Velocity two components

1
Uniform Circular Motion

• Velocity two components
• Speed
• Direction
• Change either component
• Acceleration
• Uniform Circular Motion
• Constant Speed
• Thats the uniform part
• Circular Whats changing?
• Direction

2
Uniform Circular Motion
Magnitudes identical for uniform circular motion
3
Uniform Circular Motion

• Lets refine the acceleration
• Vector
• Direction and magnitude
• Derive the Direction

v1
v2
4
Uniform Circular Motion
Where is delta v pointed???
5
Uniform Circular Motion

• As ?t approaches zero
• v2 and v1 become parallel
• Which makes ?v perpendicular to v2 and v1
• And that is pointed directly to the center of
  rotation (center of the circle)

6
Centripetal Acceleration

• Centripetal Acceleration
• Centripetal Latin origin Center Seeking
  centri refers to centre
• Petal refers to seeking peto to seek as seen
  in a petition seeking something.
• Centrifugal (fugo to flee as seen in a
  fugitive.)
• Acceleration vector always points to the center
• How about magnitude of the acceleration vector?

7
Centripetal Acceleration
A

• Magnitude?

r
B
r
C
8
Centripetal Acceleration
As ?t gets smaller approaches zero -- ?? does
the same And chord AB ? arc AB
9
Centripetal Acceleration
Arc AB is the actual distance the object traveled
at speed v during ?t v arc AB/?t
arc AB v x ?t
v?t
10
Centripetal Acceleration
Magnitudes Only
Rearranging,
11
Centripetal Acceleration
Take the lim as ?t ? 0 then Arc AB Chord AB so
we can then take the approximation as an equality
12
Centripetal Acceleration
13
Centripetal Acceleration

• Direction Always points to center
• Magnitude

14
Centripetal Force

• By Newtons Second Law
• Object w/ acceleration
• Must have a net force other than zero
• F ma
• Same with an object in uniform circular motion
• Take F ma

• acceleration a vector ? force is a vector
• Must be in same direction

15
Centripetal Force

• Direction of Force same as acceleration
• Towards center

• Magnitude

c
16
Centripetal Acceleration

• Examples
• Twirling object on string
• Moon about earth
• Earth about sun
• Turning car
• Banked and non-banked
• Toms Twister
• Airplane in a turn

17
Run ip
Text figures
Car on Wall
IP centrip