1. Position update formula We can use this to predict the motion of an object, if we know (or can guess) v avg.

2. This formula is the key to simulating motion with computer programs. 模拟 1.Calculate new r 2.Calculate new v avg (how?...) 3.Next time step

3. My research: simulating the motion of proteins 蛋白质 Proteins are the molecular machines that must work to keep living things alive. Many diseases are caused by ‘broken’ proteins.

4. Special case: constant acceleration A common example of constant acceleration: falling.

5. Which direction is the acceleration?

7. Parallel (or anti-parallel) to the velocity, changing the speed. 平行

8. Which direction is the acceleration? Perpendicular to the velocity, changing the direction of motion. 垂直

9. Curved motion

10. Acceleration can be split into two types: (1) Acceleration that changes speed, and not direction (2) Acceleration that changes direction, and not speed

11. Acceleration can be split into two types: Change in speed: tangential acceleration a t Change in direction: radial acceleration a r

12. Let’s calculate a r.

13. θ R R After a time Δt, particle moves to position 2. RR θ θ 1 1 These are similar triangles.

14. θ R R After a time Δt, particle moves to position 2. RR θ θ 11 These are similar triangles.

15. RR θ θ 11 These are similar triangles, so:

16. The radial acceleration is also called centripetal acceleration. Its magnitude is 向心加速度 and its direction is towards the center of the circle.

17. Example: The Moon’s orbit around the Earth

18. Assume a circular orbit. (It’s really an ellipse.) 假设 R = 3.84 x 10 8 m Period of one orbit: T = 27.3 days