How Is Angular Velocity Calculated in a Hinged Rod Scenario?

[Victorian91]

Homework Statement

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 vertical.

( Moment of inertia of rod about axis through one end and perpendicular to the rod = 1/3 mL² ; g =9.8m s^-2

Homework Equations

Ki + Ui = Kf + Uf

The Attempt at a Solution

0 + mgh_i = 1/2 Iw² + 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...

 

[tiny-tim]

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 ) ?

Hi Victorian91!

(have a theta: θ )

potential energy can be measured from anywhere …

it's your choice …

if you chose to measure it from θ = 0, then you have make sure that it's 0 at θ = 0