Warm-up (12/9): Circular Motion
LOOK! Is it a bird? Is it a plane?
No! It’s Percy the Physics Pig!! =)
*Do not touch planes / pigs / lab
equipment (that includes string)
5 point deduction each time it occurs
before lab - yes – I’m serious.
1. Take out “Give it a whirl” data table.
2. Dig out Plickers or pick up a new card.
Not sure of your number – check the
number next to your name on roster.
(12/9/15) Wednesday Agenda:
• Warm-up / Review: plickers or traditional
(with demo – 10-15 min.)
• Address questions or concerns remaining from
“Give it a whirl” lab or data discussion.” (5 min.)
• Introduce “When Pigs Fly” Challenge.
(Begin set-up and data collection20 min.)
Plicker Alternative
• What direction does centripetal force act in
horizontal circular motion?
• What direction does centripetal
acceleration occur?
• What created the centripetal force in the
Give it a Whirl – stopper lab?
• What will happen to a piece of cork
floating in water if it is rotated in a circle?
• What will happen to air bubble in a liquid if
it is spun on the International Space
Station?
Tasks:
• Complete “Give it a whirl” activity and
analysis
• Conduct lab: Choose guided inquiry or
design your own experiment
• EXPERIENCE THE DERIVATION
Time Management: set-up, collect data
today – debrief and conduct analysis of data
as a team tomorrow.
Think back to Newton’s Laws
and Give it a Whirl lab
• The net force is related to the acceleration
of an object…and is stated in the following
three equations:
• Circumference = 2*pi*Radius
Circular Motion
Objectives this week:
• Describe circular motion in terms of
inertia and centripetal force.
• Use lab data, to determine the
relationships among mass, centripetal
force, velocity and radius when motion is
circular.
• Apply equation for calculating centripetal
force to every day situations.
When Pigs Fly Challenge
• Describe circular motion in terms of
centripetal acceleration and centripetal
force.
• Use lab data, to determine the
relationships among velocity and angle of
when motion is circular (Conical Pendulum).
• Apply equation for calculating centripetal
force to every day situations.
OSHA Safety Video
• When battling the
storm troopers,
• what did the Ewok
forget to do in this
battle scene?
• PIG LAB – Goggles
for Murphy’s Law! =)
Ticket out the door
1. Use sticky note up front
Name on one side question on other
2. List one thing you learned from Circular Motion lab
3. List a burning question about lab you still need
answered.
4. Stick on the board on your way out of the door.
Circular Motion Terms
• Axis- is the straight line
around which rotation takes
place.
Two types of circular motion
• Rotation- also called spin; when
an object turns around an
internal axis.
• Revolution- When an object
turns around an external axis
Rotating
around
an Axis
Demo 1:
Have you ever swung a pail of
water over your head?
Centripetal force (Fc)
– Any force directed toward the center of the
circle.
– The inward force is perpendicular to the
velocity of the object at that instant.
Centripetal force (Fc)
– What could cause an object to stay in orbit
giving a centripetal force
• A rope:
• Gravity:
• Friction:
Fc = FT
Fc = Fg
Fc = Ff
tension in the rope
gravity
friction
Demo 2:
The Horizontal vs. Vertical
Twirl…
Give it a Whirl !
What direction is the force of the
string pulling?
Demo 3:
What would happen if an object
were released from its orbit?
• Draw the direction it would travel if released at 1
and 2
1
2
What would happen if an object
were released from its orbit?
• Draw the direction it would travel if released at 1
and 2
1
2
• The object would travel tangent to the circle in a
straight line
Linear/Tangential Velocity
• Objects moving in a circle still have a
linear velocity = distance/time.
• This is often called tangential velocity,
