Transcript Chapter 4 1011x

Chapter 4
Kinematics in 2 Dimensions
Separate Components of Velocity
dx
 v cos 
dt
dy
vy 
 v sin 
dt
vx 
v
vx  v y
tan  
2
vy
vx
2
Constant Acceleration
1
x f  xi  vix t  a x t 2
2
v fx  vix  a x t
1
y f  yi  viy t  a y (t ) 2
2
v fy  viy  a y t
vo sin 2 
range 
g
2
Practice Problems
• Conceptual Questions
– 1,2,5
• Problems
– 8,12,
Circular Motion
• An object moving in a circular path at a
constant speed around a circle of radius,
or partial circle.
• Velocity tangential is along the edge of
circle.
• T is period, r – radius, and ac – centripetal
acceleration
2
2r
v
v
ac 
T
r
Examples
• Problems #26
Circular Motion in terms of angular postion,
velocity, and acceleration
• A particle that moves at a constant speed
around a circle of constant radius.
• Terms
– Period – time per 1 revolution
– Angular position ()– position measured
counterclockwise around circle
– Angular displacement ()-change of angular
position.
– Angular velocity (w) – rate of change of angular
displacement
Centripetal Acceleration
• Center seeking
acceleration.
• An object moving at a
constant speed, but
moving in a circular path
experiences acceleration.
– A body moving within this
accelerating system
experiences a fictitious
force called ‘centrifugal
force’.
– Example: As a person
makes a hard turn in their
car their body tends to
move away from the
turning direction.

v
wr 
ar 

 w 2r
r
r
2
2
Connection between angular
motion and linear motion
s  r
v  rw
a  r
• Which has a greater perimeter a
circle radius of 1 m, or 2 m?
• 2m
• When riding a carousal, who
travels a greater distance the
inside horses or the outside
horses?
• Outside
• When playing ‘crack the whip’ on
ice skates, who travels faster the
person within the line of skaters
or the one at the end?
• One at the end
Nonuniform Circular Motion
-w
• Circular motion with a
changing speed
• Positive angular displacement
is considered counterclockwise
displacement in a circular path.
• Positive angular velocity is
counterclockwise motion in a
circular path.
• Positive angular acceleration is
counterclockwise acceleration
as an object moves in a
circular path.
-
w
+
Angular Motion vs time graphs
• Angular motion graphs
can be treated very
similarly to linear motion
graphs.
• For Example
– Slope of angular position
vs time is equal to the
angular velocity
– Area below angular velocity
vs time graph is equal to
the angular displacement

t
Create the angular velocity vs
time graph from this graph.
w
t
Examples
• Conceptual #14
• Problem #22,#33,#36
Relative Velocity Explanation
• Objects have velocity based
on their coordinate system.
Sitting here we are stationary
relative to earth, but moving
fast relative to moon, and
faster relative to sun.
• Vab velocity of a with respect to
b
• Vbc velocity of b with respect to
c
• Equation 1 to right
• Inverse situations below
vab  vba
vac  vab  vbc
Relative Motion Situations
• You are moving at 80 km/h north and a car passes you going 90
km/h. Draw the relative motion velocity vectors, and determine how
the faster car appears to you.
• A boat heading north crosses a wide river with a velocity of 10 km/h
relative to the water. The river has a uniform velocity of 5 km/h due
east. Determine the boat’s velocity with respect to an observer on
shore.
• Two planes are headed from the same airport in different directions.
Airplane A is headed at 200 m/s at a direction of 30* S of W, while
Airplane B is headed at 250 m/s at a direction of 60 N of E. What is
the relative velocity and direction of B in relation to A?
• Practice Problem - 58