angular velocity

Rotation: circular motion around an inside
axis - example the earth spinning on its own
Revolution: circular motion around an
outside axis - example the earth
moving around the sun.
Circular motion
• We have several ways to describe the speed
at which an object turns
• Tangential speed
• Linear speed
• Rotational speed
• Angular velocity
Circular motion
Tangential velocity or VT which
describes the speed at which an ant on the
outside of the spinning turntable would be
traveling at any instant relative to an outside
observer. This is also known as linear
This can also be thought of as the speed the
ant would be going if he suddenly flew off
of the rotating disk.
Circular motion
• Rotational velocity or  (the greek lower case
letter omega).
• This is a measure of how fast an object is
moving with relation to its axis of rotation.
This motion will be described by how many
revolutions the object makes around it axis of
rotation. We will measure it in Revolutions
per minute or RPMs in this class.
Linear speed or velocity = tangential speed or velocity =
distance/time and is measured in “meter/second”
The red arrow represents the linear velocity
rotational speed or velocity or
angular speed or velocity, (omega), =
 = number of rotations
and is measured in RPM’s or degrees or radians
Measure the time it takes for the blue arrow to go
around once, its period,T, and calculate its angular
speed in rotations per second.
On a spinning turn table which point has
the fastest speed?
Well, it really depends!
Which has the greatest vT?
Which has the greatest ?
To calculate the linear
velocity we could take
Or the circumference/time
v = 2πr/T
If the diameter of the circle
is 4 m and the period is 3
seconds calculate the
linear velocity.
If something moves in curved path must there be
a force on it?
A ball is going around in a circle attached to a
string. If the string breaks at the instant shown,
which path will the ball follow?
Centripetal Force
– A center-seeking force that causes an object to
follow a circular path.
Centripetal force
Centripetal force
Causes circular motion it is
a real force
“center seeking”
What is the direction of the centripetal force?
What direction would the acceleration be?
G Force, 10 m/s/s or your weight
0 stationary or moving at a constant velocity
0.4 "pedal to the metal" in a typical American car
1.7 "pedal to the metal" in a Formula One race car
2 Extreme Launch™ roller coaster at start
3 space shuttle, maximum at takeoff**; jet fighter landing on
aircraft carrier
8 limit of sustained human tolerance
25 R. F. Gray, centrifuge*, 5 s duration,
40 USAF chimpanzee, centrifuge*, 60 s duration,
35 - 40J. P. Stapp, rocket powered impact sled, 1 s duration,
60 chest acceleration limit during car crash at 48 km/h with airbag
70 - 100 crash that killed Diana, Princess of Wales,
83 E. L. Beeding, rocket powered impact sled, 0.04 s duration,
247 USAF chimpanzee, rocket powered impact sled, 0.001 s
Centrifugal force
“center-fleeing”, away from center
Apparent outward force experienced by a
rotating body
Fictitious force – it is not real but do to the
effect of inertia
What is the direction of the centrifugal force?
Centrifugal Force
The whiteboard was
being carried along a
straight line path; the
ball rest on top of the
whiteboard and
followed the same
straight-line path.
Then suddenly, the
board was turned
leftward to begin a
circular motion; yet the
ball kept moving
An accelerometer measures the
acceleration. When the water in this
accelerometer feels a lurch, a fictitious
force, due to the effect of inertia
When the accelerometer is accelerated
uniformly in a straight line it will look like
When the accelerometer is
rotated it will look like this
Linear velocity
Angular acceleration
Centripetal Force
Centrifugal Force
 = revolutions/time
v = 2πr/T
Fc = mv2/r
A linebacker rides on the outside horse
of a merry-go-round. The merry-goround’s diameter is 10 m it takes 5
seconds to complete 1 rotation. If the
linebacker has a mass of 100 kg…
Is he revolving or rotating?
He is revolving…..
The merry-go-round is
A linebacker rides on the outside horse
of a merry-go-round. The merry-goround’s diameter is 10 m it takes 5
seconds to complete 1 rotation. If the
linebacker has a mass of 100 kg…
Calculate his linear velocity.
V T
2 5m
V T
 6.28m / s
10 s
of a merry-go-round. The merry-goround’s diameter is 10 m it takes 5
seconds to complete 1 rotation. If the
linebacker has a mass of 100 kg…
Calculate his centripetal
force .
FC 
100kg(6.28m / s) 2
FC 
FC  789 2 or 789 Ninward
A linebacker rides on the outside horse
of a merry-go-round. The merry-goround’s diameter is 10 m it takes 5
seconds to complete 1 rotation. If the
linebacker has a mass of 100 kg…
Calculate his centrifugal force.
It’s not real, just like…..
How does a train stay on the tracks?
Believe it or not it is not the inner rim. The
rail often does not touch it
The wheels of the
train are tapered. A
cylinder rolls
straight, whereas a
cone will roll in a
Which part of the tapered
wheel moves with a
greater VT? The part with
the smaller radius A, or
the larger radius B?
Since B is moving faster it
covers more distance and
causes it turn.
Let’s see what happens if we roll a
cylinder wheel down a Curved track
Will the wheel stay on the track?
If the track starts turning right, underneath the train,
(which has plenty of momentum), what will
There will be nothing to make the wheels turn right
It does not correct itself as it slides off the track
It is a train wreck
Let’s see what happens if we roll
a tapered wheel like the one
shown down a track
Will the wheel stay on the track,
if the track starts turning left?
The trains momentum tries to
carry it straight forward.
It does not correct itself, it wants
to go right which is opposite
of direction it needs to go!
What happens if the track turns left
The right wheel will move faster, with the
same rotational speed but a larger VT, and the
left wheel will move slower, so the train will
roll to the left and self corrects. Staying on
Slower Slower
So if you want Thomas the Train to
turn, you let its momentum do the
work for you!
If you want the train to turn left, you just make
the tracks turn left and the rest happens by
itself!! Horray for Thomas the Train!
Trains are really smart, and very
useful. But some are Evil!
Artificial Gravity Space Station
What would happen
if the rotation was
What would happen
if you increased
the radius of the
space station?
To feel 1 g force, if
the space station
is larger would it
have to be
spinning as fast?
Does an astronaut have to
apply a force to an
apple keep it moving in
a circle?
Would the astronaut feel
“weight” from the
What would happen if he
lets go of it?
Is there a net force on it
when he lets it go?
What direction does the
apple go as seen by the
Inertia - resists acceleration, a property of
matter, a kind of laziness of matter depends on the mass
Rotational Inertia “The moment of inertia”
“I”, resists rotational acceleration, depends
on the distribution of the mass, that is where
the mass is located
The further the mass is away from the
axis of rotation, fulcrum, the greater
the rotational inertia, that is the more
lazy it to change its rotational motion.
If these two rods have the
same mass and CG but rod
A has the mass located in
the center and rod B has
most of the mass located at
the ends.
Which is harder to rotate?
What happens when you put an equivalent force
on each roll?
Which one will rotate easier?
Which of these would have the least rotational
inertia in their legs?
Which would have the fastest gate?
A solid hoop and a hollow cylinder roll down an
Which one will have the greatest rotational inertia?
Which one will be more sluggish?
Which one will win the race?
angular momentum (A.M.) is equal to
 - rotational velocity
 - angular velocity,
I - rotational inertia or the moment of inertia
A.M. = I
conservation of angular momentum
the total angular momentum of a system
does NOT change,
unless an outside force
acts on it, therefore,
angular momentum before = angular
momentum after
Ibefore = Iafter