Welcome back to Physics 211

1. Welcome back to Physics 211 Today’s agenda: Announcements Relative motion Tomorrow’s workshop: Kinematics in context (Review)

2. Reminder • Homework this week: • Tutorial HW Motion in two dimensionsp. 19 - 22. (due in Tues/Wed workshop) • MP homework due 11:00 pm Friday.

3. Exam 1 on Thursday! • Seating arrangement by last name will be posted outside Stolkin Auditorium by Thursday morning. • Calculators and rulers may be helpful. Closed book • Practice exams/solns online: http://www.phy.syr.edu/courses/PHY211

4. Relative motion

5. Kinematics • Consider 1D motion of some object • Observer at origin of coordinate system measures pair of numbers (x,t) • (observer) + coordinate system + clock called frame of reference • (x,t) not unique – different choice of origin changes x

6. Change origin ? • Physical laws involve velocities and accelerations which only depend on Dx • Clearly any frame of reference (FOR) with different origin will measure same Dx, v, a etc

7. Inertial Frames of Reference • Actually can widen definition of FOR to include coordinate systems moving at constant velocity • Now different frames will perceive velocities differently ….

8. Moving Observer • Often convenient to associate a frame of reference with a moving object. • Can then talk about how some physical event would be viewed by an observer associated with the moving object.

9. Reference frame (clock, meterstick) carried along by moving object B A

10. B A B A B A

11. Discussion • From point of view of A, car B moves to right. We say velocity of B relative to A, vBA. Here vBA>0 • But from point of view of B, car A moves to left. In fact, vAB<0 • In fact, can see that vAB=-vBA

12. demo with two carts

13. Galilean transformation t vAB P vABt xA xB • xPA=xPB-vABt --- transformation coords • D xPA/Dt=D xPB/ Dt –vAB vPA=vPB –vAB --- transformation of velocities

14. Notice • Notice: • vAB=-vBA follows • Two objects a and b moving with respect to say Earth then find (Pa, Ab, BE) vab=vaE-vbE

15. You are driving East on I-90 at a constant 65 miles per hour. You are passing another car that is going at a constant 60 miles per hour. In your frame of reference (i.e., as measured relative to your car), is the other car 1. going East at constant speed 2. going West at constant speed, 3. going East and slowing down, 4. going West and speeding up.

16. Conclusion • If we want to use moving FOR then velocities are not same in different frames • Nevertheless there is a simple way to relate velocities measured by different frames.

17. Why bother ? • Why want to use moving frames ? • Can simplify motions • Have no way in principle of knowing whether any given frame is at rest • Stolkin is NOT at rest (as we have been assuming!)

18. Whats more … • Better hope that the laws of physics don’t depend on the velocity of my frame of reference (as long as it is moving at constant velocity …..) • Elevate to Principle of relativity – respected by Newton’s mechanics

19. The diagram shows the positions of two carts on parallel tracks at successive instants in time. Is the average velocity vector of cart B relative to cart A (or, in the reference frame of cart A) in the time interval from 1 to 2…? 1. to the right 2. to the left 3. zero 4. unable to decide

20. Is the instantaneous velocity vector of cart B relative to cart A (or, in the reference frame of cart A) at instant 3…? 1. to the right 2. to the left 3. zero 4. unable to decide

21. Dropping a ball from moving cart • Show demo with camera on cart. • Film will be shown and discussed in workshop Thu/Friday.

22. Relative Motion 2D • Motion may look quite different in different FOR, eg. dropping ball from moving cart complicated! Cart frame Earth frame simple! Motion of cart

23. Accelerations ? • Seen that different (observers) FOR perceive different velocities • Is there something which they do agree on ? • Previous example: cart and Earth observer agree on acceleration (time to fall)

24. Is the average acceleration vector of cart B relative to cart A (or, in the reference frame of cart A) in the time interval from 1 to 5: 1. to the right 2. to the left 3. zero 4. unable to decide

25. If car A moves with constant velocity relative to the road, then the acceleration of any other object (e.g., car B) measured relative to car Ais the same as the acceleration measured relative to the road.

26. Acceleration is same for all inertial FOR! • We have: vPA=vPB –vAB For velocity of P measured in frame A in terms of velocity measured in B • D vPA/Dt= D vPB/ Dt since vAB is constant • Thus acceleration measured in A or B frame is same!

27. Physical Laws • Since all FOR agree on the acceleration of object they all agree on the forces that act on that object • All such FOR equally good for discovering the laws of mechanics

28. Two spaceships and a shuttle A B t=0 A B S t=T S From B’s frame ? What is velocity of shuttle in B’s frame ?