Newton's

1. Sir Evance
NEWTONIAN MECHANICS
 Dynamics is a branch of mechanics that deals with the motion of bodies under the action of forces. Motion
is caused by a force.
 Definitions
o Length
 Interval between two points along an object.
 SI unit is the meter (m).
o Distance
 The length between an initial and a final point and which includes the lengths for the routes
taken to reach the final point.
 Route(s) could be consisting of curves and straight intervals.
 Ground covered between the two points.
 A scalar quantity.
 SI unit is the meter (m).
o Displacement
 The length between an initial and a final point and which does not include the lengths for the
routes taken to reach the final point.
 An object’s change in position considering its initial and final points.
 A vector quantity.
 SI unit is the meter (m).
o Speed
 Change in distance per unit time.
 A scalar quantity.
 SI unit is the meter per second (m/s).
o Velocity
 Change in displacement per unit time.

2. Sir Evance
 A vector quantity.
 SI unit is the meter per second (m/s).
o Acceleration
 Change in velocity per unit time.
 A vector quantity.
 SI unit is the meter per second squared (m/s2
)
 If 𝑣 denotes velocity and 𝑡 denotes time, then the acceleration
⃗
𝑣
𝑡
If 𝑣 is the initial velocity at time 𝑣 and 𝑣 is the final velocity at time 𝑡 , then the acceleration
⃗
𝑣 𝑣
𝑡 𝑡
Note: If within a given time interval ∆𝑡 it’s found that 𝑣 𝑣 , then acceleration is zero. It’s said
that an object is moving at constant (or uniform velocity) or it is not accelerating
Equations of motion
 For a body of mass m moving with velocity v from initial velocity u after a distance/displacement s, the
following equations holds,
𝑣 𝑡
𝑣
𝑡 𝑡
 Motion under the influence of gravity have little modifications to the motion equation, i.e. a body falling
freely will have the value of a replaced by positive value of g. the initial velocity is always zero for this
case. The reverse will have the value g as negative and final velocity as zero.
 Objects with horizontal as well as vertical motion, we resolve any initial velocity into its horizontal and
vertical components which are then treated separately. The vertical component determines the time of flight
(and any vertical distances) and the horizontal component determines the range.
Examples
1. An object is dropped from a height of 45m. Assuming g=10 m/s2
, calculate
a. The time taken to reach the ground [3.0s]
b. Its maximum velocity [30m/s]

3. Sir Evance
2. A man stands at the edge of a cliff and throws a stone vertically upwards at 15m/s. after what time will the
stone hit the ground 20m below?
3. A stone is projected horizontally with a velocity 3.0m/s from the top of a vertical cliff 200m high,
neglecting air resistance, calculate
a. Time it takes to reach the ground [6.3s]
b. The distance from the foot of the cliff to where the stone hits [19m]
c. The vertical and horizontal components of velocity when it hits the ground.[vert=63m/s,
horizontal=3.0m/s]
NEWTONS LAWS
 Inertia: Inertia is an important property of matter. It can be treated as property of matter that resists
changes in its motion.
 Basically, because of inertia, objects want to maintain whatever motion they have. This was described
initially by Galileo; later Sir Isaac Newton formulated it into one of his basic laws of motion.
 Inertia is proportional to mass. The more mass something has the more inertia it has.
Mass  measurement of inertia
The unit for mass is the kilogram (kg). Mass is also defined as the amount of matter something has. Mass is
different from weight, which is the gravitational force of attraction between the earth and an object.
 Some important definitions under this study include;
o Force  push or pull
o Contact Force  physical contact exists between the object and source of the force
o Field Forces  No contact exists between the source of the force and the body being acted upon:
gravity, magnetic force, &etc.
o Friction  A force that resists the motion between two objects in contact with one another
The First Law:
Newton’s First Law: An object at rest remains at rest, and an object in motion remains in motion with constant
velocity unless it is acted upon by an outside force.
 This law really deals with inertia. It is because of its inertia that matter behaves according to this law. The
idea that something would keep moving at a constant velocity for like forever is something that we don’t see
happen very often on the earth, because when something is moving, there is almost always an outside force

