Transcript Uniform Circular Motion - Mr. Romero

BELL RINGER!
Based on your knowledge and everything we have seen
in this class, How would you relate Thanksgiving to
Physics?
UNIFORM CIRCULAR MOTION

https://www.youtube.com/watch?v=31MMw3E
azqw&list=PLajRX1HxHcZNgivoEWVPDMWb5h
GLCNrB6
UNIFORM CIRCULAR MOTION
Uniform circular motion is motion along a
circular path in which there is no change in
speed, only a change in direction.
v
Fc
Constant velocity V
tangent to path.
Constant force Fc
toward center.
Question: Is there an outward force on the ball?
UNIFORM CIRCULAR MOTION (CONT.)
The question of an outward force can be resolved by
asking what happens when the string breaks!
v
Ball moves tangent to path,
NOT outward as might be
expected.
When central force is removed, ball
continues in straight line.
Centripetal force is needed to change direction.
CIRCULATION MOTION
The direction of the velocity vector at any instant is in the direction of a
tangent line drawn to the circle at the object's location. (A tangent line is a
line that touches a circle at one point but does not intersect it.)
CENTRIPETAL FORCE
What is Centripetal Force?
A force that acts on a body moving in a circular
path and is directed toward the center around
which the body is moving.

CENTRIPETAL FORCE


Where is Centripetal Force pointed towards?
Gravitational Force
What is this Force called?
EXAMPLES OF CENTRIPETAL FORCE
You are sitting on the seat next to
the outside door. What is the
direction of the resultant force on
you as you turn? Is it away from
center or toward center of the turn?

Car going around a
curve.
Fc
Force ON you is toward the center.
BELL RINGER!
DO NOT COPY THE QUESTIONS!
Draw the circle from the right with the respective vector from the bottom
based on each question.
1. Which vector below represents the direction of the
force vector when the object is located at point A on
the circle?
2. Which vector below represents the direction of the
force vector when the object is located at point C on
the circle?
3. Which vector below represents the direction of the
velocity vector when the object is located at point B on
the circle?
4. Which vector below represents the direction of the velocity vector when
the object is located at point C on the circle?
NASCAR VIDEO
http://science360.gov/obj/tkn-video/5f385cf55046-4279-984e-27f911c6ca07
NASCAR VIDEO QUESTIONS
 1.
Explain the different forces a race car
experiences while it is going in speeds in
excess of 200 mph. around a turn.
Include a picture with these different
forces.
BELL RINGER!

In your own words, explain centripetal motion
and provide an example.
CENTRIPETAL FORCE


Where is the Centripetal Force pointed towards?
What is this force called?
PAP
DERIVING ACCELERATION
vf
Dv
ac =
Definition:
ac =
Dv
t
v2
=
t
R
Centripetal
acceleration:
2
v
ac  ;
R
mv
Fc  mac 
R
2
EXAMPLE 1:
A 3-kg rock swings in a circle of radius 5 m. If its constant
speed is 8 m/s, what is the centripetal acceleration?
v
v = 8 m/s
R=5m
m
ac = 12.8 m/s2
R
What is the Force (F)?
m = 3 kg
ac = 12.8 m/s2
F = (3 kg)(12.8 m/s2)
Fc = 38.4 N
EXAMPLE 2:
mv
Fc  mac 
R
Solve for mass(m)
v = 15 m/s

Fc R
450 N
30 m
m=?
Speed skater
2



F = mv2/R
FR = mv2
FR/v2 = m,
Substitute
m=(450N)(30m)/(15m/s)2
m=60 kg
MOTION IN A VERTICAL CIRCLE
v
Resultant force toward
center
mg
T
Fc =
R
Consider TOP of circle:
v
mg + T =
AT TOP:
R
+
mg
T=
T
mv2
mv2
R
- mg
mv2
R
VERTICAL CIRCLE; MASS AT BOTTOM
v
Resultant force
toward center
Fc =
mv2
R
T
v
mg
Consider bottom of circle:
T - mg =
R
AT Bottom:
T
+
mg
mv2
T=
mv2
R
+ mg
R
FOR MOTION IN CIRCLE
v
AT TOP:
+
R
mg
T=
mv2
- mg
R
T
v
AT BOTTOM:
T
+
mg
T=
mv2
R
+ mg
EXAMPLE :
A 2-kg rock swings in a vertical circle of radius 8 m. The speed of the rock
as it passes its highest point is 10 m/s. What is tension T in rope?
mg + T =
At Top:
mv2
R
v
mg
T
T=
R
mv2
- mg
R
v
(2 kg)(10 m/s) 2
2
T
 2 kg(9.8 m/s )
8m
T = 25 N - 19.6 N
T = 5.40 N
EXAMPLE (CONT):
A 2-kg rock swings in a vertical circle of radius 8 m. The speed of the rock
as it passes its lowest point is 10 m/s. What is tension T in rope?
T - mg =
At Bottom:
v
mv2
R
R
T=
mv2
+ mg
R
T
v
mg
(2 kg)(10 m/s) 2
T
 2 kg(9.8 m/s 2 )
8m
T = 25 N + 19.6 N
T = 44.6 N