PHY354H1 Lecture Notes - Taylor Series, Angular Frequency
Document Summary
Here is a practice problem on motion in plane, polar coordinates: Example (kleppner and kolenkov): a bead with unit mass moves outward with constant speed u along the spoke of a wheel that rotates with angular frequency . The bead starts from the center at t = 0. Find the velocity, acceleration, and the magnitude of the force on the bead, and make a sketch of the motion. Answer: the radial coordinate of the bead (distance from centre) is given by r = ut since u is constant, and the azimuthal velocity is = . The velocity is therefore (cid:126)v = r r + r = u r + ut (1) The acceleration is (cid:126)a = ( r r 2) r + (2 r + r ) = ut 2 r + 2u . (2) As the particle spirals outward, the force required to main- For t (cid:29) 1, the force increases linearly with time.
