# What are the different laws of motion?

Contributed by:
Motion, in physics, changes with the time of the position or orientation of a body. Motion along a line or a curve is called translation.
1. Physics 111: Mechanics
Lecture 4
Dale Gary
NJIT Physics Department
2. The Laws of Motion
 Newton’s first law
 Force
 Mass
 Newton’s second law
 Newton’s third law
 Examples
Isaac Newton’s work represents
one of the greatest
contributions to science ever
Feb. 11-15, 2013
3. Dynamics
 Describes the relationship between the
motion of objects in our everyday world
and the forces acting on them
 Language of Dynamics
 Force: The measure of interaction between two
objects (pull or push). It is a vector quantity – it has a
magnitude and direction
 Mass: The measure of how difficult it is to change
object’s velocity (sluggishness or inertia of the object)
Feb. 11-15, 2013
4. Forces
 The measure of interaction
between two objects (pull or
push)
 Vector quantity: has
magnitude and direction
 May be a contact force or
a field force
 Contact forces result from
physical contact between two
objects
 Field forces act between
disconnected objects
 Also called “action at a
distance”
Feb. 11-15, 2013
5. Forces
 Gravitational Force
 Archimedes Force
 Friction Force
 Tension Force
 Spring Force
 Normal Force
Feb. 11-15, 2013
6. Vector Nature of Force
 Vector force: has magnitude and direction
 Net Force: a resultant force acting on
    
object Fnet  F F1  F2  F3  ......
 You must use the rules of vector addition to
obtain the net force on an object

| F | F12  F22 2.24 N
F1
 tan  1 ( )  26.6
F2
Feb. 11-15, 2013
7. Newton’s First Law
 An object at rest tends to stay at rest and an
object in motion tends to stay in motion with
the same speed and in the same direction
unless acted upon by an unbalanced force
 An object at rest remains at rest as long as no net force acts on it
 An object moving with constant velocity continues to move with
the same speed and in the same direction (the same velocity) as
long as no net force acts on it
 “Keep on doing what it is doing”
Feb. 11-15, 2013
8. Newton’s First Law
 An object at rest tends to stay at rest and an
object in motion tends to stay in motion with
the same speed and in the same direction
unless acted upon by an unbalanced force
 When forces are balanced, the acceleration of the object is
zero
 Object at rest: v = 0 and a = 0
 Object in motion: v  0 and a = 0
 The net force is defined as the vector sum of all the
external forces exerted on the object. If the net force is
zero, forces are balanced. When forces are balances, the
object can be stationary, or move with constant velocity.
Feb. 11-15, 2013
9. Mass and Inertia
 Every object continues in its state of rest, or uniform
motion in a straight line, unless it is compelled to change
that state by unbalanced forces impressed upon it
 Inertia is a property of objects
to resist changes is motion!
 Mass is a measure of the
amount of inertia.
 Mass is a measure of the resistance of an object
to changes in its velocity
 Mass is an inherent property of an object
 Scalar quantity and SI unit: kg
Feb. 11-15, 2013
10. Newton’s Second
Law
 The acceleration of an object is directly
proportional to the net force acting on
it and inversely proportional to its mass
 

a
F

Fnet
m m
  
Fnet  F ma
Feb. 11-15, 2013
11. Units of Force
 Newton’s second law:
  
Fnet  F ma
 SI unit of force is a Newton (N)
kg m
1 N 1
s2
 US Customary unit of force is a pound (lb)
 1 N = 0.225 lb
 Weight, also measured in lbs. is a force (mass
x acceleration). What is the acceleration in
that case?
Feb. 11-15, 2013
Law
 You must be certain about which body we are
applying it to
 Fnet must be the vector sum of all the forces
that act on that body
 Only forces that act on that body are to be
included in the vector sum
 Net force component along an
axis gives rise to the acceleration
along that same axis
Fnet , x ma x Fnet , y ma y
Feb. 11-15, 2013
13. Sample Problem
 One or two forces act on a puck that moves over frictionless
ice along an x axis, in one-dimensional motion. The puck's
mass is m = 0.20 kg. Forces F1 and F2 and are directed
along the x axis and have magnitudes F1 = 4.0 N and F2 = 2.0
N. Force F3 is directed at angle  = 30° and has magnitude F3
= 1.0 N. In each situation, what is the acceleration
a) F1 ma xof the
puck? a  1
F 4.0 N
20 m/s 2
x
m 0.2 kg
b) F1  F2 ma x
F1  F2 4.0 N  2.0 N
ax   10 m/s 2
m 0.2 kg
c) F3, x  F2 max F3, x F3 cos 
Fnet , x ma x F3 cos   F2 1.0 N cos 30  2.0 N
ax    5.7 m/s 2
m 0.2 kg
Feb. 11-15, 2013
14. Gravitational Force
 Gravitational force is a vector
 Expressed by Newton’s Law of Universal
Gravitation: mM
Fg G
R2
 G – gravitational constant
 M – mass of the Earth
 m – mass of an object
 R – radius of the Earth
 Direction: pointing downward
Feb. 11-15, 2013
15. Weight
 The magnitude of the gravitational force acting on
an object of mass m near the Earth’s surface is
called the weight w of the object: w = mg
 g can also be found from the Law of Universal
Gravitation
 Weight has a unit of N
mM
Fg G 2 w Fg mg
R
M
g G 2 9.8 m/s 2
R
 Weight depends upon location R = 6,400 km
Feb. 11-15, 2013
16. Normal Force
 Force from a solid
surface which
keeps object from w Fg mg
falling through
 Direction: always
perpendicular to
the surface N  Fg ma y
 Magnitude:
N  mg ma y
depends on
situation N mg
Feb. 11-15, 2013
17. Tension Force: T
 A taut rope exerts
forces on whatever
holds its ends
 Direction: always
along the cord (rope,
cable, string ……) T1
and away from the T1 = T = T2
object T2
 Magnitude: depend
on situation
Feb. 11-15, 2013
18. Newton’s Third Law
 If object 1 and object 2 interact, the force
exerted by object 1 on object 2 is equal
in magnitude but opposite in direction to
the force exerted by object 2 on object 1
 