4. Sir Evance
acting on it – usually friction. This is why a ball rolling along a straight section of road will come to a stop
all on its own. Friction slows it down and makes it stop.
 When the net external force acting on an object is zero, the acceleration on the object is zero and it moves
with a constant velocity. Of course if it is at rest, it will remain at rest. (Unless and outside force changes
its course….)
The Second Law:
 States, The acceleration of an object is directly proportional to the net force acting on it and inversely
proportional to its mass. This is usually written as a simple formula, ⃗ ⃗ or ∑ ⃗. This means that
the acceleration of an object is a function of the sum of all forces acting on it. The sum of these forces is
known as the net force.
 Newton’s second law is responsible for weight. Weight is a force, the force of gravity acting on something.
Using the second law, we see that the weight of an object is ⃗ where ⃗ is acceleration due to gravity
Weight  force exerted by gravity on an object with mass
 The weight of an object depends on the acceleration of gravity. If the acceleration brought about by gravity
changes, then the weight can change. This does not happen with mass - the mass of an object is a constant
and has the same value everywhere. If you were to travel to the moon, your weight would be only 1/6 of its
value on earth, but your mass would be the same. This is because the gravity on the moon is much smaller
than the earth’s gravity.
Examples
1. A 450 kg mass is accelerated at 2.5 m/s2
. What is the net force causing this acceleration?
2. A 2500 kg car is pushed with a net force of 250 N, what is the acceleration acting on the car?
3. An artillery shell has a mass of 55 kg. The projectile is fired from the piece and has a velocity of 770 m/s
when it leaves the barrel. The gun barrel is 1.5 m long. Assuming the force and therefore the acceleration is
constant while the projectile is in the barrel, what is the force that acted on the projectile?
The Third Law:
 Third Law states, If two objects interact, the force exerted on object 1 by object 2 is equal in magnitude but
opposite in direction to the force exerted on object 2 by object 1.
 The classic way of saying this is, “For every action there is an equal and opposite reaction”.
 Newton’s third law simply says that forces come in pairs. You push on a wall and the wall pushes on you.
We call these action/reaction force pairs.

5. Sir Evance
Reference Frames
 We have learned about velocity, acceleration, and displacement. But all these quantities need a frame of
reference from which they are measured.
 Imagine you threw and caught a ball while you were on a train moving at a constant velocity past a station.
 To you, the ball appears to simply travel vertically up and then down under the influence of gravity.
 However, to an observer stood on the station platform the ball would appear to travel in a parabola, with a
constant horizontal component of velocity equal to the velocity of the train
 The different observations occur because the two observers are in different frames of reference.
 A frame of reference is a set of coordinates that can be used to determine positions and velocities of objects
in that frame; different frames of reference move relative to one another.
 Think of another situation illustrated below,
 If we ask A what velocity of B is, he will say it is at rest. But if we ask the same question to C, he will say B
is moving with a velocity V in the positive X direction.
 So we can see before specifying the velocity we have to specify in which frame we are or in simple terms,
we need to define a frame of reference.
Example
Two cars on a road are travelling in the same direction, with velocities of 20 m/s and 23 m/s, in the road's frame
of reference. What is the speed of the slower car in the rest frame of the faster one?

6. Sir Evance
Types of frame of reference
Once we have chosen our reference they can be of two types:
 Inertial Frame of Reference
 Non-inertial Frame of Reference
Inertial Frame of Reference
 An inertial frame of reference is a frame where Newton’s law of inertia holds true.
 That means if no external force is acting on a body it will stay at rest or remain in uniform motion (moves at
constant velocity).
 Suppose a body is kept on the surface of the earth, for a person on earth it is at rest while for a person on the
moon it is in motion so which is my inertial frame here?
 Actually, the term inertial frame is relative i.e. first we assume a reference frame to be the inertial frame of
reference.
 So a more general definition of an inertial frame would be: Inertial frame is at rest or moves with constant
velocity with respect to my assumed inertial reference frame.
Non-inertial Frame of Reference
 Now we can define a non-inertial frame as a frame that is accelerated with respect to the assumed inertial
frame of reference.
 Newton’s law will not hold true in these frames.
 So in the above example if I assume earth to be an inertial reference frame the moon becomes a non-inertial
reference frame as it is in accelerated motion with respect to earth.
 But if we want to make Newton’s law hold here we need to take some mysterious forces also known as
pseudo forces.
 Examples of non-inertial frames include;
o A turning car with constant speed
o A rotating frame
***Read about Galilean transformations***