Lecture 8

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Transcript Lecture 8

Physics 101: Lecture 08
Exam
2
Centripetal Acceleration
and Circular Motion
Exam 1 Review session
Tuesday 9-10AM
144Loomis
Physics 101: Lecture 8, Pg 1
Circular Motion
B
A
C
v
A ball is going around in a circle attached to a
string. If the string breaks at the instant shown,
which path will the ball follow?
Physics 101: Lecture 8, Pg 2
10
Acceleration in Uniform
Circular Motion
v2
R
R
v1
v2
a
R
centripetal acceleration
Acceleration is due to change in direction, not speed.
Since turns “toward” center, must be a force toward
center.
Physics 101: Lecture 8, Pg 3
12
Acceleration in Uniform
Circular Motion
Draw in forces.
v1
Physics 101: Lecture 8, Pg 4
12
Common Incorrect Forces
SF = ma
 Force of Motion (Inertia not a force)
 Centrifugal Force (wrong object!)
 Centripetal Force (tension, gravity, friction,
 Acceleration:
normal)
Physics 101: Lecture 8, Pg 5
Example: ball in vertical circle
Draw in forces.
v1=10m/s
A ball of mass 2kg is being swung in
a vertical circle with a speed of
10m/s. What is the tension in the
rope at the top of the circle?
g
Physics 101: Lecture 8, Pg 6
12
Example: ball in vertical circle
Draw in forces.
A ball of mass 2kg is being swung in
a vertical circle with a speed of
10m/s. What is the tension in the
rope at the bottom of the circle?
g
v1=10m/s
Physics 101: Lecture 8, Pg 7
12
Clicker Question
Suppose you are driving through a valley whose bottom has a
circular shape. If your mass is m, what is the magnitude of the
normal force FN exerted on you by the car seat as you drive
past the bottom of the hill
A. FN < mg
a=v2/R
B. FN = mg
C. FN > mg
R
FN
v
mg
Physics 101: Lecture 8, Pg 8
20
Example: roller coaster
What is the minimum speed you must have at the
top of a 20 meter roller coaster loop, to keep
the wheels on the track.
Y Direction: F = ma
N
Let N = 0, just touching
mg
Physics 101: Lecture 8, Pg 9
25
Circular Motion



Angular displacement q = q2-q1
How far it has rotated
Units radians 2p = 1 revolution
Angular velocity w = q/t
How fast it is rotating
Units radians/second 2p = 1 revolution
Angular acceleration is the change in angular velocity
w divided by the change in time. α = w/t
How much is it speeding up or slowing down
Units radians/second2
Physics 101: Lecture 8, Pg 10
27
Comparison to 1-D
kinematics
Angular
  constant
w  w 0  t
1
q  q0  w 0 t  t 2
2
Linear
a  constant
v  v 0  at
x  x0  v 0t 
1 2
at
2
And for a point at a distance R from the rotation axis:
x = Rqv = wR
a = R
Physics 101: Lecture 8, Pg 11
Example: 48x cd-rom

A 48x cd-rom spins at about 9600 rpm. If it takes 1.5
sec. to get up to speed, what is the angular
acceleration? How many revolutions does the disk make
before it is at the proper speed?
Physics 101: Lecture 8, Pg 12
48
Summary of Concepts

Uniform Circular Motion
 Speed is constant
 Direction is changing
 Acceleration toward center a = v2 / r
 Newton’s Second Law F = ma
Physics 101: Lecture 8, Pg 13
50