Transcript Uniform Circular Motion

Uniform Circular Motion
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What is uniform circular motion?
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• Constant speed
• Circular path
• Must be an
unbalanced force
acting towards axis of
rotation- think free
body diagrams!
• Ex of forces: tension,
banked curves,
gravitation
Period and Speed
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• Often easier to use
period T= time to
complete 1 revolution
instead of linear speed
• Circle=2r
• So if v=d/t then
V= 2r/T
REMEMBER: speed may
be constant but velocity
is not! Acceleration
changes the direction.
Vectors in circular motion
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• Velocity points
tangent to circle
• Acceleration points
in to axis of rotation
because a=v/ t
and v is always
towards center
Centripetal Acceleration and Force
• ac=v2/r and points in
• Fc=macdue to
Newton’s 2nd law
• Sometimes written
by replacing a so:
Fc=mv2/r
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What provides Fc?
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DRAW Free body diagrams
•
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• Ex: An athlete who
weights 800N is running
around a curve at a
speed of 5.0m/s in an
arc whose radius is
5.0m. What provides
the centripetal force?
• Draw a free body
diagram!
FRICTION!
Now solve…
• What is the
centripetal force?
• What would happen
if the radius of the
curve were smaller?
• Fc=mv2/r
• Mass=Fw/g
Fc=400N
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Now take it 2 step further…
• If the coefficient of static friction btwn
the shoe and the track =1 then will the
runner slip?
• How does changing the radius of the
curve affect whether the runner will slip?
Another example
• A roller coaster enter as
loop. At the very top the
speed of the car is
25m/s and the
acceleration points
straight down. If the
diameter of the loop is
50m and the total mass
of the car=1200kg, what
is the magnitude of the
normal force?
• Start with a free body
diagram- what forces
are acting?
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If net force is straight
down, why doesn’t the car
fall off the track?
Banked Curves
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Nsin is component of force
keeping car on curve- even
without any friction.
• Draw a free body
diagram for a car
traveling around a
banked curve- even
without friction
Circular motion and universal
gravitation
• Satellites, planets,
moons, etc can
travel in circular
paths- to solve,
equate Fc to
gravitational force
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Kepler’s Laws: 1 and 2
• Every planet moves
in elliptical orbit with
sun at 1 focus
• As planet moves in
its orbit, a line drawn
from sun to planet
sweeps out equal
area in equal time
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Kepler’s 3rd Law
• Remember Newton’s Universal
Gravitation, G?
• Kepler equated the force of G with the
laws of circular motion to get:
T2/R3 is a constant =42/GM
Where T is period, M is mass of sun, R is
radius of circular orbit (even though it’s
not quite circular)