This document discusses various topics related to motion including: 1) Motion can be classified as one-dimensional, two-dimensional, or three-dimensional depending on the number of axes the object moves along. 2) Key concepts in three-dimensional motion include location vectors, displacement, velocity, acceleration, and equations of motion. 3) Forces obey Newton's Laws - the acceleration of an object is directly proportional to net force and inversely proportional to mass, and every action has an equal and opposite reaction. 4) Circular motion involves centripetal force which acts towards the center of the circle, and centripetal acceleration which is required to move in a circular path.

2. Presented By
Presented To
DR. MUHAMMAD ASIF

3. Motion
Position
Velocity
Acceleration
Force
Newton’s Laws
Circular Motion
Centripetal Force
Centripetal Acceleration
Relative Motion
Relative Velocity
Drag Force
Terminal Velocity
Projectile Motion

5. Motion can be classified as
● One Dimensional Motion
● Two Dimensional Motion
● Three Dimensional Motion

6. It is also known as rectilinear or linear motion. A
particle moving along a straight line is said to
undergo one dimensional motion. In such a
case, only one of the three rectangular
coordinates changes with time.
For example, if we consider one dimensional
motion along the X-axis, then when the particle
moves from A to B, as shown in the figure
below, the X coordinate changes from x1 to x2.

7. A particle moving along a curved path in
a plane has two dimensional motion. The
figure below, illustrates a two dimensional
motion, where a particle moves from
P (x1, y1) to Q (x2, y2) along a curved path.
e.g. a satellite revolving round the Earth
projectile motion, i.e., the two dimensional
motion of a particle thrown indirectly into
the air, like a baseball or a golf ball.

9. A particle moving in space has three
dimensional motion. In this type of motion, all
the three rectangular coordinates change with
time. The prime factors involved in three
dimensional motion are velocity,acceleration
and position.
The following figure
Illustrates the
phenomena

10. In three dimensions, the location of a particle is
specified by its location vector, r:
r = xi + yj + zk
If during a time interval t the position vector of the
particle changes from r1 to r2, the
displacement r for that time interval is
r = r1 − r2
= (x2 - x1)i + (y2 − y1)j+ (z2 − z1)k

11. If a particle moves through a displacement
∆r in a time interval ∆t then its average
velocity for that interval is
V= ∆r = ∆r i + ∆r j + ∆r k
∆t ∆t ∆t ∆t
As before, a more interesting quantity is the
instantaneous velocity v, which is the limit
of the average velocity when we shrink the time
interval ∆ t to zero. It is the time derivative
of the position vector r:
v= vxi + vyj + vzk

12. If a particle’s velocity changes by ∆v in a
time period ∆ t, the average acceleration
a for that period is
a = ∆v = ∆vx i + ∆vy j + ∆vz k
∆t ∆t ∆t ∆t

13. Motion in three dimensions with constant acceleration particles moves the
acceleration does not vary either in magnitude or direction
Acceleration is a vector quantity.
Particle moves in a curved path

14. As in one dimension motion we can derive equation in
three dimensional equation of motion
vx = Vox + ax t
vy = Voy + ay t
vz = Voz + az t
overall
V = u + at

15. Force is a vector quantity. It has both
magnitude as well as direction.
It obeys addition rule of vectors as represented
in diagram:

17. The acceleration of an object is directly
proportional to the net force acting on it
and inversely proportional to mass.
∑ F = m a
Force is a vector so it justified that the this law is
also vector form.
∑ Fx = m ax
∑ Fy = m ay
∑ Fz = m a z

18. Does a stick of Dynamite contain a force?
A) Yes B) No
This stick of dynamite does not contain a
force, but it does contain energy, and that
energy can be used to create a force
remember Force is a push or pull on an
object.

19. Every action and reaction are equal in
magnitude but opposite in direction
FAB = -FAB
so it is the vector representation of newton’s third
law

21. UNIFORM CIRCULAR MOTION

24. CENTRIPETAL FORCE
“THE FORCE REQUIRED TO MOVE AN
OBJECT IN CIRCULAR PATH”
EXPLANATION
When a car turns a corner, there is a centripetal
force towards the center of the circle. The force that
is being applied to the center of the circle is coming
from static friction between the car and the ground.
If the rubber on the car cannot handle the centripetal
force, the car will slide.

25. CENTRIPETAL
ACCELERATION
Object moves in circular path
At time t0 it is at point O with a
velocity tangent to the circle
At time t, it is at point P with a
velocity tangent to the circle
The radius has moved through
angle

26. Draw the two velocity vectors so that
they have the same tails.
The vector connecting the heads is v
Draw the triangle made by the change in
position and you get the triangle in (b)
Since the triangles have the same angle
are isosceles, they are similar

30. “A set of objects used to measure a
change in position.”
DEPENDENCE OF RELATIVE SPEED
AND VELOCITY

31. vB/A = vB – vA

34. “Objects that move through the air also
experience a “friction” type force.”

35. The drag force has the following properties:
It is proportional to the cross sectional area of
the object.
It is proportional to the velocity of the object.
It is directed in a direction opposite to the
direction of motion.
The drag force is responsible for the object
reaching a terminal velocity (when the drag
force balances the gravitational force).

38. A projectile is an
object moving in two
dimensions under the
influence of Earth's
gravity; its path is a
parabola.

39. Projectiles have velocities in two
directions.
Horizontal Motion: Motion parallel to
the Earth’s surface.
Vertical Motion: The force of gravity
pulling down on the object.

40. A projectile’s horizontal and vertical
motion are completely independent of
each other.
Gravity will effect a projectile and a falling
object in the same way.
Therefore, if an object is dropped and
thrown at the same time they will hit the
ground at the same time. It does not
matter that the projectile travels a farther
distance.

41. A projectile is any object
that is projected by some
means and continues in
motion by its own inertia.
Without gravity, the object
would follow a linear
motion; with gravity, the
path curves.
The path is surprisingly
simple if the horizontal
and vertical components
of motion are investigated
separately.

42. If friction is ignored (and we always ignore friction),
then there are no forces acting on the x-axis.
If net force is zero, then acceleration is zero.
If acceleration is zero, then the object is either at rest
or moving at constant velocity.
Since we know that the object is already in motion,
the projectile must be moving at
constant speed on the x-axis.
It moves of its own inertia and covers equal
Distances in equal intervals of time.

44. Projectiles move just like a freely
falling object along the y-axis.
The changing motion is due only
to acceleration due to gravity.
On the way up, the object decreases
its speed as it goes against gravity.
On the way down, speed increases
as it moves with gravity

45. The path of a projectile is symmetrical…
It rises to its maximum height in the same time it
takes to fall from that height to the ground.
Because acceleration is the same all of the
time, the speed it loses while going up is the
same as the speed it gains while falling.
Therefore the speeds are the same at equal
distances from the maximum height, where the
vertical speed is zero.