A pendulum is constructed from a slender rod and disk as shown in the figure.

(a) Set up the rotational version of Newton’s second law and show that the expression for the angular frequency squared depends only on the ratio M/m and not on the individual values. 

(b) Show that  

where  

(c) Using  u=2/3 and ignoring R, determine D for an angular frequency 

(d) Using the value for D from part (c) and R= 0.05/1.8 , recalculate  w and the % difference for answers (c) & (d). 

(e) Compare the % difference in part (d) with the value of