Classical mechanics-acc. of a rod using inertia

AI Thread Summary
The discussion revolves around calculating the initial acceleration of a free end of a rod when one person holding it lets go. The moment of inertia was initially calculated incorrectly, leading to wrong acceleration results. The correct approach involves using the parallel axis theorem to find the moment of inertia about the pivot point. The final goal is to demonstrate that the initial acceleration of the free end is 3g/2. Understanding the correct application of torque and moment of inertia is crucial for solving this problem.
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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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