Irodov 1.259

 


The pulley is made of two co-axial cylinders with radii R and 2R, but having a total mass M and moment of inertia I about the central axis. The mass of the threads is negligible. Find the acceleration of the weight A after the system is set free. 

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IE Irodov 1.267

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Simultaneous rotation is happening here about 2 mutually perpendicular axes. Rotational kinetic energy is found about both the axes and their algebraic sum gives total KE.  Aliter:  In the alternative method,  KE of centre of mass(translational) about the external axis is added with KE about centre of mass (which is purely rotational). The aggregate is then added with rotational KE about it's own axis to give total KE. 
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