Transcript Circular Motion - Goshen Community Schools

Chapter 9
Circular Motion
Period
The time it takes for 1 full
rotation of an object.
T = 1/ƒ
Period = 1/frequency
s = 1/Hz
How
long??
?
Frequency
How
many?
?
The number of rotations
per unit of time.
Measured in Hz. (Hertz)
Linear (Tangential) Speed
When an object spins in a circle…
distance = circumference
vc = 2πr
T
Linear speed = 2π * radius
Period
m/s = m
s
Please note…
An object can move around a circle with a
CONSTANT SPEED, yet still be accelerating!
How?????????
Because its direction is
always changing!
Centripetal Acceleration
Always directed toward the center of the circle.
ac = v2
r
Centripetal acc = (linear speed)2
radius
m/s2 = m/s
m
Centripetal Force
Always directed toward the center of the circle.
Fc = mac
Centripetal force = mass * centripetal acc.
N = kg * m/s2
Example 1
After closing a deal with a client,
Kent leans back in his swivel chair
and spins around with a frequency
of 0.5 Hz. What is Kent’s period of
spin?
T = 1/ƒ
2s
Example 2
Curtis’ favorite disco record has a scratch
0.12 m from the center that makes the
record skip 45 times each minute. What
is the linear speed of the scratch as it
turns?
1st find the period: T = 1/f
T = 1.3 s
2nd find the linear speed: v = 2πr/T
V = .58 m/s
Example 3
Missy’s favorite ride at the fair is the rotor,
which has a radius of 4.0 m. The ride takes
2.0 s to make one full revolution.
What is Missy’s linear speed?
v = 2πr/T
v = 13 m/s
What is Missy’s centripetal acceleration?
ac = v2/r
ac = 42 m/s2
Example 4
Captain Chip pilots a 60,500 kg plane. He
must circle above the airport to wait his turn to
land. If Chip flies his plane in a circle whose
radius is 50,000. m every 1,800. s, what
centripetal force must the air exert against the
wings to keep the plane moving in a circle?
First, find the speed: v = 2πr/T
v = 175.0 m/s
Next find centripetal force: Fc = mv2/r
Fc = 37,100 N
Abby 
A ball on a string is swung in a circle. The string breaks.
Which trajectory does the ball follow?
A?
B?
C?
C. The line
that is
tangent!!
D?
Ball on a string
The tension in the string
provides the necessary
centripetal force to keep
the ball going in a circle.
path of ball if the string
breaks
Centripetal Force
The force required to cause an object
to follow a circular path.
Centripetal means “center seeking”
The net
force is
towards
the center!
A car turning a corner…
MUST have a centripetal
force in order to put it
into a circular path!
Friction between the
road and tires is the
centripetal force.
No friction (ice) = No
centripetal force 
 This
makes the car slide.
Centrifugal force
Centrifugal means “center
fleeing.”
The red object will make the
turn only if there is enough
friction on it…otherwise it
goes straight.
object on
the dashboard
straight line
object naturally
follows
The apparent outward force
is called the centrifugal
force…
But it isn’t a force at allit’s actually the absence
of a centripetal force!!!
Silly Silo (Rotor)
Friction between
Bart and wall
wall pushing
in on Bart
Bart’s
weight
The inward wall force keeps Bart in the circle.
Friction keeps him from falling down.
Very little gravity in space…
Earth orbit
6-Dec-05
Very little gravity in
space…
But we can make our
own to make it easier!
The faster it rotates, the more people will weigh.
The
International
Space Station
Ladybug on the inside of
a bike tire…
Just like the space station, it would feel like
gravity for the ladybug!!!
The faster the bike goes, the more the
ladybug will weigh!
Ladybug on a Turntable
Which ladybug has a
greater velocity?
a.
b.
The inside ladybug.
The outside ladybug.
B. The outside ladybug!
Why???
It must cover more distance in the same amount
of time!
Basically, the velocity
depends on the radius.
Larger radius = larger velocity!
Smaller radius = smaller velocity!
Lab Set Up
tape
Goal: The weight (N) hanging down = the Centripetal Force (N)