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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
Does a figure skater rotate or revolveAs they spin?
“Normal” or linear speed
Slow
Fast
Rotational speed
Slow
Fast
Linear speed is the distance moved divided by the time
Rotational speed is the number of complete rotations divided by the time
ms
rotationss
rotationsmin
Rotations Per Minute
The most common unit of rotational speed
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 times does it spin around in 1 second?How many rotations does it make in 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 speedBut 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 the dots have the same radial distance?Do the dots have the same tangential speed?Do the records have the same rotational speed?
vt = r Tangential Speed
Radial distance
Rotational speed*
*In order for the number to work out,the rotational speed has to be in radians/sec
v = r 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 = r If the blue dot is twice as far from the center as the red dot then it tangential speed is __________twice as much
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?
.75 m
.20 m
What is the distance traveled by each dot if the disk makes 1 rotation?
The points travel the circumference of a circle.
What is the tangential speed of the blue 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 problemsPage 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
When the rails get unaligned, which will self-correct?Note that the wheel is like the tapered 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
Does the ball accelerate?What causes it to accelerate?What direction is the force?
Does the speed of the ball change?Is it accelerating?In what direction is the force 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
Centripetal means “center-seeking”
A Centripetal force causes an object to travel in a circle at a constant speed.
FC
vt
Does a centripetal force do work on an object?
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 on the penny that keeps in moving in a circle on a record?
FF
What provides the centripetal force in the scenarioThat keeps the riders moving in a circle?
FN
What forces do you experience on a merry go round as it spins?
It feels like a force is pushing you to the outside of the circle, what is the dealer of this force?
Fg
FNFN
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
AB
C
D
E
F
Anything curved has to go if no force is acting on the ball
AB
D
Let’s try it and find out?
What direction was the ball headed just before the string broke
AB
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.
Fg
FNFF
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
Centripetal force
(tension)
There is NO outward directed force referred to as centifugal force it only feels like it.
An overhead view of a car on a circular track, what provides the centripetal force
FN
When you are in a spinning ride it feels like you are being PRESSED against the walls by a “Force”
If the walls suddenly vanished which way would you fly?
The wall must constantly push you towards the circle, fighting your inertia to move in a straight line
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 rotational speedsCompare the tangential speedsCompare the artificial gravity felt by each 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 circleThe FNET between FG & FT supply the centripetal force
FC
FG
At the bottom of the swing, the string has to pull hardest to provide a Net force to the middle of the circle
FC
FG
FCFT
At the TOP of the swing, the string pulls the least because gravity pulls toward the center.
FC
FGFC
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….
Fg
Fc
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.
