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Angle Traced in Nth Second (Accelerated Rotatory Motion) Formula

GoAngular Displacement given Initial Angular Velocity Angular Acceleration and Time 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 + (\frac{2 \cdot n th - 1}{2}) \cdot α

θ - Angular Displacement?ω_o - Initial Angular Velocity?n_th - Nth Second?α - Angular Acceleration?

Angle Traced in Nth Second (Accelerated Rotatory Motion) Example

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Here is how the Angle Traced in Nth Second (Accelerated Rotatory Motion) equation looks like with Values.

Here is how the Angle Traced in Nth Second (Accelerated Rotatory Motion) equation looks like with Units.

Here is how the Angle Traced in Nth Second (Accelerated Rotatory Motion) equation looks like.

120 = 15.2 + (\frac{2 \cdot 66 - 1}{2}) \cdot 1.6

120rad = 15.2rad/s + (\frac{2 \cdot 66s - 1}{2}) \cdot 1.6rad/s²

120 = 15.2 + (\frac{2 \cdot 66 - 1}{2}) \cdot 1.6

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Angle Traced in Nth Second (Accelerated Rotatory Motion) Solution

Follow our step by step solution on how to calculate Angle Traced in Nth Second (Accelerated Rotatory Motion)?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

θ = 15.2rad/s + (\frac{2 \cdot 66s - 1}{2}) \cdot 1.6rad/s²

Next Step Prepare to Evaluate

∴

θ = 15.2 + (\frac{2 \cdot 66 - 1}{2}) \cdot 1.6

LAST Step Evaluate

∴

θ = 120rad

Angle Traced in Nth Second (Accelerated Rotatory Motion) 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

Nth Second

Nth Second is the time required for an object to cover a certain distance or displacement during its motion.

Symbol: n_th

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Nth Second

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 Angular Displacement given Initial Angular Velocity Angular Acceleration and Time

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

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 Angle Traced in Nth Second (Accelerated Rotatory Motion)?

Angle Traced in Nth Second (Accelerated Rotatory Motion) evaluator uses Angular Displacement = Initial Angular Velocity+((2*Nth Second-1)/2)*Angular Acceleration to evaluate the Angular Displacement, Angle Traced in Nth Second (Accelerated Rotatory Motion) formula is defined as a measure of the angle swept by a body moving in a circular path with constant angular acceleration, describing the rotational motion of an object in terms of its angular displacement. Angular Displacement is denoted by θ symbol.

How to evaluate Angle Traced in Nth Second (Accelerated Rotatory Motion) using this online evaluator? To use this online evaluator for Angle Traced in Nth Second (Accelerated Rotatory Motion), enter Initial Angular Velocity (ω_o), Nth Second (n_th) & Angular Acceleration (α) and hit the calculate button.

FAQs on Angle Traced in Nth Second (Accelerated Rotatory Motion)

What is the formula to find Angle Traced in Nth Second (Accelerated Rotatory Motion)?

The formula of Angle Traced in Nth Second (Accelerated Rotatory Motion) is expressed as Angular Displacement = Initial Angular Velocity+((2*Nth Second-1)/2)*Angular Acceleration. Here is an example- 118.4 = 15.2+((2*66-1)/2)*1.6.

How to calculate Angle Traced in Nth Second (Accelerated Rotatory Motion)?

With Initial Angular Velocity (ω_o), Nth Second (n_th) & Angular Acceleration (α) we can find Angle Traced in Nth Second (Accelerated Rotatory Motion) using the formula - Angular Displacement = Initial Angular Velocity+((2*Nth Second-1)/2)*Angular Acceleration.

What are the other ways to Calculate Angular Displacement?

Here are the different ways to Calculate Angular Displacement-

Angular Displacement=Initial Angular Velocity*Time Taken to Travel the Path+(Angular Acceleration*Time Taken to Travel the Path^2)/2
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 Angle Traced in Nth Second (Accelerated Rotatory Motion) be negative?

Yes, the Angle Traced in Nth Second (Accelerated Rotatory Motion), measured in Angle can be negative.

Which unit is used to measure Angle Traced in Nth Second (Accelerated Rotatory Motion)?

Angle Traced in Nth Second (Accelerated Rotatory Motion) is usually measured using the Radian[rad] for Angle. Degree[rad], Minute[rad], Second[rad] are the few other units in which Angle Traced in Nth Second (Accelerated Rotatory Motion) can be measured.

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