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How did you get the equation T=(3/2)mc*a?

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Step 1: Concept

$T o t a l space M o m e n t space o f space i n e r t i a space o f space c y l i n d e r space a b o u t space t h e space p o i n t space o f space c o n t a c t space o f space c y l i n d e r space a n d space a n y space p e r p e n d i c u l e r space a x i s space o f space c y l i n d e r I equals I subscript C M end subscript plus M subscript c R squared I equals 1 half M subscript c R squared plus M subscript c R squared I equals 3 over 2 M subscript c R squared N o w space a n g u l e r space t o r q u e space r e q u i r e d space t o space m o v e space t h e space c y l i n d e r tau equals I alpha W h e r e space alpha equals a n g u l e r space a c c e l e r a t i o n equals a over R a equals L i n e a r space a c c e l e r a t i o n s o comma space tau equals I a over R W o r k d o n e space d u e space t o space b o x space m o v e m e n t w equals T R T equals T e n s i o n space i n space t h e space r o p e T h e r e f o r e space d u e space t o space c o n s e r v t i o n space e n e r g y w e space c a n space w r i t e tau equals w I a over R equals T R T equals I a over R squared$

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