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EGR 280 Mechanics 9 – Particle Kinematics II

EGR 280 Mechanics 9 – Particle Kinematics II. Curvilinear motion of particles Let the vector from the origin of a fixed coordinate system to the particle be the position vector r The time derivative of position is velocity:. P. z. s. r. y. x.

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EGR 280 Mechanics 9 – Particle Kinematics II

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  1. EGR 280 Mechanics 9 – Particle Kinematics II

  2. Curvilinear motion of particles Let the vector from the origin of a fixed coordinate system to the particle be the position vector r The time derivative of position is velocity: P z s r y x

  3. The magnitude of velocity is speed, and is the time rate of change of arc length. Speed is a scalar quantity. The time derivative of velocity is acceleration:

  4. Motion of several particles rB = rA + rAB = rA + rB/A vB = vA + vB/A aB = aA + aB/A A y rAB=rB/A rA B rB x z

  5. Intrinsic coordinate system Define a coordinate system that moves with the particle: et = unit tangent vector. Always tangent to the path of the particle en = unit normal vector. Perpendicular to et,, always points into the curve As the particle moves along the curve, the unit tangent vector moves in the direction of the unit normal vector: det/dθ = en et en dθ

  6. Intrinsic coordinate system The velocity, by definition, is always tangent to the curve: v = v et The acceleration is the time rate of change of velocity: The intrinsic coordinate system is used often to describe circular motion.

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