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Acceleration of Follower after Time t for Cycloidal Motion Formula

GoAcceleration of Follower for Circular Arc Cam if there's Contact on Circular Flank Formula

GoAcceleration of Follower for Roller Follower Tangent Cam, there's Contact with Straight Flanks Formula

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Acceleration of follower is the rate of change in velocity to the change in time. Check FAQs

a = \frac{2 \cdot π \cdot ω^{2} \cdot S}{{θ o}^{2}} \cdot \sin (\frac{2 \cdot π \cdot θ r}{θ o})

a - Acceleration of Follower?ω - Angular Velocity of Cam?S - Stroke of Follower?θ_o - Angular Displacement of Cam During Out Stroke?θ_r - Angle Through Which Cam Rotates?π - Archimedes' constant?

Acceleration of Follower after Time t for Cycloidal Motion Example

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Here is how the Acceleration of Follower after Time t for Cycloidal Motion equation looks like with Values.

Here is how the Acceleration of Follower after Time t for Cycloidal Motion equation looks like with Units.

Here is how the Acceleration of Follower after Time t for Cycloidal Motion equation looks like.

18.8346 = \frac{2 \cdot 3.1416 \cdot 27^{2} \cdot 20}{22^{2}} \cdot \sin (\frac{2 \cdot 3.1416 \cdot 0.349}{22})

18.8346m/s² = \frac{2 \cdot 3.1416 \cdot {27rad/s}^{2} \cdot 20m}{{22rad}^{2}} \cdot \sin (\frac{2 \cdot 3.1416 \cdot 0.349rad}{22rad})

18.8346 = \frac{2 \cdot 3.1416 \cdot 27^{2} \cdot 20}{22^{2}} \cdot \sin (\frac{2 \cdot 3.1416 \cdot 0.349}{22})

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Acceleration of Follower after Time t for Cycloidal Motion Solution

Follow our step by step solution on how to calculate Acceleration of Follower after Time t for Cycloidal Motion?

FIRST Step Consider the formula

a = \frac{2 \cdot π \cdot ω^{2} \cdot S}{{θ o}^{2}} \cdot \sin (\frac{2 \cdot π \cdot θ r}{θ o})

Next Step Substitute values of Variables

∴

a = \frac{2 \cdot π \cdot {27rad/s}^{2} \cdot 20m}{{22rad}^{2}} \cdot \sin (\frac{2 \cdot π \cdot 0.349rad}{22rad})

Next Step Substitute values of Constants

∴

a = \frac{2 \cdot 3.1416 \cdot {27rad/s}^{2} \cdot 20m}{{22rad}^{2}} \cdot \sin (\frac{2 \cdot 3.1416 \cdot 0.349rad}{22rad})

Next Step Prepare to Evaluate

∴

a = \frac{2 \cdot 3.1416 \cdot 27^{2} \cdot 20}{22^{2}} \cdot \sin (\frac{2 \cdot 3.1416 \cdot 0.349}{22})

Next Step Evaluate

∴

a = 18.8345518910704m/s²

LAST Step Rounding Answer

∴

a = 18.8346m/s²

Acceleration of Follower after Time t for Cycloidal Motion Formula Elements

Variables

Constants

Functions

Acceleration of Follower

Acceleration of follower is the rate of change in velocity to the change in time.

Symbol: a

Measurement: AccelerationUnit: m/s²

Note: Value can be positive or negative.

Formulas to find Acceleration of Follower

Angular Velocity of Cam

Angular velocity of cam refers to how fast an object rotates or revolves relative to another point.

Symbol: ω

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Angular Velocity of Cam

Stroke of Follower

Stroke of Follower is the greatest distance or angle through which the follower moves or rotates.

Symbol: S

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Stroke of Follower

Angular Displacement of Cam During Out Stroke

The Angular Displacement of Cam during Out Stroke is the angle covered by the follower during forwarding stroke.

Symbol: θ_o

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Angular Displacement of Cam During Out Stroke

Angle Through Which Cam Rotates

The angle through which cam rotates is the angle through which the cam turns while the follower remains stationary at the highest or the lowest position.

Symbol: θ_r

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Angle Through Which Cam Rotates

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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)

Other Formulas to find Acceleration of Follower

Go Acceleration of Follower for Circular Arc Cam if there's Contact on Circular Flank

a = ω^{2} \cdot (R - r 1) \cdot \cos (θ t)

Go Acceleration of Follower for Roller Follower Tangent Cam, there's Contact with Straight Flanks

a = ω^{2} \cdot (r 1 + r rol) \cdot \frac{{(2 - \cos (θ))}^{2}}{{(\cos (θ))}^{3}}

Go Acceleration of Follower of Roller Follower Tangent Cam, there's Contact with Nose

a = ω^{2} \cdot r \cdot (\cos (θ 1) + \frac{L^{2} \cdot r \cdot \cos (2 \cdot θ 1) + r^{3} \cdot {(\sin (θ 1))}^{4}}{\sqrt{L^{2} - r^{2} \cdot {(\sin (θ 1))}^{2}}})

Go Minimum Acceleration of Follower for Tangent Cam with Roller Follower

a = ω^{2} \cdot (r 1 + r rol)

Other formulas in Acceleration of the Follower category

Go Centripetal Acceleration of Point P on Circumference

a c = \frac{π^{2} \cdot ω^{2} \cdot S}{2 \cdot {θ o}^{2}}

Go Centripetal Acceleration of Point P on Circumference when Follower Moves with SHM

a c = \frac{2 \cdot {P s}^{2}}{S}

Go Maximum Acceleration of Follower on Outstroke when Follower Moves with SHM

a max = \frac{π^{2} \cdot ω^{2} \cdot S}{2 \cdot {θ o}^{2}}

Go Maximum Acceleration of Follower on Return Stroke when Follower Moves with SHM

a max = \frac{π^{2} \cdot ω^{2} \cdot S}{2 \cdot {θ R}^{2}}

How to Evaluate Acceleration of Follower after Time t for Cycloidal Motion?

