Download Lecture 16 Friday October 10

Lecture 16
Chapter 6: Circular Motion
Please sit in the first six rows
Mid Grades
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Exam 2
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Quick Review of Last Friday
•
Last Friday
•
The kinematics of uniform circular motion
•
TODAY
– The dynamics of uniform circular motion
– Circular orbits of satellites
– Newton’s law of gravity
Uniform Circular Motion
• Uniform
is constant
magnitude of velocity (speed)
 (t )  angular position
 d (t )
  angular velocity 

t
dt
 d (t )
  angular acceleration 

t
dt
• Going from angular velocity to angular
displacement:
 f  i   t
1
T  period  where f is frequency (rad/s)
f
2 rad

for uniform circular motion
T
Uniform Circular Motion
• Uniform
magnitude of velocity (speed)
ω, is constant
• But α is not zero because direction of velocity
is changing.
2
v
2
   r
r
Centrifugal Force
• NOT A REAL FORCE
• What supplies the force to make your acceleration
such as to cause you to move in a circle?
• Centripetal FORCE—towards the center.
This is the real force involved.
a
v
Vertical Circle
• Ferris wheel—free body diagram when at top
FNET
nTOP
FNET
w=mg
mv 2
FNET , y  mg  nTOP  
r
mv 2
mv 2
nTOP 
 mg 
w
r
r
Ferris Wheel
At the bottom
nBOTTOM
w=mg
mv 2
FNET , y  nBOTTOM  w 
r
mv 2
nBOTTOM  w 
r
“Apparent weight” = n is greater at bottom of
cycle than at top
Centrifuges
•
•
•
•
Diameter = 18 cm
Centripetal acceleration = 250,000 g
What is the frequency? Rev/sec and rpm
Apparent weight of a 3 mg mass in this
machine?
Workbook due today
• Go to board and explain
– 1a and c
– 1b and d
–2
–3
–4
–5
– 6a,b and c
A cyclist goes around a circular track at
constant speed. Since her speed is
constant, her acceleration is zero
33%
33%
33%
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Tr
ue
1. True
2. False
3. Need more
information
6.15
• A 1500 kg car drives around a flat 200m
diameter circular track. What are the
magnitude and direction of the net force on
the car? What causes this force?
d
ar
To
w
Ta
ng
en
tt
o
th
e
th
e
ce
n
te
c ir
c le
ro
,i
ft
n
...
1. Tangent to the
circle, in the
direction of the
ball’s motion
2. Toward the center
of the circle
he
...
When a ball on the end of a string
is swung in a vertical circle: What is
the direction of the acceleration
of
50%
50%
the ball?