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

✖Final Angular Velocity is the angular velocity of an object at the end of a specific time period or distance of motion.ⓘ Final Angular Velocity [ω₁]			+10% -10%
✖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%
✖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.ⓘ Angular Displacement of Body for given Initial and Final Angular Velocity [θ]

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Formula

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Angular Displacement of Body for given Initial and Final Angular Velocity

Formula

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

Example

120 rad = \frac{{24.8 rad/s}^{2} - {15.2 rad/s}^{2}}{2 \cdot 1.6 rad/s²}

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

STEP 0: Pre-Calculation Summary

Formula Used

Angular Displacement = (Final Angular Velocity^2-Initial Angular Velocity^2)/(2*Angular Acceleration)
θ = (ω₁^2-ω_o^2)/(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.
Final Angular Velocity - (Measured in Radian per Second) - Final Angular Velocity is the angular velocity of an object at the end of a specific time period or distance of motion.
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.
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

Final Angular Velocity: 24.8 Radian per Second --> 24.8 Radian per Second No Conversion Required
Initial Angular Velocity: 15.2 Radian per Second --> 15.2 Radian per 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 = (ω₁^2-ω_o^2)/(2*α) --> (24.8^2-15.2^2)/(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

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

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)

Normal Acceleration

Go Normal Acceleration = Angular Velocity^2*Radius of Curvature

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

Angular Displacement = (Final Angular Velocity^2-Initial Angular Velocity^2)/(2*Angular Acceleration)
θ = (ω₁^2-ω_o^2)/(2*α)

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 of Body for given Initial and Final Angular Velocity?

Angular Displacement of Body for given Initial and Final Angular Velocity calculator uses Angular Displacement = (Final Angular Velocity^2-Initial Angular Velocity^2)/(2*Angular Acceleration) to calculate the Angular Displacement, Angular Displacement of Body for given Initial and Final Angular Velocity formula is defined as a measure of the change in angular position of a rotating body, describing the rotation of an object from an initial to a final angular velocity, and is a fundamental concept in the kinematics of motion. Angular Displacement is denoted by θ symbol.

How to calculate Angular Displacement of Body for given Initial and Final Angular Velocity using this online calculator? To use this online calculator for Angular Displacement of Body for given Initial and Final Angular Velocity, enter Final Angular Velocity (ω₁), Initial Angular Velocity (ω_o) & Angular Acceleration (α) and hit the calculate button. Here is how the Angular Displacement of Body for given Initial and Final Angular Velocity calculation can be explained with given input values -> -34.3875 = (24.8^2-15.2^2)/(2*1.6).

FAQ

What is Angular Displacement of Body for given Initial and Final Angular Velocity?

Angular Displacement of Body for given Initial and Final Angular Velocity formula is defined as a measure of the change in angular position of a rotating body, describing the rotation of an object from an initial to a final angular velocity, and is a fundamental concept in the kinematics of motion and is represented as θ = (ω₁^2-ω_o^2)/(2*α) or Angular Displacement = (Final Angular Velocity^2-Initial Angular Velocity^2)/(2*Angular Acceleration). Final Angular Velocity is the angular velocity of an object at the end of a specific time period or distance of motion, Initial Angular Velocity is the velocity of an object at the start of its motion, describing its initial rotational motion around a fixed axis & Angular Acceleration is the rate of change of angular velocity, describing how fast the rotation of an object changes over time.

How to calculate Angular Displacement of Body for given Initial and Final Angular Velocity?

Angular Displacement of Body for given Initial and Final Angular Velocity formula is defined as a measure of the change in angular position of a rotating body, describing the rotation of an object from an initial to a final angular velocity, and is a fundamental concept in the kinematics of motion is calculated using Angular Displacement = (Final Angular Velocity^2-Initial Angular Velocity^2)/(2*Angular Acceleration). To calculate Angular Displacement of Body for given Initial and Final Angular Velocity, you need Final Angular Velocity (ω₁), Initial Angular Velocity (ω_o) & Angular Acceleration (α). With our tool, you need to enter the respective value for Final Angular Velocity, Initial Angular Velocity & 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 Final Angular Velocity, Initial Angular Velocity & 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*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

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