Lecture 16 - Lecture 16 INTRODUCTION RECTILINEAR...

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Dynamics: Lecture Notes for Sections 12.1-12.3 1 Lecture 16 INTRODUCTION RECTILINEAR KINEMATICS: CONTINUOUS MOTION OF COMPOSITES ERRATIC MOTION Section 12.1-12.3 Ehab Zalok 2 Today’s Objectives : Students will be able to: Find the kinematic quantities of a particle traveling along a straight path: 1. Position 2. Displacement 3. Velocity 4. Acceleration).
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Dynamics: Lecture Notes for Sections 12.1-12.3 2 3 APPLICATIONS The motion of large objects, such as rockets, airplanes, or cars, can often be analyzed as if they were particles. Why? If we measure the altitude of this rocket as a function of time , how can we determine its velocity and acceleration ? 4 APPLICATIONS (continued) A train travels along a straight length of track. Can we treat the train as a particle? If the train accelerates at a constant rate , how can we determine its position and velocity at some instant?
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Dynamics: Lecture Notes for Sections 12.1-12.3 3 5 An Overview of Mechanics Statics : The study of bodies in equilibrium. Dynamics: 1. Kinematics – concerned with the geometric aspects of motion 2. Kinetics - concerned with the forces causing the motion Mechanics: The study of how bodies react to forces acting on them. 6 RECTILINEAR KINEMATICS: CONTINIOUS MOTION (Section 12.2) A particle travels along a straight-line path defined 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. Scalar s can be positive or negative. Typical units for r and s are meters (m) or feet (ft). The displacement of the particle is defined as its change in position. Vector form: Δ r = r’ - r Scalar form: Δ 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.
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Dynamics: Lecture Notes for Sections 12.1-12.3 4 7 VELOCITY Velocity is a measure of the rate of change in the position of a particle. It is a vector quantity (it has both magnitude and direction). The magnitude of the velocity is called speed , with units of m/s or ft/s. The average velocity of a particle during a time interval Δ t is: v avg = Δ r / Δ t The instantaneous velocity is the time-derivative of position. v = d r /dt Speed is the magnitude of velocity: v = ds/dt Average speed is the total distance traveled divided by elapsed time: (v sp ) avg = S T / Δ t 8 ACCELERATION Acceleration is the rate of change in the velocity of a particle. It is a
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This note was uploaded on 02/28/2011 for the course MATH 101 taught by Professor Duke during the Spring '11 term at University of Ottawa.

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Lecture 16 - Lecture 16 INTRODUCTION RECTILINEAR...

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