Transcript File

Unit 5
Circular Motion
http://www.youtube.com/watch?v=-G7tjiMNVlc
http://www.youtube.com/watch?v=L6-kn2tB-9E
http://www.youtube.com/watch?v=ITA1rW5UraU
http://www.youtube.com/watch?v=z3BSkMj1wLc
What is “circular motion”?
An object that moves in a
circular path about an
external point is in circular
motion.
Rotation v. Revolution
 Rotation – When an object turns about an internal axis.
• Ex. Earth rotates on an axis passing through it’s geographical
poles every 24 hrs.
 Revolution – When an object turns on an external axis.
• Ex. Earth revolves around the sun every 365.25 days.
Period vs. Frequency
 Period ( T ) – time it takes for one full rotation
or revolution
• Measured in seconds
 Frequency ( f ) – number of rotations in one sec
• Measured in Hertz (Hz)
• Which is an inverse sec
1
T
f
1
f 
T
Example 1
Arc Length
 Refers to the length, in meters, that an object
travels along the circumference of a circle.
 The symbol for arc length is s
s
Angle
 Arc length depends on the radius.
 Any point on the radius will have the same
angular displacement.
 Angle in this case is measured in radians and
NOT degrees.
r
s
θ
Angular vs. Linear Velocity
 Angular velocity (w)
• Speed object travels while in
circular motion
• Does NOT depend on radius
• Units
• rotations/sec OR
revolutions/sec
 Tangential (linear) velocity
• Speed object travels when released
from circle
• Travels in a straight path tangent
to the circle
• Depends on length of radius
• Units
• m/s
w
The Value of VT
w
 The tangential speed depends on
the size of the path’s radius.
vT  w r
2r
vT 
T
vT
r
r
w
vT
 As radius decreases, vT increases
Example 2
The Change in vT
 Velocity
• Speed – constant in circular
path
• Direction-changes direction
• So…..velocity changes which
is the definition of
acceleration
 Acceleration
• Centripetal acceleration (ac)
• Direction of ac is towards the
center
vT
ac 
r
2
w
v1
v2
r
r
Example 3
Centripetal Force
 For circular motion, the net
force influencing
acceleration is called a
centripetal force.
 Force that keeps an object
going in a circular path.
 This force is directed toward
the center of rotation or
center of a curvature.
w
v1
Fnet
v2
Fnet
r
Centripetal Force
• If there was no centripetal force, what would be the
direction of the occupants of a merry-go-round?
• They would continue on a straight line due to the
object’s inertia and maintain their instantaneous
tangential velocity.
Ball on a String Example
 Inertia maintains ball’s motion in a linear path
 Tension on the string is an applied net external
force directed toward the center of rotation
 Causes a constant change in velocity, making the
ball follow a circular path
Centripetal Force
 Using Newton’s Second Law
equation (Fnet = ma),
Fc  mac
mvT
Fc 
r
2
Example 4