Calculating Angular Acceleration in a Pivoted Rod

[UrbanXrisis]

rod -- angular acceleration

A long uniform rod length L and mass M is pivoted about a horizonal, frictionless pin passing through one end. The rod is released from rest in a vertical position. The instant the rod is horizontal, what is the magnitue of its angular acceleration.

It's angular speed I know is $$\sqrt{\frac{3g}{L}}$$
using the formula $$\alpha=rw^2$$
I get then angular acceleration to be 3g. However the book tells me that the answer is 3g/2L. What am I missing?

 

[arildno]

Whatever formulas are you using?

Write down the moment-of-momentum equation about the pivot:
a) What is the moment of inertia?
b) What is the torque induced by gravity?

 

[dextercioby]

Yes,your answer is incorrect,even not knowing the physics to solve the problem,nor the book's answer.

I think you can use the law of conservation of energy...

Daniel.