welcome back to physics 215
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Welcome back to Physics 215. Today’s agenda: Tangential and radial components of acceleration Relative motion Tomorrow’s workshop: Work on practice exam. Current homework assignment. HW3: Exam-style problem (print out from course website) Ch.4 (Knight textbook): 44, 52, 56, 62, 88

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welcome back to physics 215

Welcome back to Physics 215

Today’s agenda:

Tangential and radial components of acceleration

Relative motion

Tomorrow’s workshop:

Work on practice exam

current homework assignment
Current homework assignment


  • Exam-style problem (print out from course website)
  • Ch.4 (Knight textbook): 44, 52, 56, 62, 88
  • due Wednesday, Sept 22nd in recitation

Reminder about course website:


exam 1 thursday 9 23 10
Exam 1: Thursday (9/23/10)
  • In room 208 (here!) at the usual lecture time
  • Material covered:
    • Textbook chapters 1 - 4
    • Lectures up through 9/21 (slides online)
    • Wed/Fri Workshop activities
    • Homework assignments
  • Exam is closed book, but you may bring calculator and one handwritten 8.5” x 11” sheet of notes.
  • Work through practice exam problems (posted on website)
  • Work on more practice exam problems next Wednesday in recitation workshop
what if the speed is changing
What if the speed is changing?
  • Consider acceleration for object on curved path starting from rest
  • Initially, v2/r = 0, so no radial acceleration
  • But a is not zero! It must be parallel to velocity
Acceleration vectors for object speeding up:Tangential and radial components(or parallel and perpendicular)
sample problem
A Ferris wheel with diameter 14.0 m, which rotates counter-clockwise, is just starting up. At a given instant, a passenger on the rim of the wheel and passing through the lowest point of his circular motion is moving at 3.00 m/s and is gaining speed at a rate of 0.500 m/s2. (a) Find the magnitude and the direction of the passenger’s acceleration at this instant. (b) Sketch the Ferris wheel and passenger showing his velocity and acceleration vectors.

Sample problem

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?”


  • 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.






  • 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

galilean transformation
Galilean transformation








  • xPA = xPB + vBAt -- transformation of coordinates
  • DxPA/Dt =DxPB/Dt + vBA

 vPA = vPB + vBA-- transformation of velocities

  • 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.

  • 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 bother? (1)
  • Why would we want to use moving frames?
  • Answer: can simplify our analysis of the motion
relative motion in 2d
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 2d1
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




why bother 2
Why bother? (2)
  • Have no way in principle of knowing whether any given frame is at rest
    • Room 208 is NOT at rest (as we have been assuming!)
what s more
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
reading assignment
Reading assignment
  • Forces, Newton’s Laws of Motion
  • Ch.5 in textbook
  • Review for Exam 1 !