Speed of Rotation in RPM Calculator

✖Angle b/w axis of radius of rotation & line OA is the angle made by the axis of radius of rotation and line joining a point (A) on the curve to the origin O.ⓘ Angle b/w axis of radius of rotation & line OA [φ]			+10% -10%
✖The mass of ball is the amount of "matter" in the object.ⓘ Mass of Ball [m_ball]			+10% -10%

✖Mean Equilibrium Speed in RPM is the number of revolutions the drive shaft of your car is making per minute.ⓘ Speed of Rotation in RPM [N_equillibrium]

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Formula

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Speed of Rotation in RPM

Formula

`"N"_{"equillibrium"} = 60/(2*pi)*sqrt((tan("φ"))/"m"_{"ball"})`

Example

`"2.962207"=60/(2*pi)*sqrt((tan("30°"))/"6kg")`

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Speed of Rotation in RPM Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mean Equilibrium Speed in RPM = 60/(2*pi)*sqrt((tan(Angle b/w axis of radius of rotation & line OA))/Mass of Ball)
N_equillibrium = 60/(2*pi)*sqrt((tan(φ))/m_ball)
This formula uses 1 Constants, 2 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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)
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., sqrt(Number)

Variables Used

Mean Equilibrium Speed in RPM - Mean Equilibrium Speed in RPM is the number of revolutions the drive shaft of your car is making per minute.
Angle b/w axis of radius of rotation & line OA - (Measured in Radian) - Angle b/w axis of radius of rotation & line OA is the angle made by the axis of radius of rotation and line joining a point (A) on the curve to the origin O.
Mass of Ball - (Measured in Kilogram) - The mass of ball is the amount of "matter" in the object.

STEP 1: Convert Input(s) to Base Unit

Angle b/w axis of radius of rotation & line OA: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Mass of Ball: 6 Kilogram --> 6 Kilogram No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N_equillibrium = 60/(2*pi)*sqrt((tan(φ))/m_ball) --> 60/(2*pi)*sqrt((tan(0.5235987755982))/6)

Evaluating ... ...

N_equillibrium = 2.96220726782872

STEP 3: Convert Result to Output's Unit

2.96220726782872 --> No Conversion Required

FINAL ANSWER

2.96220726782872 ≈ 2.962207 <-- Mean Equilibrium Speed in RPM

(Calculation completed in 00.004 seconds)

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< 13 Basics of Governor Calculators

Total Downward Force on Sleeve in Wilson-Hartnell Governor

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

Speed of Rotation in RPM

Go Mean Equilibrium Speed in RPM = 60/(2*pi)*sqrt((tan(Angle b/w axis of radius of rotation & line OA))/Mass of Ball)

Ratio of Length of Arm to Length of Link

Go Ratio of Length of Link to Length of Arm = tan(Angle of Inclination of Link to Vertical)/tan(Angle of Inclination of Arm to Vertical)

Corresponding Radial Force Required at Each Ball for Spring Loaded Governors

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

Go Angle b/w axis of radius of rotation & 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

Go Angle b/w axis of radius of rotation & line OA = atan(Mass of Ball*Mean Equilibrium Angular Speed^2)

Mean Equilibrium Speed in RPM

Go Mean Equilibrium Speed in RPM = (Minimum equilibrium speed in r.p.m+Maximum equilibrium speed in r.p.m)/2

Mean Equilibrium Angular Speed

Go Mean Equilibrium Angular Speed = (Minimum equilibrium angular speed+Maximum equilibrium angular speed)/2

Sleeve Load for Decrease in Speed Value when Taking Friction into Account

Go Sleeve load for decrease in speed = Total load on sleeve-Force Required at Sleeve to Overcome Friction

Sleeve Load for Increase in Speed Value when Taking Friction into Account

Go Sleeve load for increase in speed = Total load on sleeve+Force Required at Sleeve to Overcome Friction

Increased Speed

Go Increased Speed = Mean Equilibrium Speed in RPM*(1+Percentage Increase in Speed)

Governor Power

Go Power = Mean Effort*Lift of Sleeve

Height of Watt Governor

Go Height of Governor = 895/(Speed in RPM^2)

Speed of Rotation in RPM Formula

Mean Equilibrium Speed in RPM = 60/(2*pi)*sqrt((tan(Angle b/w axis of radius of rotation & line OA))/Mass of Ball)
N_equillibrium = 60/(2*pi)*sqrt((tan(φ))/m_ball)

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 Speed of Rotation in RPM?

Speed of Rotation in RPM calculator uses Mean Equilibrium Speed in RPM = 60/(2*pi)*sqrt((tan(Angle b/w axis of radius of rotation & line OA))/Mass of Ball) to calculate the Mean Equilibrium Speed in RPM, The Speed of rotation in rpm formula is defined as the number of turns of the object divided by time, specified as revolutions per minute (rpm), cycles per second (cps), radians per second (rad/s), etc. Mean Equilibrium Speed in RPM is denoted by N_equillibrium symbol.

How to calculate Speed of Rotation in RPM using this online calculator? To use this online calculator for Speed of Rotation in RPM, enter Angle b/w axis of radius of rotation & line OA (φ) & Mass of Ball (m_ball) and hit the calculate button. Here is how the Speed of Rotation in RPM calculation can be explained with given input values -> 2.962207 = 60/(2*pi)*sqrt((tan(0.5235987755982))/6).

FAQ

What is Speed of Rotation in RPM?

The Speed of rotation in rpm formula is defined as the number of turns of the object divided by time, specified as revolutions per minute (rpm), cycles per second (cps), radians per second (rad/s), etc and is represented as N_equillibrium = 60/(2*pi)*sqrt((tan(φ))/m_ball) or Mean Equilibrium Speed in RPM = 60/(2*pi)*sqrt((tan(Angle b/w axis of radius of rotation & line OA))/Mass of Ball). Angle b/w axis of radius of rotation & line OA is the angle made by the axis of radius of rotation and line joining a point (A) on the curve to the origin O & The mass of ball is the amount of "matter" in the object.

How to calculate Speed of Rotation in RPM?

The Speed of rotation in rpm formula is defined as the number of turns of the object divided by time, specified as revolutions per minute (rpm), cycles per second (cps), radians per second (rad/s), etc is calculated using Mean Equilibrium Speed in RPM = 60/(2*pi)*sqrt((tan(Angle b/w axis of radius of rotation & line OA))/Mass of Ball). To calculate Speed of Rotation in RPM, you need Angle b/w axis of radius of rotation & line OA (φ) & Mass of Ball (m_ball). With our tool, you need to enter the respective value for Angle b/w axis of radius of rotation & line OA & Mass of Ball 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 Mean Equilibrium Speed in RPM?

In this formula, Mean Equilibrium Speed in RPM uses Angle b/w axis of radius of rotation & line OA & Mass of Ball. We can use 1 other way(s) to calculate the same, which is/are as follows -

Mean Equilibrium Speed in RPM = (Minimum equilibrium speed in r.p.m+Maximum equilibrium speed in r.p.m)/2

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