KINEMATICS. [284. 



(2) Show that <au is the total acceleration of the instantaneous 

 centre C. 



(3) Show that the points of the semi-circle described over CH as 

 diameter and containing / have no tangential acceleration, and that for 

 points without the circle about CH the velocity is increasing while 

 for points within it is decreasing. 



(4) Find the locus of the points of equal tangential acceleration. 



(5) Show that the locus of the points having no normal acceleration 

 at a given instant is a circle touching the common tangent of the 

 centrodes at C and passing through /. This circle is called the circle 

 of inflexions ; give the reason for this name. 



(6) Find the locus of the points having equal normal acceleration. 



(7) Show that the diameter of the circle of inflexions is equal to the 

 radius of relative curvature of the centrodes. 



(8) Determine the locus of the points whose acceleration at any 

 instant is parallel (a) to the common normal, (b) to the common tangent 

 of the centrodes. 



