**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