FORCES AND
CIRCULAR MOTION
I. FORCE
A . Definition: a push or pull acting on a mass
1 . Force is a vector quantity with both magnitude (numeric
value) and direction
2. Force can be broken down into horizontal and vertical
components
3. Symbol: F
4. Units: Newtons ! (N)
B. Concurrent Forces: many forces acting on the same object at
the same time.
1 . Treat all forces individually to find a resultant force (break
into components)
2. This resultant of all concurrent forces is called the Net
Force
Symbol : Fnet
C. Free Body Diagram:
represents concurrent
forces acting on an
object
EXAMPLE 1: NET FORCE
 Two Physics students try pushing a car to see who is stronger.
One student pushes west with a force of 500 Newtons. The
other pushes East with a force of 700 Newtons.
 Draw a free body diagram of the situation.
 What is the Net Force ?
 What way does the car move?
EXAMPLE 2: NET FORCE
 Two Physics students are again arguing and this time are in a
tug of war. They are pulling on a box. One student pulls 30
degrees toward the northeast with a force of 400 Newtons
and the other pulls at 20 degrees toward the Northwest with
500 Newtons.
 Draw a free body diagram of the situation.
 What is the Net Force ?
JOURNAL #11
10/1
 What is net force on a box of mice being pulled with
a force of 20 Newtons due West toward a snake pit
and another force of 30 Newtons pulling due East
toward an alley filled with cats, a 50 Newton force
pulling due North toward a cliff, and a 50 Newton
force pulling due South toward a large pond?
 Draw a Free Body Diagram 1 st !!!
D. Static Equilibrium:
reached when the
resultant of all forces
acting on an object is
ZERO (balanced)
1 . At Equilibrium, objects
remain at rest or constant
velocity.
Fnet ≠= Zero
Zero
2. Net Force is equal to ZERO in static situations
Fnet =0
EXAMPLE: STATIC EQUILIBRIUM
 What forces MUST be added in order to produce static
equilibrium in the free body diagram below?
II. DYNAMICS
Ef fects of forces acting on objects
(Newtons Laws of Motion)
A . Newton’s First Law: An object maintains a state of
equilibrium unless acted on by an unbalanced force. (at rest
or constant velocity)
1 . Any unbalanced force ( F net ≠ 0) will produce a change in
an object’s velocity…either speed, direction, or both.
• the object will ACCELERATE
2. Newton’s First Law is also known as the Law of Inertia
• Inertia: the resistance of an object to a change in its
motion
 More Mass = More Inertia
• Masses resist changes in motion…
EXAMPLES: INERTIA
 What has more inertia? A 10 kg bag of feathers sitting still or
a 5 kg gold bar moving along at 10 m/s?
 What has more inertia? A 20 kg baseball sitting on a stand, or
a 5 kg bowling ball moving along at 30 m/s?
B. Newton’s Second Law: the acceleration of an object is
directly proportional to the net external force acting on an
object and inversely proportional to the object’s mass.
• force is related to mass and acceleration using the
famous expression:
Fnet  ma
• acceleration is produced by force(s )
• increasing force will increase the acceleration
1 . Units for Force…Yay!! Dimensional Analysis!
a. Newtons are the SI unit of force and are a derived unit
(combination of fundamental units)
Fnet  ma  kg 
m
s2
 1N
b. 1 Newton is equal to the force required to accelerate a 1
kilogram mass 1 meter per second squared
2. Increasing mass will increase the force needed to accelerate
that mass
Fnet  ma
larger
m  larger F net
*The equation must balance!
3. If the force is constant, then increasing the mass of an object
will decrease the resulting acceleration
Fnet
a
m
 F net   a
ma
F net = ma :
Direct
Relationship:
Increasing Force
produces more
acceleration
Acceleration (m/s 2 )
4. Graphing
Force (N)
EXAMPLE: NEWTON’S 2 ND LAW
A capybara with a mass of 100kg is tackled by a Jaguar with
a steady force of 100 N along the ground. Assuming no
friction, what is the acceleration of the rodent?
C. Newton’s Third Law: when one object exerts a force on a
second object, the second object exerts a force on the first
that is equal in magnitude, but opposite in direction .
 For every action there is an equal and opposite reaction!
• What happens to a
boat when you step
onto a dock?
Newton’s 3 rd Law!!!
 Newton’s 3rd Law also applies in space when
making objects move
III. NATURAL FORCES
A . Weight: gravitational force exerted on a small mass by a
planet/large body
1 . Weight CHANGES based on what planet/object you are
on… MASS does NOT CHANGE
2. Symbol:
Fg
3. Units:
Newtons !
4. Equation:
(N)
Fg  mg
How much do you weigh?
EXAMPLE: WEIGHT
 The fattest, ugliest Capybara has a mass of 66 kg. What is
the weight of the rodent on Earth?
 Convert the mass to pounds
if 1 kilogram = 2.2 pounds
B. Newton’s Universal Law of Gravitation: Describes the force of
attraction between dif ferent masses.
 Any two bodies attract each other with a force that is directly
proportional to the product of their masses, and inversely
proportional to the square of the distance between them
Gm1m2
Fg 
2
r
Gm1m2
Fg 
2
r
Fg = Gravitational Force
G = Universal Gravitational Constant = 6.67 x 10 -11 N•m 2/kg 2
m1 = mass of object 1
m2 = masses of object 2
r = distance between the two masses
On Your
Reference
Tables!!
(Front Cover)
• Graphical Representation:
EXAMPLE: NEWTON’S UNIVERSAL LAW
OF GRAVITATION
What is the force of gravitational attraction
between the Earth and the Moon?
Gm1m2
Fg 
2
r
m1 = Earth = 5.98 x 10 24 kg
m2 = Moon = 7.35 x 10 22 kg
r = 3.84 x 10 8 m
G = 6.77 x 10 -11 N•m 2 /kg 2
Gm1m2

Fg 
2
r
(6.67  10
11 N m 2
kg 2
)(5.98  1024 kg )(7.35  1022 kg )
(3.84  108 m)2
(2.93  1037 N  m2  kg 2 )

1.47  1017 m2  kg 2
Fg  1.99  10 N
20
2. Gravitational Fields: vectors are used to show
gravitational force
 A “unit test mass” will
accelerate along gravitational
field lines, toward the center
of the source of gravity