Solved: Rotational Dynamics | Angular Speed=3.1 rad/sec

[iamkristing]

[SOLVED] rotational dynamics

Homework Statement

A thin uniform rod has length 2.0 m and can pivot about a horizontal, frictionless pin through one end. It is released from rest as angle theta=40 above the horizontal. Use the principle of conservation of energy to determine the angular speed of the rod as it passes through the horizontal position.

Homework Equations

The Attempt at a Solution

I used mgh=.5mv^2 and found v=6.26

Since w=v/r I found the angular speed to be 6.26/2=3.1 rad/sec

I think this is how the problem is worked out...I'm just not sure. Thanks!

 

[Doc Al]

What about the rotational KE?

 

[iamkristing]

Would the rotational KE be .5Iwf^2?

Where I=(1/12)ML^2 and then you just add that on to the final kinetic energy and solve for vf?

 

[Doc Al]

You could find the total KE by adding the KE of the center of mass to the rotational KE about the center of mass. But much easier to treat the rod as purely rotating about one end.

 

[iamkristing]

ok thanks I got it!