- 18

- 0

**1. The problem statement, all variables and given/known data**

A uniform rod AB is hinged smoothly at A. The length L of the rod is 50cm. Determine

a) The angular velocity,

of the rod when it makes an angle (Theta) =30

^{o}with the verticle.

( Moment of inertia of rod about axis through one end and perpendicular to the rod = 1/3 mL

^{2}; g =9.8m s

^{-2}

**2. Relevant equations**

Ki + Ui = Kf + Uf

**3. The attempt at a solution**

0 + mgh

_{i}= 1/2 Iw

^{2}+ mgh

_{f}

Where h

_{i }= 1/2 L

and h

_{f}= 1/2 L ( 1-cos Theta )

Then plugging in the information given,

Angular velocity = 7.1 rad s

^{-1}

When the rod is vertical, let the horizontal line which passes through the center of the rod be the reference line where h=0 and U=0.

Can anybody tell me why the final potential energy is not just 1/2 L cos Theta.

Or is it 1/2 L ( 1-cos Theta ) ?

Thanks...