chapt3 - 2. Kinetics of Particles: Newtons 2nd Law...

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2. Kinetics of Particles: Newton’s 2 nd Law
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Introduction • Newton’s first and third laws are sufficient for the study of bodies at rest (statics) or bodies in motion with no acceleration. • When a body accelerates (changes in velocity magnitude or direction), Newton’s second law is required to relate the motion of the body to the forces acting on it. • Newton’s second law: - A particle will have an acceleration proportional to the magnitude of the resultant force acting on it and in the direction of the resultant force. - The resultant of the forces acting on a particle is equal to the rate of change of linear momentum of the particle. - The sum of the moments about O of the forces acting on a particle is equal to the rate of change of angular momentum of the particle about O .
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Newton’s Second Law of Motion Newton’s Second Law : If the resultant force acting on a particle is not zero, the particle will have an acceleration proportional to the magnitude of resultant and in the direction of the resultant . • Consider a particle subjected to constant forces, m a F a F a F mass, constant 3 3 2 2 1 1 = = = = = " • When a particle of mass m is acted upon by a force the acceleration of the particle must satisfy , F G a m F G G = • Acceleration must be evaluated with respect to a Newtonian frame of reference , i.e., one that is not accelerating or rotating. • If force acting on particle is zero, particle will not accelerate, i.e., it will remain stationary or continue on a straight line at constant velocity.
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Linear Momentum of a Particle • Replacing the acceleration by the derivative of the velocity yields () particle the of momentum linear = = = = L dt L d v m dt d dt v d m F G G G G G Linear Momentum Conservation Principle : If the resultant force on a particle is zero, the linear momentum of the particle remains constant in both magnitude and direction.
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Systems of Units • Of the units for the four primary dimensions (force, mass, length, and time), three may be chosen arbitrarily. The fourth must be compatible with Newton’s 2nd Law. International System of Units (SI Units): base units are the units of length (m), mass (kg), and time (second). The unit of force is derived, () 2 2 s m kg 1 s m 1 kg 1 N 1 = =
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Equations of Motion • Newton’s second law provides a m F G G = • Solution for particle motion is facilitated by resolving vector equation into scalar component equations, e.g., for rectangular components, ( ) ( ) z m F y m F x m F ma F ma F ma F k a j a i a m k F j F i F z y x z z y y x x z y x z y x ± ± ± ± ± ± G G G G G G = = = = = = + + = + + • For tangential and normal components, ρ 2 v m F dt dv m F ma F ma F n t n n t t = = = =
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Dynamic Equilibrium • Alternate expression of Newton’s second law, ector inertial v a m a m F 0 = G G G • With the inclusion of the inertial vector, the system of forces acting on the particle is equivalent to
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This note was uploaded on 11/09/2009 for the course ENG 91301 taught by Professor Lui during the Spring '08 term at Hong Kong Institute of Vocational Education.

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chapt3 - 2. Kinetics of Particles: Newtons 2nd Law...

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