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h1. Circular Motion with Constant Speed


h3. *System:*

Point particle moving in a circle of radius R at constant angular speed 
{latex} $\omegaomega$ {latex} 

. (Requires a net force of constant magnitude and direction radially inwards to the circle, i.e  no force component in the direction tangent to the velocity.) 
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h3. *Description of the system:*

\- *Object in the system*: point particle.

\- *State variables:*  .

\- *Environment:* external agents interacting with the particle which are the responsible of the *real* forces acting *on* the particle. * *

h3. *Description of the Interactions:*

\- Because we are describing the motion of a point particle we only consider force from outside the interactions as the cause of the acceleration. The total force acting on the point particle has a constant magnitude and direction pointing towards the center of the circle. 
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h3. *Multiple Representations and geometric description.*

\- Position of the particle with respect to a reference frame, in general the center of the circle:  or _q{_}_(t)_. Use of Cartesian and polar coordinates system.

\- Motion Diagrams, tables, equations, vectors.
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h3. *Law of Change (*describe the change of the state variables*)\*

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where  are vectors of constant magnitude and rotates with a constant angular velocity w.  
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h3. *Definitions and procedures:*     

  Angular velocity _w_ (rad/sec)

\-          Cartesian and Polar representation of position and velocity.

\-          Cartesian:  _x(t) = R cos (_{_}w{_}{_}t +_ _f{_}{_}{~}o{~}{_}_), y(t) = sin (_{_}w{_}{_}t +_ _f{_}{_}{~}o{~}{_}_)_ ...

\-          Differentiating Cartesian and Polar representation of position and velocity, and implications of the derivative of a vector with constant magnitude but a direction that changes with time.

\-          In uniform circular motion the acceleration points toward the center, the velocity is tangent to the circle.