Angular Displacement given Angular Acceleration Calculator

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✖The Initial angular velocity of object undergoing curvilinear motion is calculated concerning time and acceleration.ⓘ Initial angular velocity of object [ω_in]			+10% -10%
✖Time Period is what a clock reads, it is a scalar quantity.ⓘ Time Period [t_cm]			+10% -10%
✖Angular Acceleration is defined as the rate of change of angular velocity.ⓘ Angular Acceleration [α_cm]			+10% -10%

✖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.ⓘ Angular Displacement given Angular Acceleration [θ_cm]

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Formula

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Angular Displacement given Angular Acceleration

Formula

`"θ"_{"cm"} = "ω"_{"in"}*"t"_{"cm"}+1/2*"α"_{"cm"}*"t"_{"cm"}^2`

Example

`"6187.944°"="24rad/s"*"3s"+1/2*"8rad/s²"*("3s")^2`

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Angular Displacement given Angular Acceleration Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angular Displacement = Initial angular velocity of object*Time Period+1/2*Angular Acceleration*Time Period^2
θ_cm = ω_in*t_cm+1/2*α_cm*t_cm^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 of object - (Measured in Radian per Second) - The Initial angular velocity of object undergoing curvilinear motion is calculated concerning time and acceleration.
Time Period - (Measured in Second) - Time Period is what a clock reads, it is a scalar quantity.
Angular Acceleration - (Measured in Radian per Square Second) - Angular Acceleration is defined as the rate of change of angular velocity.

STEP 1: Convert Input(s) to Base Unit

Initial angular velocity of object: 24 Radian per Second --> 24 Radian per Second No Conversion Required
Time Period: 3 Second --> 3 Second No Conversion Required
Angular Acceleration: 8 Radian per Square Second --> 8 Radian per Square Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ_cm = ω_in*t_cm+1/2*α_cm*t_cm^2 --> 24*3+1/2*8*3^2

Evaluating ... ...

θ_cm = 108

STEP 3: Convert Result to Output's Unit

108 Radian -->6187.94418741405 Degree (Check conversion here)

FINAL ANSWER

6187.94418741405 ≈ 6187.944 Degree <-- Angular Displacement

(Calculation completed in 00.007 seconds)

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< 11 Curvilinear Motion Calculators

Angular Displacement given Angular Acceleration

Go Angular Displacement = Initial angular velocity of object*Time Period+1/2*Angular Acceleration*Time Period^2

Initial Angular Velocity

Go Initial angular velocity of object = Final Angular Velocity of Object-Angular Acceleration*Time Period

Final Angular Velocity

Go Final Angular Velocity of Object = Initial angular velocity of object+Angular Acceleration*Time Period

Average Angular Velocity

Go Angular Velocity = (Initial angular velocity of object+Final Angular Velocity of Object)/2

Radius of Curvilinear Motion given Linear Acceleration

Go Radius = Acceleration for Curvilinear Motion/Angular Acceleration

Angular Acceleration given Linear Acceleration

Go Angular Acceleration = Acceleration for Curvilinear Motion/Radius

Linear Acceleration in Curvilinear Motion

Go Acceleration for Curvilinear Motion = Angular Acceleration*Radius

Velocity in Curvilinear Motion given Angular Velocity

Go Velocity of Curvilinear Motion = Angular Velocity*Radius

Radius of Curvilinear Motion given Angular velocity

Go Radius = Velocity of Curvilinear Motion/Angular Velocity

Angular Velocity given Linear Velocity

Go Angular Velocity = Velocity of Curvilinear Motion/Radius

Angular Velocity of Body Moving in Circle

Go Angular Velocity = Angular Displacement/Time Period

Angular Displacement given Angular Acceleration Formula

Angular Displacement = Initial angular velocity of object*Time Period+1/2*Angular Acceleration*Time Period^2
θ_cm = ω_in*t_cm+1/2*α_cm*t_cm^2

What is angular displacement?

Angular displacement 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.

How to Calculate Angular Displacement given Angular Acceleration?

Angular Displacement given Angular Acceleration calculator uses Angular Displacement = Initial angular velocity of object*Time Period+1/2*Angular Acceleration*Time Period^2 to calculate the Angular Displacement, Angular Displacement given Angular Acceleration is defined as the sum of product of initial angular velocity, time and half of the product of angular acceleration, square of time. Angular Displacement is denoted by θ_cm symbol.

How to calculate Angular Displacement given Angular Acceleration using this online calculator? To use this online calculator for Angular Displacement given Angular Acceleration, enter Initial angular velocity of object (ω_in), Time Period (t_cm) & Angular Acceleration (α_cm) and hit the calculate button. Here is how the Angular Displacement given Angular Acceleration calculation can be explained with given input values -> 354543.1 = 24*3+1/2*8*3^2.

FAQ

What is Angular Displacement given Angular Acceleration?

Angular Displacement given Angular Acceleration is defined as the sum of product of initial angular velocity, time and half of the product of angular acceleration, square of time and is represented as θ_cm = ω_in*t_cm+1/2*α_cm*t_cm^2 or Angular Displacement = Initial angular velocity of object*Time Period+1/2*Angular Acceleration*Time Period^2. The Initial angular velocity of object undergoing curvilinear motion is calculated concerning time and acceleration, Time Period is what a clock reads, it is a scalar quantity & Angular Acceleration is defined as the rate of change of angular velocity.

How to calculate Angular Displacement given Angular Acceleration?

Angular Displacement given Angular Acceleration is defined as the sum of product of initial angular velocity, time and half of the product of angular acceleration, square of time is calculated using Angular Displacement = Initial angular velocity of object*Time Period+1/2*Angular Acceleration*Time Period^2. To calculate Angular Displacement given Angular Acceleration, you need Initial angular velocity of object (ω_in), Time Period (t_cm) & Angular Acceleration (α_cm). With our tool, you need to enter the respective value for Initial angular velocity of object, Time Period & Angular Acceleration and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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