Download Circular Motion and Gravitation

Circular Motion and
Gravitation
What is Circular Motion?
• Objects that move in a
circle
• Even if the speed is
constant ,the velocity and
acceleration is changing.
• WHY?
Circular Motion Terms
The point or line that is the center of the circle
is the axis of rotation.
Rotation- If the axis of rotation is inside the
object, the object is rotating (spinning). Ex.
Earth rotates around its center point
Revolution- If the axis of rotation is
outside the object,
the object is revolving.
Ex. Earth revolves around the sun
Circular Motion
• Period (T)-The amount
of time it takes to
make one rotation.
– Time/cycle
– SI unit is seconds
• Frequency (f)- the
number of rotations
per second.
– Cycles/second
– SI unit is Hertz (Hz)
Tangential Speed
• Objects moving in a circle still have a
linear speed = distance/time. (d/t)
• Called Tangential Velocity
V=2πr
T
Recall: Circumference= 2πr OR 2d
d=diameter
r=radius
The Circumference Is your
distance.
Tangent
Rotational/aka angular Speed
• # of Rotations per
unit of time .
• measured in
degrees/second,
rotations/minute
(rpm), etc.
• Common symbol, ω
(Greek letter omega)
Rotational vs. Tangential Velocity
– If an object is
rotating:
• All points on the
object have the same
rotational velocity.
• All points on the
object do not have
the same Tangential
velocity
What type of speed is different???
fast
twice as
fast
Centripetal Acceleration
Acceleration moves towards center of
circular path
Formula: a = v²
r
a
Forces and Newton’s 2nd law
• What did that say again???
Centripetal Force
• Any force that is directed towards the
center of a circle
• This force is called a
centripetal
(center seeking) force.
Fnet
Centripetal Force
• In symbols:
recall F=ma
• Fcent= ma a=centripetal acceleration
• Fcent =
mv²
r
What furnishes the centripetal
force required to keep a car
going in a circle when the road
curves?
• FRICTION
• Race cars are wide to maximize contact
with road, curves on newer roads and race
tracks are banked
Centripetal Force Examples
• As a car makes a turn,
the force of friction
acting upon the turned
wheels of the car
provide the centripetal
force required for
circular motion
• As a bucket of water is
tied to a string and spun
in a circle, the force of
tension acting upon the
bucket provides the
centripetal force required
for circular motion.
• As the moon orbits the Earth, the force of gravity
acting upon the moon provides the centripetal force
required for circular motion.
“Centrifugal Force”
• “centrifugal force” is a fictitious force - it
is not an interaction between 2 objects,
and therefore not a real force.
Nothing pulls an object away from the
center of the circle.
“Centrifugal Force”
• What is erroneously attributed to
“centrifugal force” is actually the action of
the object’s inertia - whatever velocity it
has (speed + direction) it wants to keep.
Four Variables are involved in
circular motion
• Mass, radius, centripetal force,
and velocity
CAUTION: The mass of this product affects
every other mass in the universe, with an
attracting force that is proportional to the
product of the masses and inversely
proportional to the square of the distance
between them.
Universal Gravitation
• Law of Universal
Gravitation: Every
object attracts every
other object with a
force that for any two
objects is directly
proportional to the
mass of each object.
• Force Field: magnetic field that
surrounds a magnet
• Gravitational Field: force field
that surrounds massive
objects, such as the Earth.
Rotational Inertia
• Objects resist changes in its
rotational state
• Depends on mass (just like
regular inertia)
• The greater the distance
between the bulk of the mass
and its axis of rotation the
greater the inertia
Rotational Inertia
Rotational Inertia
How Attractive are you?
• Find 2 friends masses, the distance you are
away from them and calculate the force of
gravity between you!