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Angular Displacement given Initial Angular Velocity Angular Acceleration and Time Formula

GoAngle Traced in Nth Second (Accelerated Rotatory Motion) Formula

GoAngular Displacement given Initial Angular Velocity Final Angular Velocity and Time Formula

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Angular Displacement is the angle through which an object rotates about a fixed axis, describing the change in its orientation. Check FAQs

θ = ω o \cdot t + \frac{α \cdot t^{2}}{2}

θ - Angular Displacement?ω_o - Initial Angular Velocity?t - Time Taken to Travel the Path?α - Angular Acceleration?

Angular Displacement given Initial Angular Velocity Angular Acceleration and Time Example

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Here is how the Angular Displacement given Initial Angular Velocity Angular Acceleration and Time equation looks like with Values.

Here is how the Angular Displacement given Initial Angular Velocity Angular Acceleration and Time equation looks like with Units.

Here is how the Angular Displacement given Initial Angular Velocity Angular Acceleration and Time equation looks like.

120 = 15.2 \cdot 6 + \frac{1.6 \cdot 6^{2}}{2}

120rad = 15.2rad/s \cdot 6s + \frac{1.6rad/s² \cdot {6s}^{2}}{2}

120 = 15.2 \cdot 6 + \frac{1.6 \cdot 6^{2}}{2}

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Angular Displacement given Initial Angular Velocity Angular Acceleration and Time Solution

Follow our step by step solution on how to calculate Angular Displacement given Initial Angular Velocity Angular Acceleration and Time?

FIRST Step Consider the formula

θ = ω o \cdot t + \frac{α \cdot t^{2}}{2}

Next Step Substitute values of Variables

∴

θ = 15.2rad/s \cdot 6s + \frac{1.6rad/s² \cdot {6s}^{2}}{2}

Next Step Prepare to Evaluate

∴

θ = 15.2 \cdot 6 + \frac{1.6 \cdot 6^{2}}{2}

LAST Step Evaluate

∴

θ = 120rad

Angular Displacement given Initial Angular Velocity Angular Acceleration and Time Formula Elements

Variables

Angular Displacement

Angular Displacement is the angle through which an object rotates about a fixed axis, describing the change in its orientation.

Symbol: θ

Measurement: AngleUnit: rad

Note: Value can be positive or negative.

Formulas to find Angular Displacement

Initial Angular Velocity

Initial Angular Velocity is the velocity of an object at the start of its motion, describing its initial rotational motion around a fixed axis.

Symbol: ω_o

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Initial Angular Velocity

Time Taken to Travel the Path

Time Taken to Travel the Path is the duration required for an object to move from one point to another along a specific path or trajectory.

Symbol: t

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Time Taken to Travel the Path

Angular Acceleration

Angular Acceleration is the rate of change of angular velocity, describing how fast the rotation of an object changes over time.

Symbol: α

Measurement: Angular AccelerationUnit: rad/s²

Note: Value can be positive or negative.

Formulas to find Angular Acceleration

Other Formulas to find Angular Displacement

Go Angle Traced in Nth Second (Accelerated Rotatory Motion)

θ = ω o + (\frac{2 \cdot n th - 1}{2}) \cdot α

Go Angular Displacement given Initial Angular Velocity Final Angular Velocity and Time

θ = (\frac{ω o + ω 1}{2}) \cdot t

Go Angular Displacement of Body for given Initial and Final Angular Velocity

θ = \frac{{ω 1}^{2} - {ω o}^{2}}{2 \cdot α}

Other formulas in Kinematics category

Go Final Angular Velocity given Initial Angular Velocity Angular Acceleration and Time

ω 1 = ω o + α \cdot t

Go Final Velocity of Body

v f = u + a \cdot t

Go Final Velocity of Freely Falling Body from Height when it Reaches Ground

V = \sqrt{2 \cdot g \cdot v}

Go Normal Acceleration

a n = ω^{2} \cdot R c

How to Evaluate Angular Displacement given Initial Angular Velocity Angular Acceleration and Time?

Angular Displacement given Initial Angular Velocity Angular Acceleration and Time evaluator uses Angular Displacement = Initial Angular Velocity*Time Taken to Travel the Path+(Angular Acceleration*Time Taken to Travel the Path^2)/2 to evaluate the Angular Displacement, Angular Displacement given Initial Angular Velocity Angular Acceleration and Time formula is defined as a measure of the change in angular position of an object undergoing rotational motion, considering the initial angular velocity, angular acceleration, and time of motion. Angular Displacement is denoted by θ symbol.

How to evaluate Angular Displacement given Initial Angular Velocity Angular Acceleration and Time using this online evaluator? To use this online evaluator for Angular Displacement given Initial Angular Velocity Angular Acceleration and Time, enter Initial Angular Velocity (ω_o), Time Taken to Travel the Path (t) & Angular Acceleration (α) and hit the calculate button.

FAQs on Angular Displacement given Initial Angular Velocity Angular Acceleration and Time

What is the formula to find Angular Displacement given Initial Angular Velocity Angular Acceleration and Time?

The formula of Angular Displacement given Initial Angular Velocity Angular Acceleration and Time is expressed as Angular Displacement = Initial Angular Velocity*Time Taken to Travel the Path+(Angular Acceleration*Time Taken to Travel the Path^2)/2. Here is an example- 112.8 = 15.2*6+(1.6*6^2)/2.

How to calculate Angular Displacement given Initial Angular Velocity Angular Acceleration and Time?

With Initial Angular Velocity (ω_o), Time Taken to Travel the Path (t) & Angular Acceleration (α) we can find Angular Displacement given Initial Angular Velocity Angular Acceleration and Time using the formula - Angular Displacement = Initial Angular Velocity*Time Taken to Travel the Path+(Angular Acceleration*Time Taken to Travel the Path^2)/2.

What are the other ways to Calculate Angular Displacement?

Here are the different ways to Calculate Angular Displacement-

Angular Displacement=Initial Angular Velocity+((2*Nth Second-1)/2)*Angular Acceleration
Angular Displacement=((Initial Angular Velocity+Final Angular Velocity)/2)*Time Taken to Travel the Path
Angular Displacement=(Final Angular Velocity^2-Initial Angular Velocity^2)/(2*Angular Acceleration)

Can the Angular Displacement given Initial Angular Velocity Angular Acceleration and Time be negative?

Yes, the Angular Displacement given Initial Angular Velocity Angular Acceleration and Time, measured in Angle can be negative.

Which unit is used to measure Angular Displacement given Initial Angular Velocity Angular Acceleration and Time?

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

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