Physics 207: Lecture 2 Notes

1
Lecture 6

• Todays Goals (Ch 4.4-6)
• Discuss uniform and non-uniform circular motion
• Circular Motion
• Centripetal (or radial) acceleration (direction
  of v changes)
• Tangential acceleration (magnitude of v changes)
• Relative motion and reference frames
• 1st Exam (Chapters 1-4, 10 Multiple choice, 4
  short answer)
• Where 2103, 2223 2241 Chamberlin Hall ( quiet
  room)
• When Monday, February 20 715-845 PM
• Format Closed book, one 8 x11 sheet, hand
  written
• Electronics Any calculator is okay but no
  web/cell access
• Quiet room Test anxiety, special accommodations,
  etc.
• Conflicts E-mail for approval (on or before
  Monday, Feb 12th) , academic/UW athletic reasons
  only

2
Circular Motion is common so specialized terms

• Angular position q (CCW CW -)
• Radius is r
• Arc distance s r q ds r dq
• Tangential velocity vt ds /dt
• Angular velocity, w dq/dt (CCW CW -)
• vt ds/dt r dq/dt r w

s
vt
r
q
3
Reformulating changes with vector notation

• Cartesian Coordinates Polar Coordinates

4
Circular Motion (with constant r)

• r and q

s
vt
r
q
5
Uniform Circular Motion (with constant r and
v)

• Time to go once around is the period T
• Distance once around is 2p r
• Tangential velocity is vt 2pr/T

s
vt
r
q
6
Uniform Circular Motion (UCM) has only radial
acceleration
UCM changes only the direction of
1. Particle doesnt speed up or slow down! 2.
Velocity is always tangential acceleration
perpendicular !
7
Uniform Circular Motion (UCM) has only radial
acceleration
UCM changes only in the direction of
1. Particle doesnt speed up or slow down! 2.
Velocity is always tangential, acceleration
perpendicular !
8
Again
Uniform circular motion involves only changes in
the direction of the velocity vector Acceleration
is perpendicular to the trajectory at any point,
acceleration is only in the radial direction.
Centripetal/radial Acceleration -ac ar
-v2/r Circular motion involves continuous
radial acceleration
9
Mass-based separation with a centrifuge
How many gs (1 g is 10 m/s2)?
ar vt2 / r w2 r f 6000 rpm 100
rev. per second is typical with r 0.10 m ar
(2p 102)2 x 0.10 m/s2
ar 4 x 104 m/s2 or ca. 4000 gs !!! but a
neutron star surface is at 1012 m/s2
bb5
10
Consequence of no radial accelerationa demo

• In this demonstration we have a ball tied to a
  string undergoing horizontal UCM (i.e. the ball
  has only radial acceleration)
• 1 Assuming you are looking from above, draw the
  orbit with the tangential velocity and the radial
  acceleration vectors sketched out.
• 2 Suddenly the string brakes.
• 3 Now sketch the trajectory with the velocity and
  acceleration vectors drawn again.

11
Concept test

• What does the path look like once the string is
  cut?
• A
• B
• C
• D
• E

12
Non UCM (with constant r and changing v)

• The speed of the particle increases or decreases
• dv/dt ? 0
• Always tangent to the path!

s
vt
r
q
13
Acceleration with both speed and direction change
1. Particle speeds up or slows down! 2.
Acceleration has tangential and radial components
!
14
Non-uniform Circular Motion
For an object moving along a curved trajectory,
with varying speed Vector addition a ar
at (radial and tangential)
at
ar
a
15
Total acceleration

• A stunt plane is performing a loop-the-loop of
  radius 100 m while accelerating (see figure).
  When its nose is pointed directly down, the speed
  of the plane is 50 m/s and the acceleration,
  tangent to the path, is 2g (i.e., 20 m/s2).
• What is magnitude of the total acceleration?
• In x,y vector notation, what is the total
  acceleration?

vT
r
16
Concept Check Which answer is best

• E1. You drop a ball from rest, how much of the
  acceleration from gravity goes to changing its
  speed?
• A. All of it
• B. Most of it
• C. Half of it
• D. None of it
• E2. A hockey puck slides off the edge of a
  horizontal table, just at the instant it leaves
  the table, how much of the acceleration from
  gravity goes to changing its speed?
• A. All of it
• B. Most of it
• C. Half of it
• D. None of it

17
Relative Motion and reference frames?

• If you are moving relative to another person do
  you see the same physics?
• Two observers moving relative to each other
  generally do not agree on the outcome of an
  experiment (path)
• For example, observers A and B below see
  different paths for the ball

18
Reading Assignment

• Chapter 5.1-6