Download centripetal force

Chapter 9- Circular Motion
AXIS OF ROTATION
This is an imaginary line through the center
of the spinning
The points on the axis
of rotation don’t move
due to the spinning
As the circle spins the point on the axis of rotation appears is still
As the circle spins the point on the axis of rotation appears is still
Here the axis of rotation is not in the center, where is
it?
If the axis of rotation is through the object it is called
ROTATION
If the axis of rotation is outside of the object it is called
REVOLUTION
The earth rotates and revolves
The earth rotates and revolves
Does a figure skater rotate or revolve
As they spin?
“Normal” or linear speed
Slow
Fast
Rotational speed
Slow
Fast
Linear speed is the distance moved divided
by the time
m
s
Rotational speed is the number of complete
rotations divided by the time
rotations
s
The most common unit of rotational speed
rotations
min
Rotations Per Minute
RPM’s
Where have you heard of RPMs
A record player makes 100 complete spins in 25 s
seconds what is its rotational speed?
Could an object have a rotational
speed of .75 rot/s. What would it
mean?
A typical DVD player spins a DVD at
about 900 RPM
How many
many rotations
times does
it spin
around
How
does
it make
in in
1 second?
10.5
s?
The speed (in m/s) of an object in a circular path is
called its
Tangential Speed, vt
Its direction is always tangent to the circular path
Compare rotational speed of each dot.
They both complete
1 rotation in the same
amount of time
Compare their tangential speeds
The outer dot has to
move faster in order to
travel the longer path in
the same amount of time
Both dots have the same rotational speed
But different tangential speeds
The tangential speed depends
on what?
HOW FAR THE POINT IS
AWAY FROM…..
The axis of rotation
This is called its radial distance
Do
Do
the
records
dots
have
the
the
same
same
tangential
rotational
speed?
speed?
Dothe
the
dotshave
have
the
same
radial
distance?
vt = r w
Tangential Speed
Rotational speed*
Radial distance
*In order for the number to work out,
the rotational speed has to be in radians/sec
v=rw
A spot moves fastest on a record which is
spinning fast and is far away from the center
If the record doubles its rotational speed, the tangential speed of an object…
v=rw
If the blue dot is
twice as far from
the center as the
red dot then it
tangential speed
twice as much
is __________
30 cm
90 cm
Where is the axis of rotation?
If the 30 cm mark is moving at 2 m/s, how
fast is the 90 cm mark moving?
A record player spins at 5 rpm’s.
One penny is placed 1 cm away from the center of
the record and has a tangential speed of 2 m/s.
What will be the rotational and tangential speed of a
penny placed at 3 cm away from the center?
What is the distance traveled by each dot if
the disk makes 1 rotation?
.75 m
.20 m
What
Theispoints
the travel
tangential
the circumference
speed of
theofblue
a circle.
dot if the
disk has a rotational
speed of 1.0 rotation
per second?
3 rps?
For the most excitement where do you
want to be on this ride? A horse close to
the middle or towards the edge?
A wheel can both rotate and move (linearly)
Rotating
moving linearly
A wheel which is rolling along the ground both
moves linearly and rotates at the same time.
How far does a wheel move across the
ground if it makes 1 rotation? Any guesses
If the wheel doesn’t skid, as the
wheel makes 1 rotation. If will
move a distance equal to its
circumference
A wheel on a bicycle travels 4 m
across a road. If the radius of the
wheel is 0.25 m, how many rotations
did the tire make?
If the bike crossed the road in 5 seconds, what was
the angular speed of the wheel and the linear speed
of the bike?
Book problems
Page 133 – 135
#’s 2, 4, 5, 6, 20
A car wheel with a radius of 0.34 m, rotates
4.5 times. How far did the car travel?
How many rotations does a cup make as it
travels 1.0 m across a desk. The cup radius
is 12 cm?
Rotation and cups activity
Train track demo
To keep the train centered on its
tracks which is the best design?
Train track demo
Note that
When
the the
railswheel
get unaligned,
is like the which
tapered
will self-correct?
cup.
Which side of the wheel will go
faster?
Train track demo
How will that cause each train to turn?
Train track demo
Which one keeps the train on the tracks?
The differential gear allows a
car to turn more easily
The outer wheel has to
travel a greater
distance and tries to
spin the axles at more
RPM’s
animation of a differential gear
What
What
Doesdirection
causes
the ballitaccelerate?
istothe
accelerate?
force?
IsDoes
it accelerating?
the
speed is
ofthe
theforce
ball change?
In
what
direction
acting?
The velocity of an object moving about
in a circle changes (even if its speed is
constant)
What does the
arrow represent?
This force only changes the direction
not the speed. Can you see why?
It is always
perpendicular
to the velocity
This inward force is called a centripetal force
A Centripetal
Centripetal
forcemeans
causes
an object
“center-seeking”
to travel in a
circle at a constant speed.
