Classical mechanics-acc. of a rod using inertia

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SUMMARY

The discussion focuses on calculating the initial acceleration of a free end of a rod when one person lets go. The correct moment of inertia for a rod of length l and mass M about the pivot point is determined using the parallel axis theorem. The initial acceleration is established as 3g/2, correcting previous miscalculations involving the center of mass. The key formulas used include torque (T = I * angular acceleration) and the moment of inertia (I = Ml²/12).

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  • Understanding of classical mechanics principles
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  • Knowledge of torque and angular acceleration relationships
  • Proficiency in applying the parallel axis theorem
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Homework Statement



two people are holding the ends of a rod length l and mass M, show that if one person let's go the initial acceleration of the free end is 3g/2


The Attempt at a Solution


i worked out the moment of inertia about centre mass (cm) and got = Ml2/12

because L=Iw
dL/dt = I*dw/dt
Torque (T) = I*ang.acc. (a)
so
a = T/I = mglsin[90] / Ml2/12
= 12g/l
this is wrong so i used l=l/2 as this is the distance to the cm.
so a = 24g/l also wrong

what am i doing wrong?
 
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Calculate the moment of inertia about the pivot point using the parallel axis theorem.
 

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