Introduction to
Uniform Circular Motion
Uniform Circular Motion
An object moves at uniform
speed in a circle of constant
radius.
Uniform circular motion is
accelerated motion. Why?
Centrifugal Force
It’s a myth!
We need to go back to
Newton’s Laws to properly
explain the feeling you get on
a merry-go-round or in a
turning car.
When a car accelerates
You, as a passenger,
feel as if you are flung
backward.
Your inertia (mass)
resists acceleration.
You are NOT flung
backward. Your body
wants to remain at rest
as the car accelerates
forward.
When a car decelerates
You, as a passenger, feel as
if you are flung forward.
Your inertia (mass) resists
the negative acceleration.
You are NOT flung
forward. Your body wants
to remain in motion at
constant velocity as the
car accelerates backwards.
When a car turns
You feel as if you are flung to the
outside. Your inertia resists acceleration.
You are not flung out, your body simply
wants to keep moving in straight line
motion!
As a general rule
Whenever you feel you are flung in a
certain direction, you can bet the
acceleration is pointing in the
opposite direction.
Remember the elevator problems?
When you feel you are flying up,
acceleration of the elevator is down.
When you feel you are sinking down,
acceleration is up.
Acceleration in Uniform
Circular Motion
The velocity vector at any given
point is subjected to an acceleration
that turns it, but does not speed it
up or slow it down.
The acceleration vector is always at
right angles to the velocity.
The acceleration points toward the
center of the circle.
Acceleration in Uniform
Circular Motion
The acceleration responsible
for uniform circular motion
is referred to as centripetal
acceleration.
• ac =
Centripetal
Acceleration
2
v /r
ac: centripetal
acceleration in m/s2
v: tangential speed in
m/s
r: radius in meters
v
a
c
v ac
Centripetal acceleration always points
toward center of circle!
ac
v
Force in Uniform Circular
Motion
A force responsible for uniform
circular motion is referred to as
a centripetal force.
Centripetal force is simply mass
times centripetal acceleration.
Fc = mac
Centripetal Force
• Fc = m ac
2
• Fc = m v / r
Fc: centripetal
force in N
v: tangential speed
in m/s
r: radius in meters
v
Fc
v
Fc
Fc
v
Always toward
center of circle!
More on Centripetal
Force
Centripetal force is not a unique
type of force.
Centripetal forces always arise from
other forces.
You can always identify the real force
which is causing the centripetal
acceleration.
Nearly any kind of force can act as a
centripetal force.
Friction as centripetal force
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.
Tension as centripetal force
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.
Gravity as centripetal force
As the moon orbits the
Earth, the force of
gravity acting upon the
moon provides the
centripetal force
required for circular
motion.
Normal force as centripetal
force
An automobile turning
on a banked curve uses
the normal force to
provide the necessary
centripetal force.
Weight on a string
moving in vertical
circle
Centripetal
force arises
from a
combination
of tension
and gravity.
Tennessee Tornado at
Dollywood
Centripetal force
when you are upside
down arises from a
combination of
normal force and
gravity.
Centripetal Force can do no
work
A centripetal force alters the
direction of the object without
altering its speed.
Since speed remains constant,
kinetic energy remains constant,
and work is zero.
The Universal Law of Gravity
Fg = -Gm1m2/r2
 Fg:
Force due to gravity (N)
 G: Universal gravitational
constant
6.67
x 10-11N m2/kg2
 m1 and m2:
the two masses (kg)
 r: the distance between the
centers of the masses (m)
Acceleration due to gravity
2
/r
Fg = mg = GmME
What is g equivalent
to?
g
2
= GME/r
Acceleration and distance
Planet
Radius(m Mass (kg) g (m/s2)
Mercury
2.43 x 106 3.2 x 1023
Venus
6.073 x
4.88 x1024 8.83
106
3.38 x 106 6.42 x 1023 3.75
Mars
Jupiter
3.61
Saturn
6.98 x 106 1.901 x
26.0
1027
5.82 x 107 5.68 x 1026 11.2
Uranus
2.35 x 107 8.68 x 1025 10.5
Neptune
2.27 x 107 1.03 x 1026 13.3
Pluto
1.15 x 106 1.2 x 1022
0.61
Kepler’s Laws
1.
2.
3.
Planets orbit the sun in elliptical
orbits.
Planets orbiting the sun carve out
equal area triangles in equal times.
The planet’s year is related to its
distance from the sun in a
predictable way.
Kepler’s Laws
Satellites
From geometry, we can calculate
orbital speed at any altitude.
Orbital Motion
•
•
Gmems / r2 = mev2 / r =
The mass of the orbiting body
does not affect the orbital
motion!
Geosynchronous satellite
A geosynchronous satellite is one
which remains above the same
point on the earth. Such a satellite
orbits the earth in 24 hours, thus
matching the earth's rotation. How
high must a geosynchronous
satellite be above the surface?
(Mearth = 5.98x1024 kg, Rearth = 6.37
x 106 m)