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 2 π Radian = 360° or 1 Revolution

So 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