LINEAR AND ANGULAR
KINEMATICS
BY
DR.AJAY KUMAR
KINEMATICS
• Kinematics has been referred to as the
geometry of motion.
• It describes the motion in term of time,
displacement, velocity and acceleration.
• The motion may be occurring in a straight
line. (Linear Kinematics) or about a fix
point (angular kinematics.)
• Kinematics is not concerned with force
which causes the motion.
DISTANCE & DISPLACEMENT
• Distance is a scalar quantity which refers
to "how much ground an object has
covered" during its motion.
• Displacement is a vector quantity which
refers to "how far out of place an object
is"; it is the object's overall change in
position
Dist & Displ (cont)
• To test your understanding of this
distinction, consider the motion depicted in
the diagram on next slide. A teacher walks
4 meters East, 2 meters South, 4 meters
West, and finally 2 meters North.
Even though the teacher has
walked a total distance of 12
meters, her displacement is 0
meters.
SPEED & VELOCITY
• Just as distance and displacement have
distinctly different meanings (despite their
similarities), so do speed and velocity.
• Speed is a scalar quantity which refers to
"how fast an object is moving."
• Speed can be thought of as the rate at
which an object covers distance.
SPEED & VELOCITY (CONT)
• A fast-moving object has a high speed and
covers a relatively large distance in a short
amount of time.
• A slow-moving object has a low speed and
covers a relatively small amount of
distance in a short amount of time.
• An object with no movement at all has a
zero speed.
SPEED & VELOCITY (CONT)
• Velocity is a vector quantity which refers to "the
rate at which an object changes its position."
• Imagine a person running rapidly – on the spot.
While this might look like an activity, but it would
result in a zero velocity. Because the person
does not move from his original position. Since
velocity is defined as the rate at which the
position changes, this motion results in zero
velocity.
SPEED & VELOCITY (CONT)
• Calculating Average Speed and
Average Velocity
• The average speed and average velocity
during the course of a motion is often
computed using the formula on next slide.
ACCLERATION
• Acceleration is a vector quantity which is
defined as the rate at which an object
changes its velocity. An object is
accelerating if it is changing its velocity.
• Acceleration has nothing to do with going
fast.
ACCLERATION (CONT)
• A person can be moving very fast and still
not be accelerating.
• Acceleration has to do with changing how
fast an object is moving.
• If an object is not changing its velocity,
then the object is not accelerating.
• Anytime an object's velocity is changing,
the object is said to be accelerating; it has
an acceleration.
Constant / Uniform Acceleration
• Sometimes an accelerating object will
change its velocity by the same amount
each second. This is referred to as a
constant acceleration since the velocity
is changing by a constant amount each
second.
Constant / Uniform
Acceleration(Cont)
• If an object is changing its velocity whether by a constant amount or a varying
amount - then it is an accelerating object.
• If the body experience a constant
increase/ decrease in velocity in equal
interval of time however small these
intervals may be the body is said to be
moving with the constant or uniform
acceleration.
Uniform Velocity
• An object with a constant acceleration
should not be confused with an object with
a constant / uniform velocity.
• A body is said to be in constant / uniform
velocity if it covers equal distance in equal
intervals of time however small these
interval may be.
Angular Motion
• Angular Velocity/: - Number of revolution
per unit time or radians per unit time or
degree per unit time.
• Angular acceleration:- Rate of change of
angular velocity.
• Radian:- A radian is an angle represented
by an arc of a circle that equals in length
of the radius of that circle.
• And
So
2 π Radian = 360° or 1 Revolution
1 Radian = 360° / 2 π Radian
= 57.27°
Related Terms in Angular Motion
• Time period:- It is the time taken by an
object to complete 1 (one) revolution.
• Frequency:- In case of the circular motion
the term frequency refers to number of
revolution performed by an object in one
second. Or in a unit time.
Relationship Between Angular
Velocity & Frequency
• Suppose there is an object which is
revolving with a frequency of “n” revolution
per second.
Angle described in 1 rev = 2π rad
Angle described in “n” rev = 2π n rad
= Angular Velocity
Relationship Between Linear &
Angular Velocity
• Linear distance (θ) in 1 rev = 2πr
Linear distance covered in “n” rev = 2πr . n
or = 2πn . r
OR
Linear Distance = Angular Vel x Radius