This document discusses Newton's laws of motion. It begins by defining dynamics as the relationship between motion and the forces that cause it. It then explains that Newton's laws of motion are the fundamental principles of classical mechanics. The document goes on to define key concepts such as force, mass, and inertia. It proceeds to explain each of Newton's three laws of motion - the law of inertia, the second law relating force and acceleration, and the third law of action and reaction. Several examples are provided to illustrate the laws. The document concludes by presenting five assignment problems applying Newton's laws.

1. Newton’s Laws
of Motion
Peter Huruma Mammba
Department of General Studies
DODOMA POLYTECHNIC OF ENERGY AND EARTH RESOURCES MANAGEMENT (MADINI
INSTITUTE) –DODOMA
peter.huruma2011@gmail.com

2. Laws of motion
•The Newton’s laws of motion are the
principles of dynamics.
•Dynamics means; the relationship of
motion to the forces that cause it.

3. Laws of motion…
•The dynamic principles are the
foundation of classical mechanics
which also called Newtonian
Mechanics.

4. Laws of motion…
•Since these dynamic principles are phrased
in terms of force and mass , it will be
helpful to have some understanding of these
two concepts before dealing with Newton’s
laws of motion.

5. The Concept of Force
•Force is a push or pull acting on a body.
•When force involves direct contact
between two bodies , we call it a Contact
force.

6. Force…
•The force of gravitation attraction that
the Earth exert on your body is called
weight.
•The net force is the vector sum of all the
forces acting on the object.

7. Force…
•Force has magnitude as well as
direction ,it is a vector quantity.
•The SI unit of magnitude of force is
Newton (N).

8. Force…
•The fundamental forces in nature are
all field forces:
1. Gravitational force between objects
2. Electromagnetic forces between the
charges

9. Force…
3. Strong forces between subatomic
particles
4. Weak forces that arises in a certain
radioactive decay processes

10. Force…
•In classical Mechanics, we are
concerned only with Gravitational
force and Electromagnetic force.

11. Mass
•Mass defines as the quantity of matter
contained in the body.
•More precisely, mass is a measure of the
inertia of the body.
•i.e. the more mass a body has, the harder it is
to change its state of motion.

12. Mass should not be confused with weight
•Mass and weight are two different quantities.
The weight of an object is equal to the
magnitude of the gravitational force exerted on
the object and varies with location.
•For example, a person weighing 180 lb on the
Earth weighs only about 30 lb on the Moon.

13. M & W are different quantities…
On the other hand, the mass of an object
is the same everywhere: an object having
a mass of 2 kg on the Earth also has a
mass of 2 kg on the Moon.

14. Inertia
•Is the tendency of a body to maintain its
state of rest or of uniform motion in a
straight line.
•Object do not change their state of motion
unless acted upon by some net external
force.

15. Inertia…
•The inertia of the body depends upon its
mass.
•The greater the mass of the body, the greater
is its inertia
•Both mass and inertia are measured in the
same units.

16. Types of inertia
•Inertia of the body is of three type
I. Inertia of rest
II. Inertia of motion
III.Inertia of direction

17. Inertia of rest
•This is the resistance of the body to change its
state.
•For example when a train suddenly starts, the
passenger sitting inside tends to fall backward. It
is because the lower part of his body starts
moving with the train while the upper part tends
to be at rest due to inertial at rest.

18. Inertia of motion
•This is the resistance of the body to change its state
of motion.
•For example. When a bus suddenly stops, a
passengers siting in it tends to fall forward. It is
because the lower part of the body comes to rest
while the upper part of the body tends to remain in
motion due to inertia of motion

19. Inertia of direction
•This is the resistance of the body to change
its direction of motion.
•In other words a body will continue to move
in the same straight line unless some
external force tends to change its direction.

20. 1st Law of Motion
(Law of Inertia)
State that
Every body will continues in it
state of rest or uniform motion
in a straight line unless it is
compelled by some external
force to change the state

21. Law of Inertia…
•The following conclusion can be drawn
from this law:-
(i) If a body is at rest or moving with
constant velocity, the net force acting on
the body is zero.

22. Law of Inertia…
(ii) when you move an object on the ground
with constant velocity, the force you exert is
not zero. But the net force is zero because the
fractional force on the object is equal and
opposite to the force you exert on the object.

23. Law of Inertia…
(iii) If a body is moving with a constant
speed in a straight line, then in order to
change its direction , force has to be
applied on the body.

24. Law of Inertia…
(iv) If a body is moving with a constant
speed in a circle, then force is required to
keep it going in circular path. This is due
to change in direction continuously.

25. Newton's 1st Law and You
Don’t let this be you. Wear seat belts.
Because of inertia, objects (including you) resist changes in their motion.
When the car going 80 km/hour is stopped by the brick wall, your body
keeps moving at 80 m/hour.

