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Rotational Kinetics

Terms and Formulae

Introduction and Summary

Defining Rotation and its Variables

Terms

Rotational motion  -  The motion of any object in which every part of the object rotates about a common axis in a circular path.
Angular displacement  -  The angle swept out by the circular motion of a particle. See definition of angular displacement
Radians  -  A unit of measuring an angle. The relation between radians and degrees is as follows:

1 revolution = 2Π radians = 360 o    

Average angular velocity  -  The average rate at which an object rotates in a circular path. See formula.
Instantaneous angular velocity  -  The instantaneous rate at which an object rotates in a circular path. See formula.
Angular acceleration  -  The rate of change of angular velocity. See formula.
Right hand rule  -  The rule by which the direction of a rotational vector can be found: take your right hand, curl your fingers and stick your thumb straight up. If you let the curl of your fingers follow the path of the rotating particle or body, your thumb will point in the direction of the angular velocity of the body.

Formulae

 
Definition of angular displacement μ = s/r
 
Conversion between radians and degrees 2Π rad = 1 revolution = 360 o
 
Formula for average angular velocity =
 
Formula for instantaneous angular velocity σ =
 
Formula for angular acceleration α =
 
Kinematic equations for rotational motion
  • σ f = σ o + αt
  • μ f = μ o + σ o t + αt 2
  • σ f 2 = σ o 2 +2αμ
  • μ = (σ o + σ f)t
 
Relation of linear and angular displacement s = μr
 
Relation of linear and angular velocity v = σr
 
Relation of tangential and angular acceleration a T = αr
 
Relation of radial acceleration and angular velocity a R = σ 2 r

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