Angle Traced in Nth Second (Accelerated Rotatory Motion) Calculator

✖Initial Angular Velocity is the velocity of an object at the start of its motion, describing its initial rotational motion around a fixed axis.ⓘ Initial Angular Velocity [ω_o]			+10% -10%
✖Nth Second is the time required for an object to cover a certain distance or displacement during its motion.ⓘ Nth Second [n_th]			+10% -10%
✖Angular Acceleration is the rate of change of angular velocity, describing how fast the rotation of an object changes over time.ⓘ Angular Acceleration [α]			+10% -10%

✖Angular Displacement is the angle through which an object rotates about a fixed axis, describing the change in its orientation.ⓘ Angle Traced in Nth Second (Accelerated Rotatory Motion) [θ]

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Angle Traced in Nth Second (Accelerated Rotatory Motion) Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angular Displacement = Initial Angular Velocity+((2*Nth Second-1)/2)*Angular Acceleration
θ = ω_o+((2*n_th-1)/2)*α
This formula uses 4 Variables

Variables Used

Angular Displacement - (Measured in Radian) - Angular Displacement is the angle through which an object rotates about a fixed axis, describing the change in its orientation.
Initial Angular Velocity - (Measured in Radian per Second) - Initial Angular Velocity is the velocity of an object at the start of its motion, describing its initial rotational motion around a fixed axis.
Nth Second - (Measured in Second) - Nth Second is the time required for an object to cover a certain distance or displacement during its motion.
Angular Acceleration - (Measured in Radian per Square Second) - Angular Acceleration is the rate of change of angular velocity, describing how fast the rotation of an object changes over time.

STEP 1: Convert Input(s) to Base Unit

Initial Angular Velocity: 15.2 Radian per Second --> 15.2 Radian per Second No Conversion Required
Nth Second: 66 Second --> 66 Second No Conversion Required
Angular Acceleration: 1.6 Radian per Square Second --> 1.6 Radian per Square Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = ω_o+((2*n_th-1)/2)*α --> 15.2+((2*66-1)/2)*1.6

Evaluating ... ...

θ = 120

STEP 3: Convert Result to Output's Unit

120 Radian --> No Conversion Required

FINAL ANSWER

120 Radian <-- Angular Displacement

(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur

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< Kinematics Calculators

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Normal Acceleration

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Angle Traced in Nth Second (Accelerated Rotatory Motion) Formula

LaTeX Go

Angular Displacement = Initial Angular Velocity+((2*Nth Second-1)/2)*Angular Acceleration
θ = ω_o+((2*n_th-1)/2)*α

Why Angular Displacement is Dimensionless?

Angular displacement is measured in angles, angles measured in radians are considered to be dimensionless because the radian measure of angles is defined as the ratio of two lengths θ=sr (where s is some arc measuring s-units in length, and r is the radius) however the degree measure is not defined in this way and it is said to be dimensionless too.

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

Angle Traced in Nth Second (Accelerated Rotatory Motion) calculator uses Angular Displacement = Initial Angular Velocity+((2*Nth Second-1)/2)*Angular Acceleration to calculate 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 calculate Angle Traced in Nth Second (Accelerated Rotatory Motion) using this online calculator? To use this online calculator 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. Here is how the Angle Traced in Nth Second (Accelerated Rotatory Motion) calculation can be explained with given input values -> 118.4 = 15.2+((2*66-1)/2)*1.6.

FAQ

What is Angle Traced in Nth Second (Accelerated Rotatory Motion)?

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 and is represented as θ = ω_o+((2*n_th-1)/2)*α or Angular Displacement = Initial Angular Velocity+((2*Nth Second-1)/2)*Angular Acceleration. Initial Angular Velocity is the velocity of an object at the start of its motion, describing its initial rotational motion around a fixed axis, Nth Second is the time required for an object to cover a certain distance or displacement during its motion & Angular Acceleration is the rate of change of angular velocity, describing how fast the rotation of an object changes over time.

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

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 is calculated using Angular Displacement = Initial Angular Velocity+((2*Nth Second-1)/2)*Angular Acceleration. To calculate Angle Traced in Nth Second (Accelerated Rotatory Motion), you need Initial Angular Velocity (ω_o), Nth Second (n_th) & Angular Acceleration (α). With our tool, you need to enter the respective value for Initial Angular Velocity, Nth Second & Angular Acceleration 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 Angular Displacement?

In this formula, Angular Displacement uses Initial Angular Velocity, Nth Second & Angular Acceleration. We can use 3 other way(s) to calculate the same, which is/are as follows -

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)

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