27. 2nd law of Motion
•State that
the rate of change of momentum of a body
with time is directly proportional to the net
external force applied on it and the change
takes place in the direction of force.

28. 2nd law of Motion
•If 𝑝 is the momentum of the body and 𝑓 is the
net external force acting on the body, then
according to newton’s 2nd law of motion;
𝑓 ∝
𝑑 𝑝
𝑑𝑡
Or 𝑓 = 𝑘
𝑑 𝑝
𝑑𝑡
where k = 1

29. 2nd law of Motion
𝑓 =
𝑑 𝑝
𝑑𝑡
• 𝑓 =
𝑑
𝑑𝑡
𝑚 𝑣 but mass of an object does not change.
𝑓 = m
𝑑𝑣
𝑑𝑡
but
𝑑𝑣
𝑑𝑡
= 𝑎
∴ 𝑓 = 𝑚 𝑎
Magnitude of force, 𝒇 = 𝒎𝒂

30. 2nd law of Motion
•If 𝑎 is the resultant acceleration produced in
3D and 𝑎 𝑥, 𝑎 𝑦 and 𝑎 𝑧 are the magnitude of the
components of acceleration along x- axis, y-
axis and z- axis respectively then;
𝒇 = 𝒎 𝒊𝒂 𝒙 + 𝒋𝒂 𝒚+ 𝒌𝒂 𝒛

31. 2nd law of Motion
•If 𝑓𝑥, 𝑓𝑦 and 𝑓𝑧 are the components of
force along x- axis, y- axis and z-axis
respectively, then,
𝒇 = 𝒊𝒇 𝒙 + 𝒋𝒇 𝒚 + 𝒌𝒇 𝒛

32. 2nd law of Motion
•When mass is in kilogram (Kg) and
acceleration is in 𝑚𝑠2
, the unit of force is in
Newton (N).
•One newton is equal to the force required to
accelerate one kilogram of mass at one meter in
a second.

33. 3rdLaw
of
Motion

34. 3rd Law of Motion
•State that
For every action, there is an equal and
opposite reaction.

35. 3rd Law According to Newton,
whenever objects A and B
interact with each other, they
exert forces upon each other.
When you sit in your chair, your
body exerts a downward force
on the chair and the chair exerts
an upward force on your body.

36. 3rd Law
There are two forces
resulting from this
interaction - a force on the
chair and a force on your
body.
These two forces are called
action and reaction forces.

37. Action - Reaction
• When the rocket fuel is ignited, a hot gas is
produced.
• As the gas molecules
collide with the inside
engine walls, the walls
exert a force that pushes
them out of the bottom of
the engine.

38. Action – Reaction…
• This downward push is the action force.
• The reaction force is the upward push on the
rocket engine by the gas molecules.
• This is the thrust that propels the
rocket upward.

39. Other examples of Newton’s Third Law
•The baseball forces the
bat to the left (an action);
the bat forces the ball to
the right (the reaction).

40. 3rd Law
•Consider the motion of a car
on the way to school. A car is
equipped with wheels which
spin backwards. As the
wheels spin backwards, they
grip the road and push the
road backwards.

41. Example 1
• What force is required to
accelerate 2000 Kg car from 5
m/s to 25 m/s in a time of 5
seconds?

42. Assignment 1
•The mass of an elevator (lift) is 500 Kg.
calculate the tension in the cable of the
elevator when the elevator is (i) stationary (ii)
ascending with an acceleration of 2 m/s (iii)
descending with the same acceleration. Take
g = 9.8 m/s/s.

43. Assignment 2
•A particle of mass 0.4 Kg moving with a constant speed
of 10 m/s to the north is subjected to a constant force of
8 N directed towards the south for 30 s. Take the instant
the force is applied to be t = 0, the position of the
particle at that time to be x = 0 and predict position of
the particle at t = -5 s, 25 s, 100 s.

44. Assignment 3
•Two blocks, A of mass m and B of mass 3 m,
are side by side in contact with each other.
They are pulsed along a smooth floor under
the action of a contact force f applied to A.
Find (i) accelerations of the blocks (ii) The
force exerted on B by A.

45. Assignment 4
A 68 Kg man is standing on the floor of a lift.
Calculate the apparent weight of the man when the
lift is (i) at rest (ii) moving upward with constant
speed (iii) moving upward with an acceleration of
1m/s/s (iv) moving downward with an acceleration
of 1 m/s/s.

46. Assignment 5
•A monkey of mass 40 Kg climbs on a rope which can
stand a maximum tension of 600 N. In which of the
following cases the rope will break:
(i) If monkey climbs up with an acceleration of 6 m/s/s
(ii) If monkey climbs down with an acceleration of 4
m/s/s.

47. Assignment 5 …
(iii) If monkey clims up with a uniform speed of 5
m/s
(iv) If monkey falls down the rope nearly freely under
gravity.
Ignore the mass of the rope and take g = 9.8 m/s/s.