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### Welcome back to Physics 211

### demo with two carts

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!

- 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

- 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 ?

- 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.

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

Camera on one cart gives observations from moving frame

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:
- vAB=-vBA follows
- Two objects a and b moving with respect to say Earth then find (Pa, Ab, BE)

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 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 want to use moving frames ?
- Can simplify motions

Dropping a ball from moving cart

- Show demo with camera on cart.
- Film on FOR will be shown and discussed in workshop Friday.

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

Why bother ? 2.

- 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 …

- 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

- 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 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 ?

- 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 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 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!

- 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

- 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

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