Lecture 16
Friday, October 3
Chapter 6:
Circular Motion
Review Example
Macie pulls a 40 kg rolling trunk by a strap angled at 30° from
the horizontal. She pulls with a force of 40 N, and there is a 30
N rolling friction force acting on trunk. What is the trunk’s
acceleration?
Slide 5-17
For uniform circular motion, the
acceleration
ge
lar
a
rf
or
is
lar
ge
ct
ed
Is
di
re
t. .
.
rb
i
th
e
ar
ds
to
w
th
e
o
lt
le
al
Is
pa
r
33% 33%
...
ve
lo
c it
y
33%
ro
1. Is parallel to the
velocity
2. Is directed towards
the center of the
circle
3. is larger for a
larger orbit at the
same speed
Problem, interacting bodies
Glider on a air track
m1
m2
Massless, frictionless pulley
Special Assignment
• Special assignment to be handed in
Monday: Workbook pages 4-5 and 4-6,
exercises 17-22 and page 5-5, exercises 13-15.
Chapter 6
Circular Motion, Orbits and Gravity
Topics:
• The kinematics of uniform
circular motion
•
The dynamics of uniform
circular motion
•
•
Circular orbits of satellites
Newton’s law of gravity
Sample question:
The motorcyclist in the “Globe of Death” rides in a vertical loop
upside down over the top of a spherical cage. There is a minimum
speed at which he can ride this loop. How slow can he go?
Slide 6-1
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
Circular Motion
• Note similarity to the equations for onedimensional linear motion
x  displacement
x dx(t )
v(t )  velocity 

t
dt
v dv(t )
a(t )  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
UCM continued
• Travelling at constant speed v around circle
• Period is time one around circle = T
vT  2 r
v  r
UCM cont
• s is distance travelled around circumference
and the definition of the radian tell us
s  r
v  r
a  r
then
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
Uniform Circular Motion
Slide 6-13
Newton’s Second Law
• Net force must point towards center of circle
FNET
 mv 2

 ma  
, toward center of circle 
 r

Example
A level curve on a country road
has a radius of 150 m. What is
the maximum speed at which
this curve can be safely
negotiated on a rainy day when
the coefficient of friction between
the tires on a car and the road is
0.40?
Slide 6-24
Top View
•
v
fs
Checking Understanding
When a ball on the end of a string is swung in a vertical circle:
What is the direction of the acceleration of the ball?
A. Tangent to the circle, in the direction of the ball’s
motion
B. Toward the center of the circle
Slide 6-11
Problems due today
• 5: 24, 25, 29, 30, 31, 35, 36, 37, 39