Kinetic energy and joints

Pin joint connection

Example 5.B.7 of the lecture book describes a system made up of bar OC pinned to ground at O, and pinned to the center of a disk at C, as shown below. In that problem, we are asked to relate the angular speed of OC to its angular position (using conservation of energy). For this problem, OC rotates about O and the disk translates without rotation. Therefore, the initial potential energy of the system goes into rotational KE for the bar and translational only KE for the disk.

 

Welded joint connection

Consider a problem similar to Example 5.B.7 described above, except here the disk is welded to arm OC. For this case, OC rotates about O and the disk both rotates and translates. Therefore, the initial potential energy of the system goes into rotational KE for the bar and both translational + rotational KE for the disk.

 

CONCLUSION: For a given angular orientation for OC, OC will be rotating more slowly in the welded joint case than for the pinned connection case. Can you see this in the following animation of the motion simulation for these two systems?