Acceleration of Follower after Time t for Cycloidal Motion evaluator uses Acceleration of Follower = (2*pi*Angular Velocity of Cam^2*Stroke of Follower)/(Angular Displacement of Cam During Out Stroke^2)*sin((2*pi*Angle Through Which Cam Rotates)/(Angular Displacement of Cam During Out Stroke)) to evaluate the Acceleration of Follower, Acceleration of Follower after Time t for Cycloidal Motion formula is defined as a measure of the rate of change of velocity of the follower in a cycloidal motion, which is a fundamental concept in kinematics, describing the motion of a point on a circle that rolls without slipping on a fixed circle. Acceleration of Follower is denoted by a symbol.

How to evaluate Acceleration of Follower after Time t for Cycloidal Motion using this online evaluator? To use this online evaluator for Acceleration of Follower after Time t for Cycloidal Motion, enter Angular Velocity of Cam (ω), Stroke of Follower (S), Angular Displacement of Cam During Out Stroke (θ_o) & Angle Through Which Cam Rotates (θ_r) and hit the calculate button.

FAQs on Acceleration of Follower after Time t for Cycloidal Motion

What is the formula to find Acceleration of Follower after Time t for Cycloidal Motion?

The formula of Acceleration of Follower after Time t for Cycloidal Motion is expressed as Acceleration of Follower = (2*pi*Angular Velocity of Cam^2*Stroke of Follower)/(Angular Displacement of Cam During Out Stroke^2)*sin((2*pi*Angle Through Which Cam Rotates)/(Angular Displacement of Cam During Out Stroke)). Here is an example- 0.439959 = (2*pi*27^2*20)/(22^2)*sin((2*pi*0.349)/(22)).

How to calculate Acceleration of Follower after Time t for Cycloidal Motion?

With Angular Velocity of Cam (ω), Stroke of Follower (S), Angular Displacement of Cam During Out Stroke (θ_o) & Angle Through Which Cam Rotates (θ_r) we can find Acceleration of Follower after Time t for Cycloidal Motion using the formula - Acceleration of Follower = (2*pi*Angular Velocity of Cam^2*Stroke of Follower)/(Angular Displacement of Cam During Out Stroke^2)*sin((2*pi*Angle Through Which Cam Rotates)/(Angular Displacement of Cam During Out Stroke)). This formula also uses Archimedes' constant and Sine (sin) function(s).

What are the other ways to Calculate Acceleration of Follower?

Here are the different ways to Calculate Acceleration of Follower-

Acceleration of Follower=Angular Velocity of Cam^2*(Radius of Circular Flank-Radius of the Base Circle)*cos(Angle Turned by Cam)
Acceleration of Follower=Angular Velocity of Cam^2*(Radius of the Base Circle+Radius of Roller)*(2-cos(Angle Turned by Cam from Beginning of Roller))^2/((cos(Angle Turned by Cam from Beginning of Roller))^3)
Acceleration of Follower=Angular Velocity of Cam^2*Distance b/w Cam Center and Nose Center*(cos(Angle Turned by Cam When Roller is at Nose Top)+(Distance b/w Roller Centre and Nose Centre^2*Distance b/w Cam Center and Nose Center*cos(2*Angle Turned by Cam When Roller is at Nose Top)+Distance b/w Cam Center and Nose Center^3*(sin(Angle Turned by Cam When Roller is at Nose Top))^4)/sqrt(Distance b/w Roller Centre and Nose Centre^2-Distance b/w Cam Center and Nose Center^2*(sin(Angle Turned by Cam When Roller is at Nose Top))^2))

Can the Acceleration of Follower after Time t for Cycloidal Motion be negative?

Yes, the Acceleration of Follower after Time t for Cycloidal Motion, measured in Acceleration can be negative.

Which unit is used to measure Acceleration of Follower after Time t for Cycloidal Motion?

Acceleration of Follower after Time t for Cycloidal Motion is usually measured using the Meter per Square Second[m/s²] for Acceleration. Kilometer per Square Second[m/s²], Micrometer per Square Second[m/s²], Mile per Square Second[m/s²] are the few other units in which Acceleration of Follower after Time t for Cycloidal Motion can be measured.

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Acceleration of Follower after Time t for Cycloidal Motion Formula

​GoAcceleration of Follower for Circular Arc Cam if there's Contact on Circular Flank Formula

​GoAcceleration of Follower for Roller Follower Tangent Cam, there's Contact with Straight Flanks Formula

Acceleration of Follower after Time t for Cycloidal Motion Example

Acceleration of Follower after Time t for Cycloidal Motion Solution

Acceleration of Follower after Time t for Cycloidal Motion Formula Elements

Other Formulas to find Acceleration of Follower

Other formulas in Acceleration of the Follower category

How to Evaluate Acceleration of Follower after Time t for Cycloidal Motion?

FAQs on Acceleration of Follower after Time t for Cycloidal Motion

Variable Name

GoAcceleration of Follower for Circular Arc Cam if there's Contact on Circular Flank Formula

GoAcceleration of Follower for Roller Follower Tangent Cam, there's Contact with Straight Flanks Formula