LINEAR AND ANGULAR KINEMATICS BY DR.AJAY KUMAR. KINEMATICS Kinematics has been referred to as the...
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Transcript of LINEAR AND ANGULAR KINEMATICS BY DR.AJAY KUMAR. KINEMATICS Kinematics has been referred to as the...
![Page 1: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062321/56649ef35503460f94c06523/html5/thumbnails/1.jpg)
LINEAR AND ANGULAR KINEMATICS
BY
DR.AJAY KUMAR
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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.
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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
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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.
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Even though the teacher has walked a total distance of 12 meters, her displacement is 0
meters.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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• 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°
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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.
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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
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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