Angular Velocity

Angular Velocity - Angular Acceleration The rotational...

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Angular Velocity Angular displacement is an equivalent quantity to linear displacement. Indeed, by taking the linear displacement of a given particle on an object and dividing by the radius of that point, we derive angular displacement. The equivalency between linear and angular displacement leads us to a further realization: just as we define linear velocity from linear displacement, we similarly define angular velocity from angular displacement. If an object is displaced by an angle of Δμ during a time period of Δt , we define the average angular velocity as: = And, using calculus, we define the instantaneous angular velocity as: σ = Like angular displacement, angular velocity is identical for every point on a rotating object, and essentially describes the rate at which an object rotates.
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Unformatted text preview: Angular Acceleration The rotational corollary of linear acceleration is angular acceleration, the rate of change of angular velocity. In the same manner as we derived the equations for average and instantaneous velocity, we define angular acceleration: = = These equations for angular displacement, velocity, and acceleration bear striking resemblance to our definitions of translational variables. To see this, simply substitute x every time you see , v every time you see , and a every time you see . The yield are the translational equations for displacement, velocity, and acceleration. This similarity will allow us to easily derive kinematic equations for rotational motion...
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