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 = ωo+((2*nth-1)/2)*α
This formula uses 4 Variables
Variables Used
Angular Displacement - (Measured in Radian) - 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.
Initial Angular Velocity - (Measured in Radian per Second) - Initial angular velocity is the velocity at which motion starts.
Nth Second - (Measured in Second) - The Nth Second is the n seconds time covered by the body.
Angular Acceleration - (Measured in Radian per Square Second) - Angular acceleration refers to the time rate of change of angular velocity.
STEP 1: Convert Input(s) to Base Unit
Initial Angular Velocity: 14 Radian per Second --> 14 Radian per Second No Conversion Required
Nth Second: 4 Second --> 4 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 = ωo+((2*nth-1)/2)*α --> 14+((2*4-1)/2)*1.6
Evaluating ... ...
θ = 19.6
STEP 3: Convert Result to Output's Unit
19.6 Radian --> No Conversion Required
FINAL ANSWER
19.6 Radian <-- Angular Displacement
(Calculation completed in 00.004 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
Anshika Arya has created this Calculator and 2000+ more calculators!
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18 Kinematics Calculators

Angular Displacement given Initial Angular Velocity Angular Acceleration and Time
Go Angular Displacement = Initial Angular Velocity*Time Taken to Travel the Path+(Angular Acceleration*Time Taken to Travel the Path^2)/2
Displacement of Body given Initial Velocity Acceleration and Time
Go Displacement of Body = Initial Velocity*Time Taken to Travel the Path+(Acceleration of Body*Time Taken to Travel the Path^2)/2
Angular Displacement given Initial Angular Velocity Final Angular Velocity and Time
Go Angular Displacement = ((Initial Angular Velocity+Final Angular Velocity)/2)*Time Taken to Travel the Path
Angular Displacement of Body for given Initial and Final Angular Velocity
Go Angular Displacement = (Final Angular Velocity^2-Initial Angular Velocity^2)/(2*Angular Acceleration)
Final Angular Velocity given Initial Angular Velocity Angular Acceleration and Time
Go Final Angular Velocity = Initial Angular Velocity+Angular Acceleration*Time Taken to Travel the Path
Displacement of Body given Initial Velocity and Final Velocity
Go Displacement of Body = ((Initial Velocity+Final Velocity)/2)*Time Taken to Travel the Path
Angle Traced in Nth Second (Accelerated Rotatory Motion)
Go Angular Displacement = Initial Angular Velocity+((2*Nth Second-1)/2)*Angular Acceleration
Displacement of Body given Initial Velocity Final Velocity and Acceleration
Go Displacement of Body = (Final Velocity^2-Initial Velocity^2)/(2*Acceleration of Body)
Final Velocity of Body
Go Final Velocity = Initial Velocity+Acceleration of Body*Time Taken to Travel the Path
Final Velocity of Freely Falling Body from Height when it Reaches Ground
Go Velocity on Reaching Ground = sqrt(2*Acceleration due to Gravity*Height of Crack)
Distance Travelled in Nth Second (Accelerated Translatory Motion)
Go Distance Traveled = Initial Velocity+((2*Nth Second-1)/2)*Acceleration of Body
Resultant Acceleration
Go Resultant Acceleration = sqrt(Tangential Acceleration^2+Normal Acceleration^2)
Angle of Inclination of Resultant Acceleration with Tangential Acceleration
Go Inclination Angle = atan(Normal Acceleration/Tangential Acceleration)
Tangential Acceleration
Go Tangential Acceleration = Angular Acceleration*Radius of Curvature
Centripetal or Radial Acceleration
Go Angular Acceleration = Angular Velocity^2*Radius of Curvature
Normal Acceleration
Go Normal Acceleration = Angular Velocity^2*Radius of Curvature
Angular Velocity given Tangential Velocity
Go Angular Velocity = Tangential Velocity/Radius of Curvature
Average Velocity of Body given Initial and Final Velocity
Go Average Velocity = (Initial Velocity+Final Velocity)/2

Angle Traced in Nth Second (Accelerated Rotatory Motion) Formula

Angular Displacement = Initial Angular Velocity+((2*Nth Second-1)/2)*Angular Acceleration
θ = ωo+((2*nth-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) is the angular displacement of a body that is the angle in radians (degrees, revolutions). A point revolves around a center or line rotated in a specified sense about a specified axis. 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 o), Nth Second (nth) & 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 -> 19.6 = 14+((2*4-1)/2)*1.6.

FAQ

What is Angle Traced in Nth Second (Accelerated Rotatory Motion)?
Angle traced in nth Second (accelerated rotatory motion) is the angular displacement of a body that is the angle in radians (degrees, revolutions). A point revolves around a center or line rotated in a specified sense about a specified axis and is represented as θ = ωo+((2*nth-1)/2)*α or Angular Displacement = Initial Angular Velocity+((2*Nth Second-1)/2)*Angular Acceleration. Initial angular velocity is the velocity at which motion starts, The Nth Second is the n seconds time covered by the body & Angular acceleration refers to the time rate of change of angular velocity.
How to calculate Angle Traced in Nth Second (Accelerated Rotatory Motion)?
Angle traced in nth Second (accelerated rotatory motion) is the angular displacement of a body that is the angle in radians (degrees, revolutions). A point revolves around a center or line rotated in a specified sense about a specified axis 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 o), Nth Second (nth) & 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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