Rotational Kinematics

Rotational Kinematics

1. Uniform circular motion

   • This type of motion describes an object moving in a circular path with a constant speed.

2. Uniform circular motion

   • This type of motion describes an object moving in a circular path with a constant speed.
     • When an object moves at a constant speed in a circular path it has an acceleration.
       • To figure out what is this acceleration first let’s take in consideration the formula for acceleration which is: a= ∆v/ ∆t
         • In the case of motion in a circular path we want to represent the change in position like this:
           • Where ri is the initial position and rf is the final
             • Also we can make a triangle with the velocity vectors that would look like this:
               • Considering that velocity vector is perpendicular to “r” we can infer that both circles are similar and then write the relation
                 • Finally considering that an object with this kind of motion has acceleration we solve by ∆v the previous formula and plug it in the formula for acceleration which is a= ∆v/ ∆t giving us a formula for something we will call centripetal acceleration which will be the force pointing towards the center of the circle
                   • Tangential and Radial Acceleration
                     • In the case where the particle moves in a curve path and its velocity changes both in direction and in magnitude
                       • As the direction of acceleration changes at every point we can define de variable of total acceleration as: A=Ar+At
                     • Tangential acceleration is the result of the change in the speed of the velocity vector and its expression is:
                     • Radial acceleration is the result of the change in direction of velocity vector and its expression is:

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