frac{R t \cdot V s}{η t}

How to Evaluate Angular Acceleration of Driven Shaft?

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

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

FAQs on Angular Acceleration of Driven Shaft

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

The formula of Angular Acceleration of Driven Shaft is expressed as Angular Acceleration of Driven Shaft = -Angular Velocity of Driven Shaft^2*cos(Angle Between Driving And Driven Shafts)*sin(Angle Between Driving And Driven Shafts)^2*sin(2*Angle Rotated By Driven Shaft)/((1-cos(Angle Rotated By Driven Shaft)^2*sin(Angle Between Driving And Driven Shafts)^2)^2). Here is an example- 14.75256 = -62^2*cos(0.0872664625997001)*sin(0.0872664625997001)^2*sin(2*0.2617993877991)/((1-cos(0.2617993877991)^2*sin(0.0872664625997001)^2)^2).

How to calculate Angular Acceleration of Driven Shaft?

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

Can the Angular Acceleration of Driven Shaft be negative?

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

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

Angular Acceleration of Driven Shaft is usually measured using the Radian per Square Second[rad/s²] for Angular Acceleration. Radian per Square Minute[rad/s²], Revolution per Square Second[rad/s²], Revolution per Square Minute[rad/s²] are the few other units in which Angular Acceleration of Driven Shaft can be measured.

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Angular Acceleration of Driven Shaft Formula

Angular Acceleration of Driven Shaft Example

Angular Acceleration of Driven Shaft Solution

Angular Acceleration of Driven Shaft Formula Elements

Other formulas in Driveline category

How to Evaluate Angular Acceleration of Driven Shaft?

FAQs on Angular Acceleration of Driven Shaft

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