Download Circular Motion

Warm Up 2-25-15
(Rewrite Question & Answer in your notebook)
• How can you tell what direction an object is going to accelerate?
A. by the force of gravity
B. its opposite the force of gravity
C. by the net force
• What is the equation to find the weight of an object?
A. Fnet = ma
B. Fg = mg
C. Fg = Gm1m2 / r2
• Why would your weight be different on another planet?
A. The acceleration due to gravity changes
B. Your mass changes
C. Your science teacher changes.
Circular Motion
How things move as they spin
Uniform circular motion
is motion along a
circular path in which
there is no change in
speed, only a change
in direction.
Foundations:
•
•
•
•
Remember this?
Speed is scalar (without direction), but
velocity is a vector (direction counts)
acceleration is a changing velocity over time
So, could you have something moving at a
constant speed, but still accelerating? How?
Newton’s Laws
Uniform circular motion
(Leave room! There will be 4 ideas)
•Idea #1 UCM has
constant speed, but
in a circular pattern
•Example: a car with
speed set at 10 mph
& wheel turned
Uniform circular motion
Imagine what
direction the car
would go if you
suddenly
straightened the
wheel
Uniform circular motion
What is happening to
the velocity as you
go in a circle?
• Idea #2 UCM means
always changing the
direction of velocity
Uniform circular motion
The velocity is
always
tangential to that
point on the
circle.
• Idea #2 UCM
means always
changing the
direction of velocity
Uniform circular motion
If Newton’s first law says
things should keep going
the direction they are
going, why does the car
turn?
• Idea #3 circular
motion is caused by
an inward force
called “centripetal
force”
Uniform circular motion
Which way is it
accelerating?
• Idea #4 the car
accelerates in the
same direction as the
force (inward)
Uniform circular motion
What about that ‘force’
which seems to push
you outward?
• Centrifugal ForceNot a true force, but
rather the tendency to
move in a straight line
due to inertia.
THIS FORCE DOES NOT EXIST!!!
In summary
Uniform circular motion . . .
• has constant speed
• has changing direction for
velocity
• is caused by an inward
“centripetal force”
• experiences inward
acceleration
How do the main points
apply to . . .
• the moon orbiting the earth?
• the friction needed to keep your car on the
road while going around a curve?
• where an astronaut would be able to stand in
a space station that simulates gravity by
rotating?
What have you remembered?
• Draw the following picture in your notes.
Label everything you can about circular
motion.
STOP!
• Let’s take a 5min break!
Centripetal Acceleration
2
v
ac = ––––
r
2
velocity
Centripetal
=
–––––––
Acceleration
radius
.
Centripetal Force
Remember F=ma?
2
v
m
Fc = ––––
r
2
velocity
centripetal mass x
=
––––––––––––
force
radius
.
Example Problem:
• A 3 kg ball on a string is rotated about
a circle of radius 2 m. The maximum
tension allowed in the string is 50 N.
What is the maximum speed of the
ball?
2m
Fc= 50 N
r= 2m
m = 3 kg
v = ? m/s
Example Problem 2:
A 3-kg rock swings in a circle of radius 5
m. If its constant speed is 8 m/s, what is
the centripetal acceleration? What is the
force?
Example Problem 3:
A skater moves with 15 m/s in a circle of
radius 30 m. The ice exerts a central
force of 450 N. What is the mass of the
skater?
Example Problem 4:
The wall exerts a 600 N force on an 80kg person moving at 4 m/s on a circular
platform. What is the radius of the
circular path?
Your turn!
• Answer the next three slides in your
notebook.
• I’ll give you 1 min per slide. If you finish
early, help your neighbor!
• Correct answers will be on the last slide.
Practice 1
A 2.0-kg mass at the end of a string 0.50 m
long revolves in a circular path at a
constant speed of 4.0 meters per second.
What force does the string exert on the
mass?
Practice 2
A 1000-kg car goes around a race
track with a speed of 20 m/s. Its
radius from the center of the circle
is 200 meters.
What is the direction of its
centripetal acceleration?
What is the direction of its velocity
vector at this moment?
What is the magnitude of the
centripetal force involved?
Practice 3
A 1.0-kg ball attached to the end of a rope
0.50 m long is swung in a circle. Its
speed along the circular path is 6.0 m/s.
What is the centripetal force?
Practice Answers
1) 64N
2) 2000N
3) 72N
Still lost?
I’ll be here
after school today.
Drop by for tutoring!!!