Section 5-2
Circular Motion; Gravitation
Reminder: AP test and solutions manual
giancoli physics principles with applications 6th edition solution manual
3rd site in google gives a pdf Physics – Comcast.net
Objectives: The student will be able
to:
• identify the type of force supplying the centripetal
force that acts on any object in uniform circular
motion.
• determine the directions of the velocity,
acceleration, and net force vectors for an object in
uniform circular motion.
• identify centrifugal force as a fictitious force and
explain how it results from an accelerated frame of
reference.
• use Newton's laws of motion and the concept of
centripetal acceleration to solve word problems.
Uniform Circular Motion: Observations

Object moving along a curved
path with constant speed
 Magnitude of velocity: same
 Direction of velocity:
changing

 Velocity v : changing
 Acceleration is NOT zero!
 Net force acting on an
object is NOT zero

“Centripetal force”
March 14, 2016


Fnet  ma
5-2 Dynamics of Uniform Circular Motion
For an object to be in uniform circular motion,
there must be a net force acting on it.
We already know the
acceleration, so can
immediately write the
force:
(5-1)
Uniform Circular Motion
Newton’s 2nd Law: The net force on a body is
equal to the product of the mass of the body and
the acceleration of the body.
*The centripetal acceleration is
caused by a centripetal force
that is directed towards the
center of the circle.
F  ma  m
2
v
r
5-2 Dynamics of Uniform Circular Motion
We can see that the force must be inward by
thinking about a ball on a string:
Demo – penny
and hanger
5-2 Dynamics of Uniform Circular Motion
There is no centrifugal force pointing outward;
what happens is that the natural tendency of the
object to move in a straight line must be
overcome.
If the centripetal force vanishes, the object flies
off tangent to the circle.
“Centrifugal Force”
• “centrifugal force” is a fictitious force it is not an interaction between 2
objects, and therefore not a real force.
• Nothing pulls an object away from
the center of the circle.
“Centrifugal Force”
• What is erroneously attributed to
“centrifugal force” is actually the action
of the object’s inertia - whatever
velocity it has (speed + direction) it
wants to keep.
Centripetal Force
• Acceleration:
v2
ac 
– Magnitude:
r
– Direction: toward the center of
the circle of motion
• Force:
– Start from Newton’s 2nd Law


Fnet  ma
– Magnitude:
mv 2
Fnet  mac 
r
– Direction: toward the center of
the circle of motion
March 14, 2016

 

ac  v Fnet  v
ac 
v2
r
Fnet
Fnet
Fnet
 
ac || Fnet
What provides Centripetal Force ?
• Centripetal force is not a new kind of force
• Centripetal force refers to any force that keeps
an object following a circular path
mv 2
Fc  mac 
• Centripetal force is a combination of
– Gravitational force mg: downward to the ground
– Normal force N: perpendicular to the surface
– Tension force T: along the cord and away from
object
– Static friction force: fsmax = µsN
March 14, 2016
r
What provides Centripetal Force ?
Fnet  N  mg  ma
v2
N  mg  m
r
Fnet  T  ma
mv
T
r
March 14, 2016
2
N
a
v
mg
Example Problem
A 2.0-kg mass is attached to the end of a 3.0 m-long rope and spun in a vertical circle
at a speed of 6.6 m/s. Determine the maximum and minimum tensions in the rope.
Problem Solving Strategy
• Draw a free body diagram, showing and labeling all
the forces acting on the object(s)
• Choose a coordinate system that has one axis
perpendicular to the circular path and the other axis
tangent to the circular path
• Find the net force toward the center of the circular
path (this is the force that causes the centripetal
acceleration, FC)
• Use Newton’s second law
– The directions will be radial, normal, and tangential
– The acceleration in the radial direction will be the centripetal
acceleration
• Solve for the unknown(s)
March 14, 2016
Circular Motion Lab
•
•
•
•
•
•
•
Looking at factors affecting velocity. (graph for each part)
Part 1: Changing hanging mass and radius constant (100g, 200g, 250g, 300g,
350g, 400g) -Select at least 3 different masses with 3 trials.
Looking at centripetal force formula which indicates that centripetal force and
velocity squared are directly related. Prepare a graph to support this.
Data Table: Hanging weight; radius, mass of twirling object, number of
revolutions, elapsed time, period, velocity of twirling mass, centripetal acceleration.
2nd Data Table: Hanging weight, Centripetal force of the twirling mass, % error
Part 2: Changing radius and keeping hanging mass constant (40 cm, 60 cm, 80
cm) – At least 3 trials.
2nd graph – see 1st bullet (think of the independent and dependent variables)
–
–
–
–
–
Use a paper clip as a marker (always keep 1 cm below tube)
Swinging must be horizontal.
Must use SI units!
Goggles must be worn.
What causes the centripetal force?
Homework for Section 5-2
• Be prepared for lab.
• Problems 7, 8,13, 16, 18
Kahoot
• Section 5-2 Giancoli Dynamics of Uniform
Acceleration