Problem 1.46: Consider the experiment of problem 1.27, in which a frictionless p

Question

Problem 1.46: Consider the experiment of problem 1.27, in which a frictionless puck is slid straight across a rotating turntable through the center O. (a) Write down the polar coordinates r, f of the puck as function of time, as measured in the inertial frame S of an observer on the ground.(Assume that the puck was lauched along the axis f = 0 at t = 0.) (b) Now write down the polar coordinates r', f' of the puck as measured by an observer(frame S') at rest on the turntable. (Choose these coordinates so that f and f' coincide at t = 0.) Describe and sketch the path seen by this second observer. Is the frame S' inertial? (Experiment in Problem 1.27: The hallmark of an inertial reference frame is that any object which is subject to zero net force will travel in a straight line at constant speed. to illustrate this, consider the following experiment: I am standing on the ground (which we shall take to be an inertial frame) beside a perfectly flat horizontal turntable, rotating with constant angular velocity ?. I lean over and shove a frictionaless puck so that it slides across the turntable, straight through the center. The puck is subject to zero net force and, as seen from my inertial frame, travels in a straight line. Describe the puck's path as observed by someone sitting at rest on the turntable. This requires careful thought, but you should be able to get a qualitative picture. For a quantitative picture, it helps to use polar coordinates) Problem 1.46: Consider the experiment of problem 1.27, in which a frictionless puck is slid straight across a rotating turntable through the center O. (a) Write down the polar coordinates r, f of the puck as function of time, as measured in the inertial frame S of an observer on the ground.(Assume that the puck was lauched along the axis f = 0 at t = 0.) (b) Now write down the polar coordinates r', f' of the puck as measured by an observer(frame S') at rest on the turntable. (Choose these coordinates so that f and f' coincide at t = 0.) Describe and sketch the path seen by this second observer. Is the frame S' inertial? (Experiment in Problem 1.27: The hallmark of an inertial reference frame is that any object which is subject to zero net force will travel in a straight line at constant speed. to illustrate this, consider the following experiment: I am standing on the ground (which we shall take to be an inertial frame) beside a perfectly flat horizontal turntable, rotating with constant angular velocity ?. I lean over and shove a frictionaless puck so that it slides across the turntable, straight through the center. The puck is subject to zero net force and, as seen from my inertial frame, travels in a straight line. Describe the puck's path as observed by someone sitting at rest on the turntable. This requires careful thought, but you should be able to get a qualitative picture. For a quantitative picture, it helps to use polar coordinates)

Explanation / Answer

(a) r = v*t

?= ? *t

(b) r = v*t

?=0

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