lecture 16 friday, october 3 chapter 6: circular motion
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Lecture 16Friday, 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
Is para
llel to
the velocit
y
Is dire
cted to
wards t
he ...
is la
rger f
or a la
rger o
rbit.
..
33% 33%33%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
Massless, frictionless pulley
m1
m2
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.
• The kinematics of uniform circular motion
• The dynamics of uniform circular motion
• Circular orbits of satellites
• Newton’s law of gravity
Chapter 6Circular Motion, Orbits and Gravity
Topics:
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 magnitude of velocity (speed) is constant
( )
( )
( )
t angular position
d tangular velocity
t dtd t
angular accelerationt dt
Circular Motion
• Note similarity to the equations for one-dimensional linear motion
( )( )
( )( )
x displacement
x dx tv t velocity
t dtv dv t
a t accelerationt dt
• Going from angular velocity to angular displacement:
1 where is frequency (rad/s)
2 rad for uniform circular motion
f i t
T period ff
T
UCM continued
• Travelling at constant speed v around circle• Period is time one around circle = T
2vT r
v r
UCM cont
• s is distance travelled around circumference and the definition of the radian tell us
thens r
v r
a r
Uniform Circular Motion
• Uniform magnitude of velocity (speed) ω, is constant
• But α is not zero because direction of velocity is changing.
22v
rr
Uniform Circular Motion
Slide 6-13
Newton’s Second Law
• Net force must point towards center of circle
2
, toward center of circleNET
mvF ma
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
sf
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
motionB. Toward the center of the circle
Checking Understanding
Slide 6-11
Problems due today
• 5: 24, 25, 29, 30, 31, 35, 36, 37, 39
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