Solve Acceleration of Rod's Centre of Mass

AI Thread Summary
The discussion focuses on calculating the acceleration of the center of mass of a vertically standing rod that is slightly disturbed. The user attempts to derive the acceleration using the equations of motion and torque but arrives at a different expression than the one provided in the solution. The key equations involved include the net force and torque equations related to angular motion. The user questions the validity of their derived expression, indicating confusion about the correct approach to the problem. Ultimately, the discussion highlights the complexities of rotational dynamics and the importance of correctly applying the relevant equations.
Diganta28
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1. Homework Statement :

A rod of length l is vertically standing on a friction less surface.
It is slightly disturbed from this position. Let w(omega) and alpha be the angular speed and angular acceleration of the rod, when it turns through an angle theta, then find the value of acceleration of centre of mass of the rod.

2. Homework Equations :

acom = ( Fnet/mnet)

tau = i * alpha

tau= force*perpendicular distance from axis of rotation

3. The Attempt at a Solution :

Tried like this (but no luck):

(mg-N)=ma , where a is the required answer.N * (l/2) sin theta = (1/12 m (l)^2) * alpha

Solved to get : a = g-(l * alpha/(6 sin theta)).

But answer given :

l *(alpha/2)* sin theta + (w^2*l/2) cos theta

 
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Ok I understood what they are doing.

But is the answer :
g - (l*alpha/(6 sin theta)) wrong?
 

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