Angular Displacement given Initial Angular Velocity Angular Acceleration and Time Solution

STEP 0: Pre-Calculation Summary
Formula Used
Angular Displacement = Initial Angular Velocity*Time Taken to Travel the Path+(Angular Acceleration*Time Taken to Travel the Path^2)/2
θ = ωo*t+(α*t^2)/2
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.
Time Taken to Travel the Path - (Measured in Second) - Time Taken to Travel the Path is the total time taken by an object to reach its destination.
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
Time Taken to Travel the Path: 6 Second --> 6 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*t+(α*t^2)/2 --> 14*6+(1.6*6^2)/2
Evaluating ... ...
θ = 112.8
STEP 3: Convert Result to Output's Unit
112.8 Radian --> No Conversion Required
FINAL ANSWER
112.8 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!
Verified by Team Softusvista
Softusvista Office (Pune), India
Team Softusvista has verified this Calculator and 1100+ more calculators!

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

Angular Displacement given Initial Angular Velocity Angular Acceleration and Time Formula

Angular Displacement = Initial Angular Velocity*Time Taken to Travel the Path+(Angular Acceleration*Time Taken to Travel the Path^2)/2
θ = ωo*t+(α*t^2)/2

What is angular displacement ?

The angular displacement of a body is the angle in radians (degrees, revolutions) through which a point revolves around a center or line that has been rotated in a specified sense about a specified axis. When a body rotates about its axis, the motion cannot simply be analyzed as a particle, as in circular motion it undergoes a changing velocity and acceleration at any time (t). When dealing with the rotation of a body, it becomes simpler to consider the body itself rigid

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

Angular Displacement given Initial Angular Velocity Angular Acceleration and Time calculator uses Angular Displacement = Initial Angular Velocity*Time Taken to Travel the Path+(Angular Acceleration*Time Taken to Travel the Path^2)/2 to calculate the Angular Displacement, Angular Displacement given Initial Angular Velocity Angular Acceleration and Time is defined as “the angle in radians (degrees, revolutions) through which a point or line has been rotated in a specified sense about a specified axis”. It is the angle of the movement of a body in a circular path. Angular Displacement is denoted by θ symbol.

How to calculate Angular Displacement given Initial Angular Velocity Angular Acceleration and Time using this online calculator? To use this online calculator for Angular Displacement given Initial Angular Velocity Angular Acceleration and Time, enter Initial Angular Velocity o), Time Taken to Travel the Path (t) & Angular Acceleration (α) and hit the calculate button. Here is how the Angular Displacement given Initial Angular Velocity Angular Acceleration and Time calculation can be explained with given input values -> 112.8 = 14*6+(1.6*6^2)/2.

FAQ

What is Angular Displacement given Initial Angular Velocity Angular Acceleration and Time?
Angular Displacement given Initial Angular Velocity Angular Acceleration and Time is defined as “the angle in radians (degrees, revolutions) through which a point or line has been rotated in a specified sense about a specified axis”. It is the angle of the movement of a body in a circular path and is represented as θ = ωo*t+(α*t^2)/2 or Angular Displacement = Initial Angular Velocity*Time Taken to Travel the Path+(Angular Acceleration*Time Taken to Travel the Path^2)/2. Initial angular velocity is the velocity at which motion starts, Time Taken to Travel the Path is the total time taken by an object to reach its destination & Angular acceleration refers to the time rate of change of angular velocity.
How to calculate Angular Displacement given Initial Angular Velocity Angular Acceleration and Time?
Angular Displacement given Initial Angular Velocity Angular Acceleration and Time is defined as “the angle in radians (degrees, revolutions) through which a point or line has been rotated in a specified sense about a specified axis”. It is the angle of the movement of a body in a circular path is calculated using Angular Displacement = Initial Angular Velocity*Time Taken to Travel the Path+(Angular Acceleration*Time Taken to Travel the Path^2)/2. To calculate Angular Displacement given Initial Angular Velocity Angular Acceleration and Time, you need Initial Angular Velocity o), Time Taken to Travel the Path (t) & Angular Acceleration (α). With our tool, you need to enter the respective value for Initial Angular Velocity, Time Taken to Travel the Path & 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, Time Taken to Travel the Path & Angular Acceleration. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • 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)
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!