since the direction of the linear velocity is
tangent to the circle.
v
Centripetal force (Fc)
Key point:
• In order for any object to move in a circular path
at uniform speed an inward, (parallel or
perpendicular) force is necessary.
Centripetal force (Fc)
Recap
• The ball’s speed may or may not be
constant – however its direction and
velocity are constantly changing.
• Thus, the object is constantly
accelerating.
• In order for an object to be accelerated a
force must act upon it- according to
Newton’s second law.
Centripetal force (Fc)
Recap:
• As the ball moves around – the rope is
exerting an (inward or outward) centripetal
force on the ball.
• Force of the rope on the ball is
(perpendicular or parallel) to the ball’s
direction of travel at that instant.
Centripetal force (Fc)
• How can circular motion be accelerated
when speed is constant?
Centripetal force (Fc)
• Velocity has BOTH speed and direction.
• In circular motion –
– Direction is always changing.
– So, velocity is ALWAYS changing.
• According to Newton’s 2nd law
• F = ma
• Acceleration requires a net force.
Your Turn
• When a car turns to the left, why do
passengers slide to the right?
• When your friend slams
on the breaks and
you feel a ‘force’
push you forward –
what causes this
sensation?
Inertia
• Newton’s 1st law
• Once an object is in motion – it stays in
motion until acted upon by an outside,
unbalanced force.
# 1 Misconception
• Inertia is often mistaken for the ‘feeling of
a force.’
• Commonly referred to as centriFugal
force.
• According to physicist, this is a fictitious or
false force.
When a car turns to the left, why
do passengers slide to the
right? What provides the inward
Centripetal force?
• Centrifugal force- a fictitious outward
force, caused by an objects inertia, felt
when an object follows a circular path.
• It feels like you would move straight out
away from the circle
It feels like you
move outward. But
you would not
• An objects inertia would take it directly
ahead tangent to the circle
What provides the centripetal
force in your washing machine?
Centripetal Force
• Helpful hint:
• When doing Newton’s 2nd Law of motion
equations – think of the Fc as the net
force.
Fc = mac
• All the forces acting on a rotating object
will add up to equal mass times the
centripetal acceleration.
Think back to Newton’s Laws
• The net force is related to the acceleration
of an object…and is stated in the following
three equations:
• Circumference = 2*pi*Radius
Warm-up:
• What is the difference between centripetal
and centrifugal force? Explain with an
example.
• What is the relationship between
centripetal force and velocity?
• What is the relationship between
centripetal force mass?
“Give it a Whirl”
Centrifugal force - stopper lab
“Give it a Whirl”
• What 4 factors could affect circular motion
of the stopper?
- Velocity
- Mass
- Centripetal force
- Radius
Useful equations for Centripetal
force (Fc) lab
Fc = mac
d
V=
V=
T=
t
2πr
T
1
T= period (s) seconds per rotation
f
f= frequency (hz) rotations per
second
Calculating the period (T)
T = time it takes for 20 revolutions
number of revolutions (20)
State three relationships you
discovered during the lab.
Let’s use these to derive the
formula for centripetal force.
Pictorial “Derivation” of
Centripetal Acceleration
a = Dv/Dt
v2
Top view:
a
a
a
a
a
a = v2/r (r is radius of curve)
v1
In uniform circular motion the
acceleration is constant,
directed towards the center.
The velocity has constant
magnitude, and is tangent to
the path.
Speed/Velocity in a Circle
Consider an object moving in a circle around
a specific origin. The DISTANCE the object
covers in ONE REVOLUTION is called the
CIRCUMFERENCE. The TIME that it takes to
cover this distance is called the PERIOD.
scircle 
d 2r

