Transcript Circular Motion

Circular Motion
Question: Is there a constant velocity when an
object moves in a circle with a constant speed?
No, the direction changes, therefore the velocity
changes.
If the velocity changed, the object is actually
ACCELERATING even while moving at the same
speed.
The change in direction is always pointed toward the
center of the circle, so the acceleration is inwardtoward the CENTER.
“centripetal”- center seeking
acceleration
Centripetal Acceleration
acceleration
EVERYTHING that moves in a circular path is
experiencing a centripetal acceleration that
points inward- toward the center of the circle!!
a
Rotating
Turning about an internal
axis
Revolving
Turning about an external
axis
Linear speed
How far you go in a certain amount of time
Miles per hour, meters per second
Rotational speed
How many times you go around in a certain
amount of time
Revolutions per minute, rotations per hour
Which horse has a larger
linear speed on a
merry go round, one
on the outside or one
on the inside?
Outside.
Which horse has a
greater rotational
speed?
Neither, all the horses
complete the circle in
the same amount of
time.
How much faster will a horse at TWICE the
distance from the center of the circle be
moving
TWICE the distance means TWICE the speed
The number of revolutions per second is called the
frequency, f.
Frequency is measured in Hertz, Hz.
The time it takes to go all the way around once is called
the period, T.
Frequency is related to period by
f=1/T
and
T=1/f
Example
A boy twirls a toy airplane around and around
at the end of a string. If it takes 2 seconds for
the airplane to complete one loop, what is
the frequency?
f=1/T
f=1/2
f = 0.5 Hz
How do you find the velocity of an object
moving in a circle if it is not directly provided?
We know that Velocity = distance / time
In circular motion, the distance traveled is all
around the circle… the circumference.
The circumference = 2pr
The time it takes the object to go all the way
around the circumference once is called the
period, T.
So…
v = 2pr / T
Example
A race car takes 1.5 minutes to go around one
lap of a circular track. If the track has a radius
of 400 m, how fast was the car traveling?
v = 2pr / T
v = 2p(400) / (1.5 x 60)
v = 27.9 m/s
Uniform Circular Motion, UCM: moving in a circle with
a constant speed.
Question: Is there a constant velocity when an object
moves in a circle with a constant speed?
No, the direction changes, therefore the velocity
changes.
If the velocity changed, the object is actually
ACCELERATING even while moving at the same
speed.
Suppose an object was moving in a straight line with some velocity,
v.
According to Newton’s 1st Law of Motion, “An object in motion
continues that motion unless a net external force acts on it”.
If you want the object to move in a circle, some force must push or
pull it towards the center of the circle.
A force that pushes or
pulls an object towards
the center of a circle is
called a centripetal force
Centripetal means “center
seeking”
What happens is the string breaks? Which
way will the ball move?
The ball will continue to move in a
straight line path that is “tangent”
to the circle.
Since the object is changing direction even
though the speed is remaining constant there
is an acceleration:
a c = v2 / r
Where r is the radius of the circle and v is the
velocity of the object.
Linear or Tangential Velocity
a
ac = v2 /r
ac = rω2
ω = Angular Speed