A disc of mass M and radius R is rolling with angular speed omega on a horizontal plane as shown in figure. The magnitude of angular momentum of the disc about the origin O is

A disc of mass M and radius R is rolling with angular speed omega on a

1.	A disc of mass M and radius R is rolling with angular speed omega on a horizontal plane as shown in figure. The magnitude of angular momentum of the disc about the origin O is
Answer» `(1/2)MR^(2)OMEGA` `MR^(2)omega` `(3/2)MR^(2)omega` `2Mr^(2)omega` Solution :The disc has two types of motion, namely, translation and rotational. Therefore there are two types of angular moment and the total angular momentum is the sum of thes two. `L=L_(T)+L_(R), L_(t)=` angular momentum due to translational motion `L_(R)=` angular momentum due to rotational motion about `CM` `L=MVxxR+I_(CM)omegaI_(CM)` `=MI` about centre of mass `C` `=M(Romega)R+1/2MR^(2)omega(V=Romega` in case of ROLLING motion and SURFACE at rest) `=3/2MR^(2)omega`