Circular Motion

Circular Motion - 2-D Particle Kinematics Motion in n-t...

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2-D Particle Kinematics – 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 The Ferris wheel has a 12 m radius and rotates clockwise as shown. (a) If the wheel is rotating at a constant rate with
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This note was uploaded on 10/02/2011 for the course AERO 1234 at Virginia Tech.

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