2D Particle Kinematics in n-t coordinates

2D Particle Kinematics in n-t coordinates - 2-D Particle...

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2-D Particle Kinematics – 2-D motion (plane motion) in n-t coordinates/path coordinates (1) Velocity: ˆ t υυ = Direction - velocity is tangent to the path, so υ is directed along the + t axis. Magnitude (speed) - ds dt = where s is the actual traveling distance along the trajectory (2) Acceleration: 22 ˆ ˆ t n tn a at an a a a = + ⇒= + Tangential acceleration – change in magnitude of velocity (speed): t d a dt = . Normal acceleration – change in direction of velocity: 2 n a R = R = radius of curvature Circular motion 2 radius of the circle t n rad R d a dt aa R = = = = Uniform circular motion: υ = constant 2 : period in sec, : frequency in 0 2 2 4 4 Hz t n rad a R Rf T R a a R Tf T π υπ = = = = = = = NOTE: In circular motion, the normal acceleration is always pointing toward the center of the circle, so it is also referred to as the centripetal acceleration or radial acceleration ( a rad ). Example
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This note was uploaded on 10/02/2011 for the course PHYS 2305 taught by Professor Tschang during the Spring '08 term at Virginia Tech.

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