C1_ParticleDyn - PARTICLE DYNAMICS Contents 1 PARTICLE...

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Unformatted text preview: PARTICLE DYNAMICS Contents 1 PARTICLE DYNAMICS 1 1.1 Newton’s second law . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Newtonian gravitation . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Inertial reference frames . . . . . . . . . . . . . . . . . . . . . 3 1.4 Cartesian coordinates . . . . . . . . . . . . . . . . . . . . . . . 3 1.5 Normal and tangential components . . . . . . . . . . . . . . . 4 1.6 Polar and cylindrical coordinates . . . . . . . . . . . . . . . . 5 1.7 Principle of work and energy . . . . . . . . . . . . . . . . . . . 6 1.8 Work and power . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.9 Conservation of energy . . . . . . . . . . . . . . . . . . . . . . 10 1.10 Conservative forces . . . . . . . . . . . . . . . . . . . . . . . . 11 1.11 Principle of impulse and momentum . . . . . . . . . . . . . . . 14 1.12 Conservation of linear momentum . . . . . . . . . . . . . . . . 15 1.13 Principle of angular impulse and momentum . . . . . . . . . . 16 1.14 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.15 Problem Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 PARTICLE DYNAMICS 1 1 PARTICLE DYNAMICS 1.1 Newton’s second law Classical mechanics was established by Isaac Newton with the publication of Philosophiae naturalis principia mathematica , in 1687. Newton stated three “laws” of motion 1. When the sum of the forces acting on a particle is zero, its velocity is constant In particular if the particle is initially stationary it will remain stationary. 2. When the sum of the forces acting on a particle is not zero the sum of the forces is equal to the rate of change of the linear momentum of the particle. 3. The forces exerted by two particles on each other are equal in magnitude and opposite in direction F ij + F ji = , where F ij is the force exerted by particle i on particle j and F ji is the force exerted by particle j on particle i . The linear momentum of a particle is the product of the mass of the particle, m , and the velocity of the particle, v L = m v . Newton’s second law may be written as F = d dt ( m v ) , (1.1) where F is the total force on the particle. If the mass of the particle is constant, m =constant, the total force equals the product of its mass and acceleration, a F = m d v dt = m a . (1.2) Newton’s second law gives interpretation to the terms mass and force . In SI units, the unit of mass is the kilogram [kg]. The unit of force is the newton PARTICLE DYNAMICS 2 [N], which is the force required to give a mass of one kilogram an acceleration of one meter per second squared 1 N = (1 kg) (1 m/s 2 )=1 kg m/s 2 . In U.S. Customary units, the unit of force is the pound [lb]. The unit of mass is the slug, which is the amount of mass accelerated at one foot per second squared by a force of one pound 1 lb = (1 slug) (1 ft/s 2 ), or 1 slug= 1 lb s 2 /lb....
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C1_ParticleDyn - PARTICLE DYNAMICS Contents 1 PARTICLE...

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