The pulley of Atwood's machine has a moment of inertia 'I' about its axis and its radius is R. Find the magnitude of acceleration of the two blocks assuming the string is light and does not slip on the pulley.

The pulley of Atwood's machine has a moment of inertia 'I' about its a

1.	The pulley of Atwood's machine has a moment of inertia 'I' about its axis and its radius is R. Find the magnitude of acceleration of the two blocks assuming the string is light and does not slip on the pulley.
Answer» Solution :Suppose the block of mass M goes down with an acceleration a. The ANGULAR acceleration of the pulley is THEREFORE `alpha=(a)/(R )` `Mg-T_(1)=Ma` `T_(2)-mg=ma` `T_(1)R-T_(2)R=Ialpha=I(a)/(R )` Solving the EQUATIONS `a=((M-m)GR^(2))/(I+(M+m)R^(2))`