Fon A  Fon B
 Equivalent to saying a single isolated force
cannot exist Feb. 11-15, 2013
19. Newton’s Third Law cont.
 F12 may be called the
action force and F21
the reaction force
 Actually, either force
can be the action or
the reaction force
 The action and
reaction forces act
on different objects
Feb. 11-15, 2013
20. Some Action-Reaction Pairs
mM
Fg G
R2
GM
Fg mg m 2
mM R
Fg G 2 Gm
R Fg Ma M 2
R
Feb. 11-15, 2013
21. Free Body Diagram
 The most important step in
solving problems involving F hand on book
Newton’s Laws is to draw
the free body diagram
 Be sure to include only the
forces acting on the object
of interest
 Include any field forces F Earth on book
acting on the object
 Do not assume the normal
force equals the weight
Feb. 11-15, 2013
22. Hints for Problem-Solving
 Read the problem carefully at least once
 Draw a picture of the system, identify the object of primary
interest, and indicate forces with arrows
 Label each force in the picture in a way that will bring to mind
what physical quantity the label stands for (e.g., T for tension)
 Draw a free-body diagram of the object of interest, based on
the labeled picture. If additional objects are involved, draw
separate free-body diagram for them
 Choose a convenient coordinate system for each object
 Apply Newton’s second law. The x- and y-components of
Newton second law should be taken from the vector equation
and written individually. This often results in two equations
and two unknowns
 Solve for the desired unknown quantity, and substitute the
numbers F ma F ma
net , x x net , y y
Feb. 11-15, 2013
23. Objects in Equilibrium
 Objects that are either at rest or moving
with constant velocity are said to be in
equilibrium

a 0 of an object can be modeled
 Acceleration
as zero:

 Mathematically, the
 F net
0 force acting on
the object is zero
 Equivalent to the set of component
 Fx by
equations given 0  Fy 0
Feb. 11-15, 2013
24. Equilibrium, Example 1
 A lamp is suspended from
a chain of negligible mass
 The forces acting on the
lamp are
 the downward force of
gravity
 the upward tension in the
chain
 Applying equilibrium gives
 Fy 0  T  Fg 0  T Fg
Feb. 11-15, 2013
25. Equilibrium, Example 2
 A traffic light weighing 100 N hangs from a vertical cable
tied to two other cables that are fastened to a support.
The upper cables make angles of 37° and 53° with the
horizontal. Find the tension in each of the three cables.
 Conceptualize the traffic light
 Assume cables don’t break
 Nothing is moving
 Categorize as an equilibrium
problem
 No movement, so acceleration is
zero
 F 0  Fy 0
 Model xas an object in equilibrium
Feb. 11-15, 2013
26. Equilibrium, Example 2
 Need 2 free-body diagrams
 Apply equilibrium equation to
light  Fy 0  T3  Fg 0 F y 0  T3  Fg 0
T3 Fg 100 N
T3 Fg 100 N
 Apply equilibrium equations  to
F
knot
x T1x  T2x  T1 cos 37 
 T2 cos 53 0
F y T1 y  T2 y  T3 y
T1 sin 37  T2 sin 53  100 N 0
 cos 37 
T2 T1   1.33T1
 
 cos 53 
T1 60 N T2 1.33T1 80 N
Feb. 11-15, 2013
27. Accelerating Objects
 If an object that can be modeled as a
particle experiences an acceleration, there
must be a nonzero net force acting on it
 Draw a free-body diagram
 Apply Newton’s Second Law in component
form  
 F ma
F x ma x F y ma y
Feb. 11-15, 2013
28. Accelerating Objects,
Example 1
 A man weighs himself with a scale in an elevator.
While the elevator is at rest, he measures a
weight of 800 N.
 What weight does the scale read if the elevator
accelerates upward at 2.0 m/s2? a = 2.0 m/s2
 What weight does the scale read if the elevator
 accelerates
Upward:  Fy downward at 2.0 m/s2? a = - 2.0 m/s2
N  mg ma N
N mg  ma m( g  a ) N 80(2.0  9.8) 624 N
N
w 800 N
m 
g 9.8 m/s 2
80 N N  mg
 Downward: N 80(  2.0  9.8) 624 N
N  mg mg mg
Feb. 11-15, 2013