Lecture_1 - Lecture #1 Part #1 - INTRODUCTION &...

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Lecture #1 Part #1 - INTRODUCTION & RECTILINEAR KINEMATICS: CONTINUOUS MOTION Today ` s Objectives : Students will be able to: 1. Find the kinematic quantities (position, displacement, velocity, and acceleration) of a particle traveling along a straight path. In-Class Activities : Reading Quiz Applications Relations between s(t), v(t), and a(t) for general rectilinear motion. Relations between s(t), v(t), and a(t) when acceleration is constant. Concept Quiz Group Problem Solving Attention Quiz
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READING QUIZ 1. In dynamics, a particle is assumed to have _________. A) both translation and rotational motions B) only a mass C) a mass but the size and shape cannot be neglected D) no mass or size or shape, it is just a point 2. The average speed is defined as __________. A) Δ r/ Δ t B) Δ s/ Δ t C) s T / Δ t D) None of the above.
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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?
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APPLICATIONS (continued) A sports car travels along a straight road. Can we treat the car as a particle? If the car accelerates at a constant rate, how can we determine its position and velocity at some instant?
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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.
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RECTILINEAR KINEMATICS: CONTINIOUS MOTION (Section 12.2) A particle travels along a straight-line path defined by the coordinate axis 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. 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
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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
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ACCELERATION Acceleration is the rate of change in the velocity of a particle. It is a vector quantity. Typical units are m/s 2 or ft/s 2 . As the book indicates, the derivative equations for velocity and
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This note was uploaded on 02/27/2012 for the course DYNAMICS 440:222 taught by Professor Pengsong during the Spring '11 term at Rutgers.

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Lecture_1 - Lecture #1 Part #1 - INTRODUCTION &...

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