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Particle Kinematics

Particle Kinematics. Inertial frame – non accelerating, non rotating reference frame Particle – point mass at some position in space. Position Vector. Velocity Vector. Direction of velocity vector is parallel to path Magnitude of velocity vector is distance traveled / time.

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Particle Kinematics

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  1. Particle Kinematics Inertial frame – non accelerating, non rotating reference frame Particle – point mass at some position in space Position Vector Velocity Vector • Direction of velocity vector is parallel to path • Magnitude of velocity vector is distance traveled / time Acceleration Vector

  2. Particle Kinematics • Straight line motion with constant acceleration • Simple Harmonic Motion • Circular Motion at const speed

  3. Summary • General circular motion • Arbitrary path

  4. Summary • Polar Coords

  5. Newton’s laws • For a particle • For a rigid body in motion without rotation, or a particle on a massless frame You MUST take moments about center of mass

  6. Calculating forces required to cause prescribed motion of a particle • Idealize system • Free body diagram • Kinematics • F=ma for each particle. • (for rigid bodies or frames only) • Solve for unknown forces or accelerations

  7. Deriving Equations of Motion for particles 1. Idealize system 2. Introduce variables to describe motion(often x,y coords, but we will see other examples) 3. Write down r, differentiate to get a 4. Draw FBD 5. 6. If necessary, eliminate reaction forces 7. Result will be differential equations for coords defined in (2), e.g. 8. Identify initial conditions, and solve ODE

  8. Motion of a projectile

  9. Work and Energy relations Rate of work done by a force (power developed by force) Total work done by a force Kinetic energy Power-kinetic energy relation Work-kinetic energy relation

  10. Potential energy Potential energy of aconservative force (pair)

  11. Energy relations for conservative systems subjected to external forces Internal Forces: (forces exerted by one part of the system on another) External Forces: (any other forces) System is conservative if all internal forces are conservative forces (or constraint forces) Energy relation for a conservative system Kinetic and potential energy at time Kinetic and potential energy at time Work done by external forces

  12. Impulse-momentum relations Impulse-momentum for a single particle Linear Impulse of a force Linear momentum of a particle Impulse-momentum relations Impulse-momentum for a system of particles Total external impulse Total linear momentum Conservation law

  13. Collisions

  14. Angular Impulse-Momentum Equations for a Particle Angular Impulse Angular Momentum Impulse-Momentum relations Useful for central force problems

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