1. Physics 218, Lecture V1 Physics 218 Lecture 5 Dr. David Toback

2. Physics 218, Lecture V2 Notes: Reading assignment for Chapter 3 is due today –Make sure to put your Section number on it Chapter 1 was due yesterday (also math quizzes)

3. Physics 218, Lecture V3 Chapter 3 Kinematics in Two or Three Dimensions Projectile Motion Uniform Circular Motion

4. Physics 218, Lecture V4

5. 5 Position in 3 dimensions

6. Physics 218, Lecture V6 Velocity in 3 dimensions

7. Physics 218, Lecture V7 Projectile Motion This is what all the setup has been for! Motion in two and three dimensions –For now we’ll ignore air friction

8. Physics 218, Lecture V8 Projectile Motion The physics of the universe: The horizontal and vertical Equations of Motion behave independently This is why we use vectors in the first place

9. Physics 218, Lecture V9 How to Solve Problems The trick for all these problems is to break them up into the X and Y directions

10. Physics 218, Lecture V10 Ball Dropping Analyze Vertical and Horizontal separately!!! A y = g (downwards) A x = 0 –Constant for Both cases!!! V x = 0V x >0

11. Physics 218, Lecture V11 A weird consequence Prove that an object projected horizontally will reach the ground at the same time as an object dropped vertically

12. Physics 218, Lecture V12 Uniform Circular Motion Fancy words for moving in a circle with constant speed We see this around us all the time –Moon around the earth –Earth around the sun –Merry-go-rounds

13. Physics 218, Lecture V13 Uniform Circular Motion - Velocity Velocity vector = |V| tangent to the circle Is this ball accelerating? –Yes! why?

14. Physics 218, Lecture V14 Centripetal Acceleration “Center Seeking” Acceleration vector= V 2 /R towards the center Acceleration is perpendicular to the velocity R

15. Physics 218, Lecture V15 Circular Motion: Get the speed! Speed = distance/time  Distance in 1 revolution divided by the time it takes to go around once  Speed = 2  r/T Note: The time to go around once is known as the Period, or T

16. Physics 218, Lecture V16 Ball on a String A ball at the end of a string is revolving uniformly in a horizontal circle (ignore gravity) of radius R. The ball makes N revolutions in a time t. What is the centripetal acceleration?

17. Physics 218, Lecture V17 Firing up in the air at an angle A ball is fired up in the air with velocity V o and angle  o. Ignore air friction. The acceleration due to gravity is g pointing down. What is the final velocity here?

18. Physics 218, Lecture V18 Next time… Reading: None, you’ve already finished Chapter 3 already Homework: –HW1 was due yesterday –HW2 covered in recitation this week; due this coming Monday –Start working on HW3 Next time: More on kinematics in two and three dimensions

19. Physics 218, Lecture V19

20. Physics 218, Lecture V20 A Mail Carrier A rural mail carrier leaves leaves the post office and drives D 1 miles in a Northerly direction to the next town. She then drives in a direction  degrees South of East for a distance D 2 to another town. What is the magnitude and angle of her displacement from the post office?

21. Physics 218, Lecture V21 Constant Acceleration

22. Physics 218, Lecture V22 Example: Adding Unit Vectors

23. Physics 218, Lecture V23 Vector stuff 1.Pythagorean theorem: We’ll use this a lot –For a right triangle (90 degrees) –Length C is the hypotenuse –A 2 + B 2 = C 2 2.Vector equations

24. Physics 218, Lecture V24 Using all this stuff