Transcript presentation - Physics 420 UBC Physics Demonstrations

Circular Motion
Kathy Buckland
What is Circular Motion?
• The circular path along which an object
travels
• The rotation around a fixed axis
What is the word used to describe this path?
ORBIT
Examples
•
•
•
•
Rollercoaster
Swinging an object on a string
Planetary objects-moon, satellites, etc.
Car going around a round-about
Back to the mid 1600’s…
Newton’s Second Law:
“Mutationem motus proportionalem esse vi motrici impressae, et
fieri secundum lineam rectam qua vis illa imprimitur”
-Principia Mathematica (1687)
Otherwise known as…
F=force (N)
m=mass (kg)
a=acceleration (m/s2)
F  ma
F=ma
What is FORCE?
• PUSH
or a…
• PULL
Examples of Forces
• Gravity
• Tension
• Impact Forces
• Friction
Circular Motion and Force
How does the object stay in its path?
This force is called…
CENTRIPETAL FORCE
centrum "center" and petere “go to” or “seek”
To get where you want “to go”,
you must….
PEDAL….
Not a new force !!
Examples of forces:
• Gravity
• Impact Forces
• Tension
• Friction
Examples of these “acting” as the
CENTRIPETAL FORCE
• Ball on a string
• Rollercoaster
• Planetary Motion
• Car going in circles
F  ma
What next?
MASS
• The amount of MATTER an object contains
• Not weight -weight changes depending on
gravitation field
F  ma
and finally…
ACCELERATION
How the velocity changes in a certain amount of time
In physics lingo
•
•
•
•
a=acceleration (m/s2)
Δ= “change in”
v=velocity (m/s)
t=time (s)
v
a
t
2007 Lamborghini Murcielago
LP640
acceleration: 0-62 mph time of 3.4 seconds
(0-100km/h in 3.4 seconds!)
F  ma
ACCELERATION
How the velocity changes in a certain amount of time
In physics lingo
•
•
•
•
a=acceleration (m/s2)
Δ= “change in”
v=velocity (m/s)
t=time (s)
v
a
t
Velocity vs. Speed
• Velocity has a DIRECTION and a
MAGNITUDE
• The speed is the MAGNITUDE
How do we represent direction and
magnitude?
VECTORS
Vector Recall
The length of the vector represents the
MAGNITUDE or SPEED
The direction it points is the
DIRECTION
Adding:
Subtracting: (remember)
a
a+b
b
a
a-b
b
Back to Circular Motion…
F  ma
How can we find the force it takes to hold on
object in orbit?
Remember:
v
a
t
Δv is a change in direction not magnitude
DEMO # 1
Finding centripetal acceleration
What will it be?
How do we get centripetal
acceleration ?
A little geometry and algebra…
Find
similar triangles
t2
t1
Three more steps..
1. Make a tiny triangle so..
•
•
have a right triangle
use sinθ = opposite
hypotenuse
•
sin θ = θ
2. Use similar triangles
3. Use some algebra
S=v(t2-t1)=vΔt
Centripetal acceleration is…
2
v
acent 
r
Finally put it all together…
v
F  ma  m
t
For circular motion…
Fcent  macent
2
v
m
r
DEMO # 2
Observing the relationship
2
Fcent
v
m
r
The difference in force holding the object in
circular motion can be seen as the device spins. As
the velocity increases the changes in force become
greater.
Force comparisons…
Compare to lifting up objectsRemember acceleration is gravity≈10 m/s2
1 N≈ force required to hold up an orange
10 N≈ force required to hold this weight
Force to lift an elephant?
m ≈ 4500 kg so…
F ≈ 45000 N !!
like lifting 40000
oranges
And us ?
Mass Earth ≈ 6 x 1024 kg
v ≈ 30 000m/sec
r ≈1.5 x 1011 m
F ≈ 3.6 x 1022N
Like lifting about
8 x 1017 or
800 million billion
elephants !!
What to remember
• What circular motion is- be able to recognize it
• Newton’s Second Law- you will see it again!
F  ma
• That velocity has direction and speed
• Centripetal acceleration deals with the change in direction
• Things that effect centripetal force are mass, velocity,
and the distance from the center
2
Fcent
v
m
r
DEMO # 3
Observing Circular Motion
fk    
2
Fcent
N
mg
v
m
r