need help with a physics torque problem

I’m trying to do this problem from a physics book but I’m getting the wrong answer.

A thin, uniform, 15.0kg post, 1.75m long, is standing vertically. A string is attached to the post 1.25m up from the base of the post, passes over a massless, frictionless, pulley, and is attached to a 5 kg weight. What is the angular acceleration of the post about its base when this system is released from rest (i.e. when you remove the cable that’s holding the post up in the image below)?

My solution is:

1. Calculate force from the weight (5 kg) * 9.8 = 49N

2. Calculate torque using the weight’s force. Since it’s perpendicular to the post, I’m using (force)(lever arm), which is (49N)(1.25m) = 61.25 N m

3. Calculate moment of inertia for the post about its base: 1/3ML^2 = 15.3125

4. Get angular acceleration:

(torque) = (moment of inertia)(angular acceleration)

(torque) / (moment of inertia) = (angular acceleration)

(61.25) / (15.3125) = 4 rad/s^2

.. but the book is saying the answer should be 2.65 rad/s^2. What am I missing here?

 

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