Transcript AP Lesson 03.ppt

Two Dimensional Motion

Y
Displacement:
r
ri
rf
X
Where: ri , rf and r may be 2-D
or 3-D vectors represented in unitvector notation AND may be
functions of time!.
Ex. r = (6t2 – 3t +5) i + (3t3 – 4t) j
*Displacement (∆r) is the difference between rf and ri

Average Velocity in Two Dimensions:
r
v 
t
Ex. Find average velocity between the times
t = 2 s and t = 6 s for the example vector
above.
AP Lesson 003
1
Two Dimensional Motion (2)

Instantaneous Velocity in Two
Dimensions:
dr
v
dt
Ex. Find the instantaneous velocity at t = 4 s
for the example vector given above.

Average Acceleration in Two
Dimensions:
v
a 

t
Instantaneous Acceleration in Two
Dimensions:
dv
a 
AP Lesson 003
dt
2
Two Dimensional Motion (3)
Projectile Motion:




ax = 0, ay = -9.80 m/s2
Neglect air resistance for now
Use same kinematics formulas from before, but
keep x & y components separate.
Uniform Circular Motion: Constant
speed maintained in a circular path.
Centripetal Acceleration:
Direction is toward Center.
2

ar
AP Lesson 003
v

r
3
Two Dimensional Motion (4)

Total Acceleration: Vector sum of
Centripetal and Tangential components
(they are perpendicular to each other)
2
a2  a2

a
r
T

Some useful circular motion
relationships:
v 
f 
AP Lesson 003
2r
T
1
T
ω  2f
v  rω
4