Welcome back to Physics 211

Welcome back to Physics 211 Today’s agenda: Announcements Relative motion Tomorrow’s workshop: Kinematics review and practice exam problems

Current homework assignments • WHW3: • In blue Tutorials in Physics homework book • HW-19 #1, HW-21 #3, HW-21 #4, HW-23 #6 • due Wednesday Sept 20th in recitation • FHW2: • From end of chapters 3 & 4 in University Physics • 3.80, 3.82, 4.6, 4.30 • due Friday Sept 29th in recitation

Exam 1: Thursday (9/21/06) • During normal lecture period, 11:00AM - 12:20PM in Stolkin Auditorium. • Seating arrangement by last name will be posted outside Stolkin. • Exam is closed book, but you may bring calculator and one handwritten 8.5” x 11” sheet of notes. • Practice exam problems posted on website and Wednesday in recitation workshop.

Exam 1: Thursday (9/21/06) • Material covered: • Textbook chapters 1, 2, and 3 • Lectures up to 9/19 (slides online) • Tutorials on Velocity, Acceleration in one dimension, and Motion in two dimensions • Problem Solving Activities 1, 2, and 3 (on Graphs,Vectors, and Problems on motion in two dimensions) • Homework assignments

Components of acceleration vector: • Parallel to direction of velocity: • (Tangential acceleration) • “How much does speed of the object increase?” • Perpendicular to direction of velocity: • (Radial acceleration) • “How quickly does the object turn?” Motion in 2D -- Summary

Acceleration vectors for object moving around oval while speeding up from rest

Vector components in 2D motion • To study 2D motion, can resolve all vectors into components. Two different methods: • Cartesian (projectile motion) • Radial/tangential – circular motion, general motion on curved paths • Either can be used. Choose easiest method for particular problem.

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 (no unique clock...) Relative motion...

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.

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…. • Accelerations?

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.

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

B A B A B A

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

Demo with two carts Camera on one cart gives observations from moving frame

Galilean transformation yA yB vBA P vBAt xB xA • xPA = xPB + vBAt -- transformation of coordinates • DxPA/Dt =DxPB/Dt + vBA  vPA = vPB + vBA-- transformation of velocities

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

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.

Conclusion • If we want to use (inertial) moving FOR, then velocities are not the same in different frames • However constant velocity motions are always seen as constant velocity • There is a simple way to relate velocities measured by different frames.

Why bother? (1) • Why would we want to use moving frames? • Answer: can simplify our analysis of the motion

Demo: ejecting a ball upwards from moving cart • Observe with camera on cart.

Relative Motion in 2D • Motion may look quite different in different FOR, e.g. ejecting ball from moving cart Earth frame = complicated! Cart frame = simple! Motion of cart

Relative Motion in 2D • Consider airplane flying in a crosswind • velocity of plane relative to air, vPA = 240 km/h N • wind velocity, air relative to earth, vAE = 100 km/h E • what is velocity of plane relative to earth, vPE ? vPE = vPA + vAE vAE vPE vPA

Why bother? (2) • Have no way in principle of knowing whether any given frame is at rest • Stolkin Auditorium is NOT at rest (as we have been assuming!)

What’s more … • Better hope that the laws of physics don’t depend on the velocity of my FOR (as long as it is inertial …) • Einstein developed Special theory of relativity to cover situations when velocities approach the speed of light

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

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

Accelerations? • We have seen that observers in different FORs perceive different velocities • Is there something which they do agree on? • Previous demo: cart and Earth observer agree on acceleration (time to fall)

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

Acceleration • If car I moves with constant velocity relative to the road, • Then the acceleration of any other object (e.g. car J) measured relative to car I is the same as the acceleration measured relative to the road.

Acceleration is same for all inertial FOR! • We have: vPA = vPB + vBA • For velocity of P measured in frame A in terms of velocity measured in B • DvPA/Dt = DvPB/Dt since vBA is constant • Thus acceleration measured in frame A or frame B is same!

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 are equally good for discovering the laws of mechanics

Reading assignment • Forces, Newton’s Laws of Motion • 4.1 - 4.6 in textbook • Review for Exam 1 !

Welcome back to Physics 211