1.46 Consider the experiment of Problem 1.27 (see below) in which a frictionless

Question

      1.46  Consider the experiment of Problem 1.27 (see below) in which a frictionless puck is slid straight across a rotating turntable through the center O. (a). Write down the polar coordinates r, /phi of the puck as functions of time, as measured in the inertial frame S of an observer on the ground. (Assume that the puck was launched along the axis phi=0 at t=0.) (b) Now write down the polar coordinates r' phi ' of the puck as measured by an observer in frame S' at rest on the turntable.  (Choose these coordinates so that phi and phi ' coincide at t=0.)

  1.27 I am standing on the ground beside a perfectly flat horizontal turntable, rotating with constant angular velocity, w. I lean over and shove a frictionless puck so that it slides across the turntable, stright through the center.  The puck is subject to zero net force, and as seem from my frame, travels in a straight line.  Describe the pucks path as observed by someone sitting at rest on the turntable.

Explanation / Answer

The radial displacement from the origin is changing with constant velocity "v".

So the polar coordinate r=vt

The phi angle of the puck's displacement vector is also changing constantly with the turntable's angular velocity ?.

So, similarly to the radial coordinate, ?=?t.

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