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Romantic Turn
 You are driving with a “friend” who is sitting to
your right on the passenger side of the front
seat. You would like to be closer to your “friend”
and decide to use your knowledge of physics to
achieve your romantic goal. So you'll make a
sharp turn. Which direction should you turn so
as to make your friend slide closer to you? If the
coefficient of static friction between your friend
and the seat of the car is 0.40, and you drive at
a constant speed of 18 m/s, what is the
maximum radius you could make your turn and
still have your friend slide your way?
Project
Sweep a bowling ball around a chair with a
broom.
Which way do you sweep to keep the ball
moving in a circle?
Why?
What does the bowling ball “want” to do?
Lesson #72
Topic: Circular Motion
Objectives:
5/8/07
(After this class I will be able to)
1. Describe and explain centripetal acceleration
and force.
Warm Up: A merry-go-round has a radius of 6m
and makes a full rotation every 5 seconds. What is
the speed of a horse on the outer edge of the ride?
Assignment: Concept Development 9-2
A merry-go-round has a radius of 6m and makes a
full rotation every 5 seconds. What is the speed of
a horse on the outer edge of the ride?
25%
25%
m
/s
30
5m
/s
7.
4m
/s
2.
2m
/s
0 of 5
25%
1.2m/s
2.4m/s
7.5m/s
30m/s
1.
1.
2.
3.
4.
25%
Tangential Velocity
A horse on a merry-go-round has velocity
tangent to the circle.
Its velocity is always perpendicular to the
radius of the circle.
r
v
Rotate vs. Revolve
 Rotation: An object spinning
around a point located
within the object.
 Example: The Earth
rotates about its axis.
 Revolution: An object
moving in a circle around a
point in space.
 Example: The Earth
revolves around the Sun.
Centripetal Force
An object in motion will stay in motion in a
straight line unless acted on by an outside
force.
This means that a force must be acting on
an object that is moving in a circle.
The force causing an object to move in a
circle is called the Centripetal Force.
Centripetal = center seeking.
demo
Centripetal Force
Centripetal Acceleration
Acceleration = an object speeding up,
slowing down, or changing direction.
An object moving in a circle is constantly
changing direction.
Centripetal force causes the object to
accelerate towards the center of the circle.
The tangential velocity prevents the object
from going straight towards the center.
Example: Moon around Earth
Centripetal Acceleration
Centripetal Acceleration Equation
2
v
a 
r
a = centripetal acceleration
v = tangential velocity
r = radius
Centripetal Force Equation
A runner moving at a speed of 8.8m/s rounds a
bend with a radius of 25m. What is the centripetal
acceleration of the runner?
m
/s
m
/s
2
10
3.
2m
35
0.
0 of 5
33%
10
33%
/s
2
33%
3.
1. 0.352m/s2
2. 3.10m/s2
3. 3.10m/s
An airplane traveling at 201 m/s makes a turn.
What is the smallest radius of the circular path (in
km) that the pilot can make and keep the
centripetal acceleration under 5.0 m/s2?
78
20
.6
km
km
8.
08
km
.2
40
80
.2
km
8080.2 km
40.2 km
8.08 km
7820.6 km
80
1.
2.
3.
4.
25% 25% 25% 25%
A 45 kg merry-go-round worker stands on the ride’s
platform 6.3 m from the center. If her speed as she goes
around the circle is 4.1 m/s, what is the force of friction
necessary to keep her from falling off the platform?
m
/s
2
m
/s
2
N
07
07
0.
12
29
.2
9
0.
12
.2
9
N
29.29 N
120.07 N
29.29 m/s2
120.07 m/s2
29
1.
2.
3.
4.
25% 25% 25% 25%
A car racing on a flat track travels at 22 m/s around a curve
with a 56 m radius. Find the car’s centripetal acceleration.
What minimum coefficient of static friction between the tires
and road is necessary for the car to round the curve without
slipping?
25% 25% 25% 25%
29
4.
86
0.
86
N
6
.8
m
/s
2
8.64
864.29 m/s2
.86 N
.86
8.
64
1.
2.
3.
4.
Project
List objects that move in circles.
List what is causing the centripetal force
for each object.
Describe the “Romantic Turn” and what
the maximum radius can be and yet still
achieve your goal. (Would this trick ever
actually work on anyone?)
Lesson #73
Topic: Lab: Circular Motion
Objectives:
4/30/07
(After this class I will be able to)
1. Solve for the tangential velocity of a
whirling object.
2. Calculate for the mass of a rubber stopper
using the centripetal force equation.
Lab Task: Find the mass of a rubber stopper using
Fc=mv2/r
Assignment: Lab Report due tomorrow
(show all calculations!)
