Physics 218 Lecture 5

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

2. 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) Physics 218, Lecture V

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

4. Physics 218, Lecture V

5. Position in 3 dimensions Physics 218, Lecture V

6. Velocity in 3 dimensions Physics 218, Lecture V

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

8. 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 Physics 218, Lecture V

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

10. Ball Dropping Analyze Vertical and Horizontal separately!!! • Ay = g (downwards) • Ax = 0 • Constant for Both cases!!! Vx = 0 Vx>0 Physics 218, Lecture V

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

12. 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 Physics 218, Lecture V

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

14. Centripetal Acceleration • “Center Seeking” • Acceleration vector= V2/Rtowards the center • Acceleration is perpendicular to the velocity R Physics 218, Lecture V

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

16. 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? Physics 218, Lecture V

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

18. 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 Physics 218, Lecture V

19. End of Lecture Notes Physics 218, Lecture V

20. A Mail Carrier A rural mail carrier leaves leaves the post office and drives D1 miles in a Northerly direction to the next town. She then drives in a direction q degrees South of East for a distance D2 to another town. What is the magnitude and angle of her displacement from the post office? Physics 218, Lecture V

21. Constant Acceleration Physics 218, Lecture V

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

23. Vector stuff • Pythagorean theorem: We’ll use this a lot • For a right triangle (90 degrees) • Length C is the hypotenuse • A2 + B2 = C2 • Vector equations Physics 218, Lecture V

24. Using all this stuff Physics 218, Lecture V