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Formula of Angular Displacement. Angular displacement of a point can be given by using the following formula, \ (\begin {array} {l}Angular displacement = \theta _ {f}- \theta _ {i}\end {array} \) Where, \ (\begin {array} {l}\theta = s/r\end {array} \)
This equation can be very useful if we know the average angular velocity of the system. Then we could find the angular displacement over a given time period. Next, we find an equation relating ω ω, α α, and t. To determine this equation, we start with the definition of angular acceleration:
Angular displacement is defined as the shortest angle between the initial and the final positions for a given object having a circular motion about a fixed point. Here angular displacement is a vector quantity. Thus it will have the magnitude as well as the direction.
Angular displacement can be calculated using the equation: When the angle is equal to one radian, the length of the arc (Δs) is equal to the radius (r) of the circle. Where: Δ θ = angular displacement, or angle of rotation (radians) s = length of the arc, or the distance travelled around the circle (m) r = radius of the circle (m)
The formula given down below is the way to find out the angular displacement. Angular Displacement (θ) = Distance travelled (s)/Radius of the circular path (r) S= length of the arc. R= radius of the circle. Θ= angular displacement. Let us take some examples on Angular displacement:
θ = s/r. Here, θ denotes the angular displacement of the object.
Combining Equations \ref{omega} and \ref{arc}, and substituting displacement \(dx\) with change in arc length, \(ds\), we obtain a relationship between angular and linear speed: \[v=\frac{ds}{dt}=R\frac{d\theta}{dt}=R\omega\]
