Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin Calculator

✖Mass of Ball is the measure of the amount of matter in a ball, typically measured in units of mass such as grams or kilograms.ⓘ Mass of Ball [m_ball]			+10% -10%
✖Mean Equilibrium Angular Speed is the average angular speed of a governor at which the governor reaches equilibrium, maintaining a stable speed.ⓘ Mean Equilibrium Angular Speed [ω_equillibrium]			+10% -10%

✖Angle B/W Axis of Radius of Rotation and Line OA is the angle between the axis of rotation of the governor and the line OA, which affects the governor's stability.ⓘ Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin [φ]

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Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle B/W Axis of Radius of Rotation and Line OA = atan(Mass of Ball*Mean Equilibrium Angular Speed^2)
φ = atan(m_ball*ω_equillibrium^2)
This formula uses 2 Functions, 3 Variables

Functions Used

tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
atan - Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle., atan(Number)

Variables Used

Angle B/W Axis of Radius of Rotation and Line OA - (Measured in Radian) - Angle B/W Axis of Radius of Rotation and Line OA is the angle between the axis of rotation of the governor and the line OA, which affects the governor's stability.
Mass of Ball - (Measured in Kilogram) - Mass of Ball is the measure of the amount of matter in a ball, typically measured in units of mass such as grams or kilograms.
Mean Equilibrium Angular Speed - Mean Equilibrium Angular Speed is the average angular speed of a governor at which the governor reaches equilibrium, maintaining a stable speed.

STEP 1: Convert Input(s) to Base Unit

Mass of Ball: 5.9 Kilogram --> 5.9 Kilogram No Conversion Required
Mean Equilibrium Angular Speed: 1.48 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

φ = atan(m_ball*ω_equillibrium^2) --> atan(5.9*1.48^2)

Evaluating ... ...

φ = 1.49357095430656

STEP 3: Convert Result to Output's Unit

1.49357095430656 Radian -->85.575312085109 Degree (Check conversion here)

FINAL ANSWER

85.575312085109 ≈ 85.57531 Degree <-- Angle B/W Axis of Radius of Rotation and Line OA

(Calculation completed in 00.004 seconds)

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< Basics of Governor Calculators

Total Downward Force on Sleeve in Wilson-Hartnell Governor

LaTeX Go Force = Mass on Sleeve*Acceleration due to Gravity+(Tension in the auxiliary spring*Distance of Auxiliary Spring from Mid of Lever)/Distance of Main Spring from Mid Point of Lever

Corresponding Radial Force Required at Each Ball for Spring Loaded Governors

LaTeX Go Corresponding Radial Force Required at Each Ball = (Force Required at Sleeve to Overcome Friction*Length of Sleeve Arm of Lever)/(2*Length of Ball Arm of Lever)

Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin O

LaTeX Go Angle B/W Axis of Radius of Rotation and Line OA = atan(Controlling Force/Radius of Rotation if Governor is in Mid-Position)

Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin

LaTeX Go Angle B/W Axis of Radius of Rotation and Line OA = atan(Mass of Ball*Mean Equilibrium Angular Speed^2)

Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin Formula

LaTeX Go

Angle B/W Axis of Radius of Rotation and Line OA = atan(Mass of Ball*Mean Equilibrium Angular Speed^2)
φ = atan(m_ball*ω_equillibrium^2)

What is Porter Governor?

Porter Governor is a modification of Watt Governor with a central load attached to the sleeve. This load moves up and down the central spindle. The additional force increases the speed of revolution required to enable the balls to rise to any predetermined level.

How to Calculate Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin?

Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin calculator uses Angle B/W Axis of Radius of Rotation and Line OA = atan(Mass of Ball*Mean Equilibrium Angular Speed^2) to calculate the Angle B/W Axis of Radius of Rotation and Line OA, Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin formula is defined as the angular displacement of the axis of rotation of a governor from its mean position, which is a critical parameter in the design and operation of governors in mechanical systems. Angle B/W Axis of Radius of Rotation and Line OA is denoted by φ symbol.

How to calculate Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin using this online calculator? To use this online calculator for Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin, enter Mass of Ball (m_ball) & Mean Equilibrium Angular Speed (ω_equillibrium) and hit the calculate button. Here is how the Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin calculation can be explained with given input values -> 4907.313 = atan(5.9*1.48^2).

FAQ

What is Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin?

Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin formula is defined as the angular displacement of the axis of rotation of a governor from its mean position, which is a critical parameter in the design and operation of governors in mechanical systems and is represented as φ = atan(m_ball*ω_equillibrium^2) or Angle B/W Axis of Radius of Rotation and Line OA = atan(Mass of Ball*Mean Equilibrium Angular Speed^2). Mass of Ball is the measure of the amount of matter in a ball, typically measured in units of mass such as grams or kilograms & Mean Equilibrium Angular Speed is the average angular speed of a governor at which the governor reaches equilibrium, maintaining a stable speed.

How to calculate Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin?

Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin formula is defined as the angular displacement of the axis of rotation of a governor from its mean position, which is a critical parameter in the design and operation of governors in mechanical systems is calculated using Angle B/W Axis of Radius of Rotation and Line OA = atan(Mass of Ball*Mean Equilibrium Angular Speed^2). To calculate Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin, you need Mass of Ball (m_ball) & Mean Equilibrium Angular Speed (ω_equillibrium). With our tool, you need to enter the respective value for Mass of Ball & Mean Equilibrium Angular Speed 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 Angle B/W Axis of Radius of Rotation and Line OA?

In this formula, Angle B/W Axis of Radius of Rotation and Line OA uses Mass of Ball & Mean Equilibrium Angular Speed. We can use 1 other way(s) to calculate the same, which is/are as follows -

Angle B/W Axis of Radius of Rotation and Line OA = atan(Controlling Force/Radius of Rotation if Governor is in Mid-Position)

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