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Angular Displacement given Angular Acceleration Formula

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Angular displacement is defined as the shortest angle between the initial and the final points for a given object undergoing circular motion about a fixed point. Check FAQs

θ cm = ω in \cdot t cm + \frac{1}{2} \cdot α cm \cdot {t cm}^{2}

θ_cm - Angular Displacement?ω_in - Initial Angular Velocity of Object?t_cm - Time Period?α_cm - Angular Acceleration?

Angular Displacement given Angular Acceleration Example

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Here is how the Angular Displacement given Angular Acceleration equation looks like with Values.

Here is how the Angular Displacement given Angular Acceleration equation looks like with Units.

Here is how the Angular Displacement given Angular Acceleration equation looks like.

6187.9442 = 24 \cdot 3 + \frac{1}{2} \cdot 8 \cdot 3^{2}

6187.9442° = 24rad/s \cdot 3s + \frac{1}{2} \cdot 8rad/s² \cdot {3s}^{2}

6187.9442 = 24 \cdot 3 + \frac{1}{2} \cdot 8 \cdot 3^{2}

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Angular Displacement given Angular Acceleration Solution

Follow our step by step solution on how to calculate Angular Displacement given Angular Acceleration?

FIRST Step Consider the formula

θ cm = ω in \cdot t cm + \frac{1}{2} \cdot α cm \cdot {t cm}^{2}

Next Step Substitute values of Variables

∴

θ cm = 24rad/s \cdot 3s + \frac{1}{2} \cdot 8rad/s² \cdot {3s}^{2}

Next Step Prepare to Evaluate

∴

θ cm = 24 \cdot 3 + \frac{1}{2} \cdot 8 \cdot 3^{2}

Next Step Evaluate

∴

θ cm = 108rad

Next Step Convert to Output's Unit

∴

θ cm = 6187.94418741405°

LAST Step Rounding Answer

∴

θ cm = 6187.9442°

Angular Displacement given Angular Acceleration Formula Elements

Variables

Angular Displacement

Angular displacement is defined as the shortest angle between the initial and the final points for a given object undergoing circular motion about a fixed point.

Symbol: θ_cm

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angular Displacement

Initial Angular Velocity of Object

Initial Angular Velocity of Object undergoing curvilinear motion is calculated concerning time and acceleration.

Symbol: ω_in

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Initial Angular Velocity of Object

Time Period

Time Period is the duration of time it takes for a repeating event or cycle to complete one full cycle.

Symbol: t_cm

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Time Period

Angular Acceleration

Angular Acceleration is defined as the rate of change of angular velocity.

Symbol: α_cm

Measurement: Angular AccelerationUnit: rad/s²

Note: Value should be greater than 0.

Formulas to find Angular Acceleration

Other formulas in Curvilinear Motion category

Go Angular Velocity of Body Moving in Circle

ω = \frac{θ cm}{t cm}

Go Angular Velocity given Linear Velocity

ω = \frac{v cm}{r}

Go Angular Acceleration given Linear Acceleration

α cm = \frac{a cm}{r}

Go Final Angular Velocity

ω fi = ω in + α cm \cdot t cm

How to Evaluate Angular Displacement given Angular Acceleration?

Angular Displacement given Angular Acceleration evaluator uses Angular Displacement = Initial Angular Velocity of Object*Time Period+1/2*Angular Acceleration*Time Period^2 to evaluate the Angular Displacement, Angular Displacement given Angular Acceleration formula is defined as a measure of the change in angular position of an object undergoing rotational motion, describing the relationship between the initial and final angular positions of the object in a given time period. Angular Displacement is denoted by θ_cm symbol.

How to evaluate Angular Displacement given Angular Acceleration using this online evaluator? To use this online evaluator for Angular Displacement given Angular Acceleration, enter Initial Angular Velocity of Object (ω_in), Time Period (t_cm) & Angular Acceleration (α_cm) and hit the calculate button.

FAQs on Angular Displacement given Angular Acceleration

What is the formula to find Angular Displacement given Angular Acceleration?

The formula of Angular Displacement given Angular Acceleration is expressed as Angular Displacement = Initial Angular Velocity of Object*Time Period+1/2*Angular Acceleration*Time Period^2. Here is an example- 354543.1 = 24*3+1/2*8*3^2.

How to calculate Angular Displacement given Angular Acceleration?

With Initial Angular Velocity of Object (ω_in), Time Period (t_cm) & Angular Acceleration (α_cm) we can find Angular Displacement given Angular Acceleration using the formula - Angular Displacement = Initial Angular Velocity of Object*Time Period+1/2*Angular Acceleration*Time Period^2.

Can the Angular Displacement given Angular Acceleration be negative?

No, the Angular Displacement given Angular Acceleration, measured in Angle cannot be negative.

Which unit is used to measure Angular Displacement given Angular Acceleration?

Angular Displacement given Angular Acceleration is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Angular Displacement given Angular Acceleration can be measured.

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Angular Displacement given Angular Acceleration Formula

Angular Displacement given Angular Acceleration Example

Angular Displacement given Angular Acceleration Solution

Angular Displacement given Angular Acceleration Formula Elements

Other formulas in Curvilinear Motion category

How to Evaluate Angular Displacement given Angular Acceleration?

FAQs on Angular Displacement given Angular Acceleration

Variable Name