^{2}+ y

^{2}= 1, its much easier to just say r = 1 for all values of θ. We define the old x and y as:

x=r cos (θ)

y=r sin(θ)

Now we replace the terms in normal motion with their angular motion counterparts.

v = δx/δt

ω = δθ/δt

velocity goes from the change in position over time to angular velocity, the change in angle over time. However, it is defined slightly differently. Velocity is defined with a vector pointing in the same direction as the motion of the object. Angular velocity is defined with a vector pointing perpendicular to the plane of the angular motion. To be more specific, the direction is defined by the cross product of the motion of a point on the edge of the object and the vector from the center of the object to the point.

a = δv/δt

α = δω/δt

Angular acceleration is also defined with a vector perpendicular to the rotational motion of the object. This means that both angular acceleration and angular velocity are defined in the z axis, and for the purposes of basic mechanics, remains stationary.

There are also analogs to the basic equations of motion. Assuming constant angular acceleration we can get:

ω

_{z}=ω

_{0z}+ α

_{z}t

θ-θ

_{0}=1/2(ω

_{0z}+ω

_{z})t

θ=θ

_{0 }+ ω

_{0z}t + 1/2α

_{z}t

^{2}

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