Croc Dundee Noisemaker
 After watching the movie "Crocodile Dundee," you and
some friends decide to make a communications device
invented by the Australian Aborigines. It consists of a
noise-maker swung in a vertical circle on the end of a
string. Your design calls for a 400 gram noise-maker on
a 60 cm string. You are worried about whether the string
you have will be strong enough, so you decide to
calculate the tension in the string when the device is
swung with an acceleration which has a constant
magnitude of 20 m/s2 . You and your friends can't agree
whether the maximum tension will occur when the noise
maker is at the highest point in the circle, at the lowest
point in the circle, or is always the same. To settle the
argument you decide to calculate the tension at the
highest point and at the lowest point and compare them.
Project
Loop the loop track
Describe what makes the ball make it
around the loop.
Draw the forces acting on the ball at the
top of the loop and at the bottom of the
loop.
Lesson #74
Topic: Non-Uniform Circular Motion
Objectives:
4/31/07
(After this class I will be able to)
1. Describe inertial and non-inertial reference
frames.
2. Define Centrifugal Force.
3. Solve problems involving Non-Uniform
circular motion.
Warm Up: A 615kg racecar completes one lap in
14.3s around a circular track with a radius of 50m.
The car moves at constant speed. What is the
acceleration of the car?
Assignment: Non- Uniform Circular motion
A 615kg racecar completes one lap in 14.3s around a circular
track with a radius of 50m. The car moves at constant speed.
What is the acceleration of the car?
m
/s
2
25%
0
m
/s
2
24
44
0.
65
0 of 5
25%
m
/s
2
25%
m
/s
2
25%
0.
9.65m/s2
0.44m/s2
0.24m/s2
0 m/s2
9.
1.
2.
3.
4.
Inertial Reference Frame
 Inertial Reference Frame = explanations of
observations where Newton’s laws hold true.
 Example: Watching a car race on a circular track.
Friction is the centripetal force accelerating the
cars towards the center of the track.
Non-Inertial Reference Frame
 Non-Inertial Reference Frame = an imaginary
force needs to exist for Newton’s laws to hold true.
 Example: Being in a car going around a circular
race track. You feel pushed towards one side of
the car.
 You can say that this “push” is some imaginary
force rather than the inertia of your body.
 This imaginary force is called the centrifugal
force.
 Centrifugal = center fleeing
Non-Uniform Circular Motion
 The motion of an object is non-uniform when other
forces are acting on it besides the centripetal
force.
 Example: An object moving in a vertical circle.
Non-Uniform Circular Motion Problems
 When solving non-uniform problems, Fnet = 0 and
use centrifugal force instead of centripetal force.
 Example: A roller coaster car speeds down a hill past
point A and then rolls up a hill past point B
 a. The car has a speed of 20m/s at point A. If the normal
force is 20600N at this point, what is the mass of the car?
r =10m
A
B
Non-Uniform Circular Motion Problems
 Example: A roller coaster car speeds down a hill past
point A and then rolls up a hill past point B
 b. What is the maximum speed the car can have
at point B for the gravitational force to hold it on
the track?
B
r = 15m
A
A carnival clown rides a motorcycle down a ramp and around a vertical
loop. If the loop has a radius of 18m, what is the slowest speed the
rider can have at the top of the loop to avoid falling?
0m
/s
18
m
/s
18
m
/s
13
.4
m
/s
24
0 of 5
4.24m/s
13.4m/s
18m/s
180m/s
4.
1.
2.
3.
4.
25% 25% 25% 25%
A 1.13kg ball is swung vertically from a 0.5m cord in circular motion at
a speed of 2.4m/s. What is the tension in the cord at the bottom of the
ball’s motion?
1.
2.
3.
4.
25%
11.3N
13.0N
24.3N
1.7N
25%
25%
25%
7N
1.
N
24
.3
N
.0
13
11
.3
N
0 of 5
A mythical warrior swings a 5.6kg mace on the end of a
magically massless 86cm chain in a horizontal circle above
his head. The mace makes one full revolution in 1.8s. Find
the tension in the magical chain.
25%
25%
25%
N
.0
28
N
68
.7
N
58
0 of 5
58
49
N
1.49N
58.7N
5868N
28.0N
1.
1.
2.
3.
4.
25%
Croc Dundee Noisemaker
Find the tension in the noisemaker at both
top and bottom of the vertical circle.
Bonus
 A passenger train traveling at constant speed rounds a
curve of radius 275m. A chandelier suspended from the
ceiling swings out to an angle of 17.5° throughout the turn.
What is the speed of the train?