Chapter12-Kinematics of Particles

# Chapter12-Kinematics of Particles - Kinematics of a...

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Kinematics of a Particle Lectures 17-18 (Chapter 12) Dr. Marina Milner-Bolotin [email protected] Check Blackboard for course web site!

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Part I: Lecture 17 – 1-D Kinematics (Motion with Constant Acceleration) Goals: Review 1-D Kinematics (constant acceleration). Review various descriptions of motion (motion diagrams, graphs, algebraic description). Problem solving: 1-D kinematics - constant acceleration. Introduction to LoggerPro VideoAnalysis. 2
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Kinematics The branch of Physics that studies MOTION without relating it to the forces that causes it. No question “WHY” is asked! Objectives: To find the kinematic quantities (position, displacement, velocity, and acceleration) of a traveling particle and their relationships. 4
24/05/10 5 1-D Kinematics 1-D Kinematics Goal: Questions to be answered: Question to be ignored: Ways of describing motion:

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Let’s denote the direction of the straight-line path by the coordinate axis s . The position of the particle at any instant, relative to the origin, O, is defined by the position vector r , or the scalar s . s can be positive or negative. Typical units for r and s are meters (m) or feet (ft). The displacement of the particle is a vector and is defined as its change in position. Vector form: r = r’ - r Scalar form: s = s’ - s The total distance traveled by the particle, s T is a positive scalar that represents the total length of the path over which the particle travels. Position & Displacement: Motion Along a Straight Line
24/05/10 7 Definitions of Kinematics Quantities Coordinate system: Position: Displacement: Distance: Elapsed time: Clock reading:

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24/05/10 8 What Do You Need to Know to Describe Motion?
24/05/10 9 Logger Pro Motion Detector: An electronic bat www.vernier.com

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PCS211 – Physics II: Mechanics 10 Describing 1-D Motion t , sec x , m 0.0 1.0 1.0 3.0 2.0 4.0 3.0 2.0 4.0 -1.0 An object started at 1 m to the right from the origin, moved to the right for 2 sec to x = 4 m , then turned around and moved to the left for 2 sec to x = – 1 m .
24/05/10 11 Example 17-1: Distance & Displacement Displacement : Find the displacement of an object and the distance traveled between t i = 0 s and t f = 4 s Distance ( odometer reading mileage ) :

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24/05/10 12 Average Speed & Average Velocity How fast is the object moving? t , sec x , m x , m t , s x/ t m/s 0 1.0 1 3.0 2.0 1 2.0 2 4.0 1.0 1 1.0 3 2.0 2.0 1 2.0 4 1.0 3.0 1 3.0 Average velocity: t x v ave = Magnitude & direction Average speed: t x v v ave ave = = Magnitude
24/05/10 13 Average and Instantaneous Velocity Average and Instantaneous Velocity Average velocity: t x v ave = Instantaneous velocity: t x v t = 0 lim

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24/05/10 14 Average & Instantaneous Acceleration Average acceleration: t v a ave = Instantaneous acceleration: t v a t = 0 lim Units of acceleration: 2 / ] [ s m s s m a = =