Does a
centripetal
force do work
on an object?
vt
FC
A centripetal force is NOT a “new” type of
force like FN, FF, FG, FT
It is simply one of the above acting in such
a way to make an object travel in a circle.
But how does it “Know” to always point to
the center, it must be COMPLICATED???
ball on a string demo
What is the centripetal force?
How does it always point to the middle?
The centripetal
force is always
perpendicular to
the velocity!
What provides the centripetal force in the scenario
Fg
What provides the centripetal force on the
penny that keeps in moving in a circle on a
record?
FF
What provides the centripetal force in the scenario
That keeps the riders moving in a circle?
FN
What forces do you experience on a merry go
round as it spins?
FN
Fg
FN
It feels like a force is pushing you to the outside
of the circle, what is the dealer of this force?
If the string were to be cut what path would the ball take?
B
A
C
D
E
F
Assume there is NO gravity
Anything curved has to go if no force is acting on the ball
B
A
C
D
E
F
Anything curved has to go if no force is acting on the ball
B
A
D
Let’s try it and find out?
What direction was the ball headed just before the string broke
B
A
D
What direction was the ball headed just before the string broke
D
Back to the rotor ride. You feel pressed against
the wall. What force does this?
Indicate all of the forces acting on the person.
FN
FF
Fg
There is NO FORCE pushing the
person outward from the center of
rotation!!!
What is the Net force acting on the
person?
Driving a car
speeding up, slowing down, making a turn
Ignoring gravity the only force on the ball is the string.
If the string is cut there are no forces on the ball, and it just moves
in a straight line at a constant speed due to …..
INERTIA
The only force is directed inward
There is NO outward directed force referred to as
centifugal force it only feels like it.
Centripetal
force
(tension)
An overhead view of a car on a circular track, what provides
the centripetal force
What happens if friction is lost?
The
constantly
push
you
towards
If
thewall
walls
suddenly
vanished
way
When
youmust
are
in
a spinning
ridewhich
it feels
like the
circle,
your inertia
to move
a by a
would
you
fly?PRESSED
you arefighting
being
against
thein
walls
straight
“Force” line
FN
Centripetal Force Activity
The faster an object goes around in a circle, the
more centripetal force is needed.
Think back to being in an elevator.
Depending on your movement, you have
feel heavier or lighter than normal.
If you were in a rotating spaceship, the “floor” would constantly be
pushing against your feet to keep you moving in a circle
From your perspective what direction would this normal force
point?
The floor would always be pushing “UP”
Is there something pushing you “DOWN”
NO but it would FEEL like it.
ARTIFICIAL GRAVITY!!!!!
All other things the same, which object
will need more centripetal force
A faster velocity increases the FC needed
How could you increase the artificial gravity on this spaceship?
If an object is moving fast and makes a sharp
a lot of centripetal force is needed.
Compare
the artificial
gravity
felt by each
Compare
Compare
the
thetangential
rotational
speeds
speeds
person
The further away from the axis of rotation, the greater the centripetal
force primarily because…
They are moving faster
When the record is spun faster which penny
will fly off first?
Just the right amount of centripetal force is needed to
keep an object moving in a circle.
In many cases the applied force will always match the
right amount
Swinging a ball on a string
What happens if the ball is swung faster?
Just the right amount of force centripetal force
If too much centripetal force is applied then the object will
If not enough centripetal force is applied then the object will
As the penny spins in a circle, what is the net
force on it?
For an object moving in a circle at a
constant speed. The NET FORCE
is the Centripetal Force.
When an object is swung in a vertical circle
The FNET between FG & FT supply the
centripetal force
FG
FC
At the bottom of the swing, the string has to
pull hardest to provide a Net force to the
middle of the circle
FC
FT
FG
FC
At the TOP of the swing, the string pulls the
least because gravity pulls toward the
center.
FC
FC
FG
FT
Let’s say a ball on a string need 4 N of
centripetal force (based on its speed). If the
ball has a weight of 3 N. What is the
tension in the string at the top and bottom of
a vertical circle?
What happens to the needed centripetal
force if it is swung slower?
Let’s say our 3 N ball now only needs 3 N
of centripetal force
Let’s say our 3 N ball now only needs 2 N
of centripetal force
The slowest speed an object can make a
vertical loop is when the (necessary) centripetal
force is equal to its weight.
Swinging water demo
If this space station is placed on earth as the
highland fling, what you feel changes based on
where you are in the rotation
If it is just spinning fast enough to keep you
from falling off
The centripetal force needed is
your weight, the floor doesn’t
have to push on you at all &
You feel…..
Fg
Fc
At the bottom, the floor has to push twice as
hard as your weight
And you feel….
Fc
Fg FN
Book problems
pages 133-135
Book problems ?’s
Page 133-135:
10, 12, 13, 16, 17, 18, 20, 21, 22, 23, 24,
28, 29
Both objects have the same tangential
speed but different radial distances
Which is accelerating more? (changing direction faster)
If the speed is the same the smaller the
radius the more force needed
If an object is moving fast and makes a sharp
a lot of centripetal force is needed.