1. Chapter 13 Outline Gravitation Newton’s law of gravitation Weight Gravitational potential energy Circular orbits Kepler’s laws Black holes

2. Gravitation

3. Gravitational Force Acts on both bodies with equal magnitude. When you jump off a diving board, Earth also accelerates towards you, but your mass is 23 orders of magnitude smaller, so this is negligible. Spherically symmetric masses look like points from the outside. Replace sphere with a single point mass at the center.

5. Weight

6. Mass of the Earth

7. Density of the Earth

8. Exam #3 Thursday, April 2 nd – 12:30p-1:45p Covers chapters 9-12 Previous material will also be incorporated Energy, kinematics, vectors… Same format as Exams #1 and #2 20 questions Multiple choice Mixture of calculation and conceptual problems Many problems will incorporate concepts from multiple chapters. Bring: Calculator (extra batteries are a good idea) Pencil Student ID

9. Exam #3 Thursday, April 2 nd – 12:30p-1:45p Recommended for last minute studying: Example questions posted on Canvas: Files > Study Material for Exams Worked textbook problems posted on Canvas: Files > Worked Example Problems Discussion questions at the end of each chapter Grades I will try to get the exams graded on Friday. If so, I should be able to post scores a couple days after the exam. Homework Because of the exam, I will not assign any homework this week. I will post two assignments on Tuesday, the short one due Thursday, and the long one the following Tuesday.

10. Example Problem

11. Four uniform rigid objects, a solid sphere, a hollow sphere, a solid cylinder, and a hollow cylinder, roll down a smooth hill without slipping. If each starts from rest at the same time, which one reaches the bottom first? A) The solid sphere B) The hollow sphere C) The solid cylinder D) The hollow cylinder E) They all hit the bottom at the same time.

12. Example Problem