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Welcome back to Physics 211. Today’s agenda: Announcements Relative motion Tomorrow’s workshop: Kinematics in context (Review). Reminder. Homework this week: Tutorial HW Motion in two dimensions p. 19 - 22. (due in Wed workshop) MPHW2 homework due 12:00 pm Friday. Exam 1 on Thursday!.

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Welcome back to physics 211

Welcome back to Physics 211

Today’s agenda:

Announcements

Relative motion

Tomorrow’s workshop:

Kinematics in context (Review)


Reminder

  • Homework this week:

    • Tutorial HW Motion in two dimensionsp. 19 - 22. (due in Wed workshop)

    • MPHW2 homework due 12:00 pm Friday.


Exam 1 on thursday
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– only my formula summary

  • Practice exams/solns (also HW1,2) online: http://www.phy.syr.edu/courses/PHY211



Kinematics
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 ..)


Change origin
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
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
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

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

B

A


B

A

B

A

B

A


Discussion
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


Demo with two carts

demo with two carts

Camera on one cart gives observations from moving frame


Galilean transformation
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


Notice
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


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
Conclusion hour. You are passing another car that is going at a constant 60 miles per hour.

  • If we want to use (inertial) moving FOR then velocities are not 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 bother ? 1. hour. You are passing another car that is going at a constant 60 miles per hour.

  • Why want to use moving frames ?

  • Can simplify motions


Dropping a ball from moving cart
Dropping a ball from moving cart hour. You are passing another car that is going at a constant 60 miles per hour.

  • Show demo with camera on cart.

  • Film on FOR will be shown and discussed in workshop Friday.


Relative motion 2d
Relative Motion 2D hour. You are passing another car that is going at a constant 60 miles per hour.

  • Motion may look quite different in different FOR, eg. dropping ball from moving cart

complicated!

Cart frame

Earth frame

simple!

Motion of cart


Why bother 2
Why bother ? 2. hour. You are passing another car that is going at a constant 60 miles per hour.

  • Have no way in principle of knowing whether any given frame is at rest

    • Stolkin is NOT at rest (as we have been assuming!)


Whats more
Whats more … hour. You are passing another car that is going at a constant 60 miles per hour.

  • Better hope that the laws of physics don’t depend on the velocity of my FOR (as long as it is inertial …)

  • Elevate to Principle of relativity POR – respected by Newton’s mechanics (accelerations …)


Einstein
Einstein hour. You are passing another car that is going at a constant 60 miles per hour.

  • Elevated this principle to cover all of physics – not just mechanics

  • Eg – electricity and magnetism – seemed to violate POR using Galilean transformation

  • Fix ? – change transformations to make POR consistent with E and M!

  • Profound consequences …..


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


Is the instantaneous tracks at successive instants in time.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


Accelerations
Accelerations ? tracks at successive instants in time.

  • 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)


Is the average tracks at successive instants in time.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


If car A moves with tracks at successive instants in time.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.


Acceleration is same for all inertial for
Acceleration is same for all inertial FOR! tracks at successive instants in time.

  • 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!


Physical laws
Physical Laws tracks at successive instants in time.

  • 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


Two spaceships and a shuttle
Two spaceships and a shuttle tracks at successive instants in time.

A

B

t=0

A

B

S

t=T

S

From B’s frame ?

What is velocity of shuttle in B’s frame ?


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