T
T
Speed is the MAGNITUDE of the velocity.
And while the speed may be constant,
the VELOCITY is NOT. Since velocity is a
vector with BOTH magnitude AND
direction, we see that the direction o the
velocity is ALWAYS changing.
We call this velocity, TANGENTIAL velocity as its
direction is draw TANGENT to the circle.
Centripetal Acceleration
Suppose we had a circle with angle, , between 2 radaii.
You may recall:
s
r
s  arc length in meters

Dv
Dvt Dv

r
v
v
v
vo

s Dv
 
r
v
s  Dvt
vo
v 2 Dv

 ac
r
t
ac  centripetal acceleration
Centripetal means “center seeking” so that means that the
acceleration points towards the CENTER of the circle
Drawing the Directions correctly
So for an object traveling in a
counter-clockwise path. The
velocity would be drawn
TANGENT to the circle and the
acceleration would be drawn
TOWARDS the CENTER.
To find the MAGNITUDES of each
we have:
2r
vc 
T
2
v
ac 
r
Circular Motion and N.S.L
2
Recall that according to
Newton’s Second Law,
the acceleration is
directly proportional to
the Force. If this is true:
v
FNET  ma ac 
r
2
mv
FNET  Fc 
r
Fc  Centripetal Force
Since the acceleration and the force are directly
related, the force must ALSO point towards the
center. This is called CENTRIPETAL FORCE.
NOTE: The centripetal force is a NET FORCE. It could be
represented by one or more forces. So NEVER draw it in
an F.B.D.
Tuesday (1/20)
• Take out your ws “ Equations for circular
motion”. Has equation bank at top.
• Complete Problem Set #1
I will finish getting recommendations this
period for next year – if you did not give it
to me on Friday.
Ex. A
• What would happen to the centripetal
force required to keep an object going in a
circle if the radius of a circle is double?
Ex. A
• What would happen to the centripetal
force required to keep an object going in a
circle if the radius of a circle is double?
mv2
FC =
r
(1)(1)2
FC =
1
= 1
(1)(1)2
FC =
2
= ½
Ex. B
• How much more or less centripetal force
would you have if a car slowed from 60
mph to 20 mph going around a curve?
– Start by figuring out how much of your initial
velocity you are going
Ex B.
• How much more or less centripetal force
would you have if a car slowed from 60
mph to 20 mph going around a curve?
mv2
FC =
FC =
r
(1)(1/3)2
= 0.111
1
Ex. C
• Kent spins in his chair with a frequency of
0.5 Hz. What is the period of his spin?
• Hint: you will need to go back to notes to
find the equation for period.
Ex. C
• Kent spins in his chair with a frequency of
0.5 Hz. What is the period of his spin?
Ex. D
• A record takes 1.3 s to make one
complete rotation. An object on this
record is 0.12 m from the center. What is
its velocity?
Ex. D
• A record takes 1.3 s to make one
complete rotation. An object on this
record is 0.12 m from the center. What is
its linear velocity?
Ex. E
•
The pilot of a 60,500 kg jet plane is flying
in circles whose radius is 5.00 x 104 m. It
takes 1.8 x 103 s to make one rotation.
a. What is the velocity of the plane?
b. What would be the centripetal force?
Ex. E
•
The pilot of a 60,500 kg jet plane is flying
in circles whose radius is 5.00 x 104 m. It
takes 1.8 x 103 s to make one rotation.
a. What is the velocity of the plane?
b. What would be the centripetal force?
Ex. F
• What is the centripetal acceleration of an
bike traveling a tangential speed of 8
meters per second in a circle that has a
radius of 5 meters?
Ex. F
• What is the centripetal acceleration of an
bike traveling a tangential speed of 8
meters per second in a circle that has a
radius of 5 meters?
Problem Set 1
What will happen to the centripetal force
required to keep an object going in a
circle if:
1. The mass of the object is doubled and
the radius of the circle is cut in half
2. Mass, radius, and velocity are all
doubled
Problem Set 1
What will happen to the centripetal force
required to keep an object going in a
circle if:
1. The mass of the object is doubled and
the radius of the circle is cut in half
Problem Set 1
What will happen to the centripetal force
required to keep an object going in a
circle if:
2. Mass, radius, and velocity are all doubled
Problem Set 1
3. A of a 50 kg girl is bicycling in circles with
a radius of 5.00 m. It takes 12 s to make
one rotation.
a. What is the velocity of the girl?
b. What would be the centripetal force?
Problem Set 1
3. A of a 50 kg girl is bicycling in circles with
a radius of 5.00 m. It takes 12 s to make
one rotation.
a. What is the velocity of the girl?
b. What would be the centripetal force?
Problem Set 1
3. A of a 50 kg girl is bicycling in circles with
a radius of 5.00 m. It takes 12 s to make
one rotation.
a. What is the velocity of the girl?
b. What would be the centripetal force?
Thought to ponder and recap:
• If you were to put a bubble in a bag of water
on the international space station and spin in
in a circle…which way would the bubble
travel?
(inward, outward, stay random throughout
liquid) Explain your reasoning
Let’s find out! PLICKERS!
Friday Warm-up:
Circular Motion
1. Take out “Flying pig /
plane Lab”
Use this time to compare
data and complete post lab
analysis.
Paper clip your lab group together – make
sure the # of your pig or plane is on front of
all papers. Turn in to top tray.
Uniform Circular Motion
Answers
• 1.
2.
3.
4.
5.
ac = 3.09 m/s2
agent exerting force = friction
.32 Newtons
Min. coefficient = 0.88
8.1 km
The force toward center of tub.
The walls of drum exert the
normal force (centripetal force)
Circular Motion Answers
continued…
6) 18 m/s
Tue. Agenda
•
•
•
•
•
•
•
•
Review any questions from lab
Review questions from ws#1
Horizontal vs Vertical circular motion
Practice
Webassign #12
Review for quiz
Re-read 109-111
Lab Thur. will deal with page 112