Mechanics Free Response Question #2 Solutions  AP Physics C 1998 Released Exam
(22:40)
This Free Response Question includes the following concepts: Center of Mass of a System of Particles, Translational and Rotational Kinetic Energy, Conservation of Linear and Angular Momentum, Angular Momentum of a System of Particles and Rigid Objects and Moment of Inertia.
AP® is a registered trademark of the College Board, which was not involved in the production of, and does not endorse, this product. Enjoy an EDpuzzle Lesson for this video. Link: AP Physics C 1998 Released Exam The problem is on pages 156  158 of this pdf. The solution is on pages 182  184 of this pdf. Please enjoy my solutions as well. 

Content Times:
0:22 Describing the Problem
0:57 Part (a i)
3:58 Part (a ii)
5:01 Part (b)
5:48 Part (b i)
7:00 Part (b ii)
7:41 Part (b iii)
9:57 Part (b iv) Describing this part of the Problem
11:48 Part (b iv) Why is Angular Momentum Conserved?
13:16 Part (b iv) Initial Angular Momentum of the Rod System
13:34 Part (b iv) Initial Angular Momentum of the Clay
16:26 Part (b iv) Final Angular Momentum of the Whole System
17:41 Part (b iv) Final Moment of Inertia of the Whole System
19:07 Part (b iv) Back to Conservation of Angular Momentum
20:09 Part (b v)
Here is a Veritasium YouTube video that explains quite well the differences between parts (a) and (b) of this problem. In other words, how the clay lump that hits off center can have a smaller change in kinetic energy than when it hits at the center of mass.
0:22 Describing the Problem
0:57 Part (a i)
3:58 Part (a ii)
5:01 Part (b)
5:48 Part (b i)
7:00 Part (b ii)
7:41 Part (b iii)
9:57 Part (b iv) Describing this part of the Problem
11:48 Part (b iv) Why is Angular Momentum Conserved?
13:16 Part (b iv) Initial Angular Momentum of the Rod System
13:34 Part (b iv) Initial Angular Momentum of the Clay
16:26 Part (b iv) Final Angular Momentum of the Whole System
17:41 Part (b iv) Final Moment of Inertia of the Whole System
19:07 Part (b iv) Back to Conservation of Angular Momentum
20:09 Part (b v)
Here is a Veritasium YouTube video that explains quite well the differences between parts (a) and (b) of this problem. In other words, how the clay lump that hits off center can have a smaller change in kinetic energy than when it hits at the center of mass.