Angular Velocity of Driven Shaft Calculator

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Driveline

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Driveline Angular Velocity

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✖The Angle between Driving and Driven Shafts is the inclination of the driven shaft with respect to the driving shaft.ⓘ Angle between Driving and Driven Shafts [α]			+10% -10%
✖Angle Rotated by Driving Shaft is the angular displacement of the the driving shaft.ⓘ Angle Rotated by Driving Shaft [θ]			+10% -10%
✖Angular Velocity of Driving Shaft is the angular displacement of the driving shaft in a given unit of time.ⓘ Angular Velocity of Driving Shaft [ω_A]			+10% -10%

✖Angular Velocity of Driven Shaft is the angular displacement of the driven shaft in a given unit of time.ⓘ Angular Velocity of Driven Shaft [ω_B]

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Formula

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Angular Velocity of Driven Shaft

Formula

`"ω"_{"B"} = (cos("α")/(1-(cos("θ"))^2*(sin("α"))^2))*"ω"_{"A"}`

Example

`"62.38063rad/s"=(cos("5°")/(1-(cos("60°"))^2*(sin("5°"))^2))*"62.5rad/s"`

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Angular Velocity of Driven Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
ω_B = (cos(α)/(1-(cos(θ))^2*(sin(α))^2))*ω_A
This formula uses 2 Functions, 4 Variables

Functions Used

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., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Angular Velocity of Driven Shaft - (Measured in Radian per Second) - Angular Velocity of Driven Shaft is the angular displacement of the driven shaft in a given unit of time.
Angle between Driving and Driven Shafts - (Measured in Radian) - The Angle between Driving and Driven Shafts is the inclination of the driven shaft with respect to the driving shaft.
Angle Rotated by Driving Shaft - (Measured in Radian) - Angle Rotated by Driving Shaft is the angular displacement of the the driving shaft.
Angular Velocity of Driving Shaft - (Measured in Radian per Second) - Angular Velocity of Driving Shaft is the angular displacement of the driving shaft in a given unit of time.

STEP 1: Convert Input(s) to Base Unit

Angle between Driving and Driven Shafts: 5 Degree --> 0.0872664625997001 Radian (Check conversion here)
Angle Rotated by Driving Shaft: 60 Degree --> 1.0471975511964 Radian (Check conversion here)
Angular Velocity of Driving Shaft: 62.5 Radian per Second --> 62.5 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ω_B = (cos(α)/(1-(cos(θ))^2*(sin(α))^2))*ω_A --> (cos(0.0872664625997001)/(1-(cos(1.0471975511964))^2*(sin(0.0872664625997001))^2))*62.5

Evaluating ... ...

ω_B = 62.3806313756233

STEP 3: Convert Result to Output's Unit

62.3806313756233 Radian per Second --> No Conversion Required

FINAL ANSWER

62.3806313756233 ≈ 62.38063 Radian per Second <-- Angular Velocity of Driven Shaft

(Calculation completed in 00.004 seconds)

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Credits

Created by Peri Krishna Karthik

National Institute of Technology Calicut (NIT Calicut), Calicut, Kerala

Peri Krishna Karthik has created this Calculator and 200+ more calculators!

Verified by sanjay shiva

national institute of technology hamirpur (NITH ), hamirpur , himachal pradesh

sanjay shiva has verified this Calculator and 100+ more calculators!

< 3 Driveline Angular Velocity Calculators

Angular Velocity of Driving Shaft given Angular Acceleration of Driven Shaft

Go 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)))

Angular Velocity of Driving Shaft

Go Angular Velocity of Driving 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 Driven Shaft

Go 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

Angular Velocity of Driven Shaft Formula

What is Hooke's Joint?

A universal joint is a particular type of connection between two shafts. whose axes are inclined to each other. The most simple type of universal joint is the Hooke's joint which is most widely used because of the fact that it is simple and compact in construction and reasonably efficient at small angles of propeller shaft movement up and down, say up to 18 degrees.

How to Calculate Angular Velocity of Driven Shaft?

Angular Velocity of Driven Shaft calculator 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 calculate 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 calculate Angular Velocity of Driven Shaft using this online calculator? To use this online calculator 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. Here is how the Angular Velocity of Driven Shaft calculation can be explained with given input values -> 56.89114 = (cos(0.0872664625997001)/(1-(cos(1.0471975511964))^2*(sin(0.0872664625997001))^2))*62.5.

FAQ

What is 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 and is represented as ω_B = (cos(α)/(1-(cos(θ))^2*(sin(α))^2))*ω_A or 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. The Angle between Driving and Driven Shafts is the inclination of the driven shaft with respect to the driving shaft, Angle Rotated by Driving Shaft is the angular displacement of the the driving shaft & Angular Velocity of Driving Shaft is the angular displacement of the driving shaft in a given unit of time.

How to calculate 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 is calculated using 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 calculate Angular Velocity of Driven Shaft, you need Angle between Driving and Driven Shafts (α), Angle Rotated by Driving Shaft (θ) & Angular Velocity of Driving Shaft (ω_A). With our tool, you need to enter the respective value for Angle between Driving and Driven Shafts, Angle Rotated by Driving Shaft & Angular Velocity of Driving Shaft and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Angular Velocity of Driven Shaft?

In this formula, Angular Velocity of Driven Shaft uses Angle between Driving and Driven Shafts, Angle Rotated by Driving Shaft & Angular Velocity of Driving Shaft. We can use 1 other way(s) to calculate the same, which is/are as follows -

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)))

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