Download Circular Motion

Reviewing Terms & Formulas
 1. Velocity – is always in the direction
of the movement
Velocity  v = d/ t + direction
2. Acceleration – is change in velocity - over time.
Any change – speeding up ( positive accel.)
- slowing down ( neg. accel. )
- changing directions is a change
in velocity too!
Accel
 a = Δv / t + direction
Δv = ( Vf – Vi )
DID YOU KNOW:
There is a scientific term for
acceleration in a circular path?
Centripetal acceleration!
Centripetal acceleration – acceleration of an
object in circular motion. It is directed toward
the center of the circular path.
Oh yeah & it has a formula ! Cool : )
2
v
ac =
r
ac = centripetal acceleration, m/s2
v = tangential speed, m/s
r = radius, m
Before you can complete
the Centripetal Acceleration
Formula …….
You must solve for v.
v= tangential speed ( m/s)
Solving for v is done a special way
for circular motion.
Let’s break down the term “tangential speed”
Root word “Tangent”  a straight line (LINEAR) or
plane that touches a curve or curved surface at a point
but does not intersect it at that point
2nd word “Speed”  d / t
For a constant tangential speed:
v = tangential speed, m/s
d
2πr
v= =
t
T
d = distance, m
t = time, s
r = radius, m
T = period, s, Time passing for
one revolution is called period
Now we have to put all the
formula components together
on a diagram for it to make
sense.
1st - Let’s review RADIUS….
What is it and how do you
measure it?
Radius = r
r
2nd – we have to add the velocity
component
Remember 
• velocity follows the path!
Path - Straight line off a circle
• AND velocity is called:
tangential speed
VELOCITY = v ( tangential speed)
r
v
Oh yeah – lets go over T.
T = time it takes for the obj. to complete 1
revolution ( see diagram below )
Start
Stop
Now, if you cannot time 1 revolution, you can time
3 - 5 revolutions. Then, divide the total time by
the # of revolutions to get the T of 1 revolution.
Example of solving for T
 You Hula Hoop for 4 seconds and the
hoop makes 5 revolutions.
 4 secs / 5 revolutions =
 1 revolution = .8 sec
3rd –We can now solve for centripetal
acceleration
Remember 
Acceleration is primarily toward
the center of the circle.
Centripetal Acceleration = ac
Remember to check the units to determine
if you need to solve for V using the formula
in the Yellow Box before you can complete
the formula for centripetal acceleration!!
2
v
ac =
r
2πr
v=
T
Problem 1:
If tangential velocity is 10 m/s and the
radius is 2m, find ac.
Problem 1 – Solution
V = 10 m/s
r =2m
ac = ? m/s2
Formula
2
v
ac =
r
ac = (10 m/s )2 =100 m2 / s2 = 50
2m
2m
m/s2
Problem 2: ( Please read carefully!! )
A 400 kg car takes 8 seconds to travel a circle
of radius 60m. Find ac .
Did you read carefully….
 m not necessary to solve
 8s = T
 r = 60 m
 ac = ? m/s2
Problem 2 Solution
2
v
ac =
r
2πr
v=
T
v = 2(3.14) 60 m = 377 m = 47.12 m/s
8s
8s
ac = (47.12 m/s)2 = 2222.3 m2 /s2
60m
=37 m/s2
60 m
Now lets move on to …..
Centripetal Force!!!
May the Force B W/ U!
Centripetal Force – the net inward force that
maintains the circular motion of an object.
There are 2 formulas to solve for Fc . Choose 1.
Fc = m  a c
Fc = centripetal force, N
m = mass, kg
ac = centripetal acceleration,
mv
Fc =
r
2
m/s2
v = tangential speed, m/s
r = radius, m
r
Fc = m  a c
m v2
Fc =
r
v
FYI:
Centripetal Force is a NET FORCE. There are different
types of NET FORCES involved with Centripetal Force.
 A car going around a curve on a flat road: Fc = Ff
(friction force)
 Orbital motion, such as a satellite: Fc = Fg
(weight or force of gravity)
• A person going around in a spinning circular room(
Barrel of Fun ): Fc = FN
(normal force)
 A mass on a string (horizontal circle, i.e.. parallel to
the ground): Fc = F
(tension force in the string)
T
FYI: Centrifugal Force
 an APPARENT FORCE that SEEMS to pull a rotating
or spinning object AWAY from a CENTER.
 Often referred to as the “ Fictional Force” because it is
NOT REAL!!
Torque – a quantity ( Force )
that causes rotational accel. of
an object.
Formula:
τ = Fr

r = radius
Units: Nm
or Fd
or
d = dist.
Nm
Which has more
tangential speed?
Object 1
Object 2