Question

A twirler's baton is made of a slender metal cylinder of mass M and length L . Each end has a rubber cap of mass m, and you can accurately treat each cap as a particle in this problem. Find the total moment of inertia of the baton about the usual twirling axis (perpendicular to the baton through its center).

Answer 1

moment of inertia of the metal cylinder=Im=(1/4)MR^2+(1/12)ML^2
moment of inertia of 1rubber cap=m(L/2)^2
=(mL^2)/4
since there are 2 identical caps at either ends,
the moment of inertia of the caps=Ic=(mL^2)/2
Therefore,
moment of inertia of the system=Im+Ic
=(1/4)MR^2+(1/12)ML^2+(mL^2)/2