# Pivoting rod about the center

https://tychosrv-s.phys.washington.edu/cgi/courses/shell/common/showme.pl?courses/phys121/spring05/homework/08/pivoting_rod_RSD/1.gif [Broken]

A uniform rod is pivoted at its center and a small weight of mass M = 5.15 kg is rigidly attached to one end. The rod has length L = 4 m and mass mrod = 12.4 kg. The system is released from rest at the q = 37° angle. The angular acceleration just after it is released is 2.17rad/s^2. What is the angular velocity when the rod is vertical?

To do this, you can use the energy conservation. Change in potential energy of the rod plus the change in potential energy of the weight equals the kinetic energy. KE = (1/2)IW^2 = delta total Potentional energy. You get the change in potential energy by finding the delta PE of weight and the rod. delta PE of weight is simply M*G*(change in Height), but how do you find the change in PE of the rod???

Last edited by a moderator:

## Answers and Replies

OlderDan
Science Advisor
Homework Helper
jhson114 said:
https://tychosrv-s.phys.washington.edu/cgi/courses/shell/common/showme.pl?courses/phys121/spring05/homework/08/pivoting_rod_RSD/1.gif [Broken]

A uniform rod is pivoted at its center and a small weight of mass M = 5.15 kg is rigidly attached to one end. The rod has length L = 4 m and mass mrod = 12.4 kg. The system is released from rest at the q = 37° angle. The angular acceleration just after it is released is 2.17rad/s^2. What is the angular velocity when the rod is vertical?

To do this, you can use the energy conservation. Change in potential energy of the rod plus the change in potential energy of the weight equals the kinetic energy. KE = (1/2)IW^2 = delta total Potentional energy. You get the change in potential energy by finding the delta PE of weight and the rod. delta PE of weight is simply M*G*(change in Height), but how do you find the change in PE of the rod???
The potential energy of the rod does not change because the pivot point is the center of mass.

Last edited by a moderator:
thats what i thought too. i wasnt getting the right answer, but i guess i did the calculations wrong. thanks !