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ps1 - Newton’s 2 nd Law ݀ܘ ݀ݐ ൌ ڮ and interpret...

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PHY 504 Problem Set #1 due 3 September 2010 1. A circular platform rotates in the horizontal plane about its center with frequency ω . In this problem, you may ignore motion in the vertical direction and the effects of gravity. (a) Write down a coordinate transformation that relates the inertial reference frame of a person standing on the ground (at some distance from the platform) to the noninertial frame of a person riding on the platform. This should be a transformation of the form x' = x' ( x,y,t ) etc., where the coordinates of the inertial frame are unprimed. (It may be convenient to first write down the transformation from the rotating frame to the inertial frame x = x ( x', y',t ) and then invert it.) (b) In the absence of forces, the equation of motion of a particle in the inertial reference frame is ܚ ௗ௧ ൌ 0 . What is it in the rotating frame? Write it in a similar form to
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Unformatted text preview: Newton’s 2 nd Law ( ݀ܘ ݀ݐ ൌ ڮ ሻ and interpret the “force” terms on the right-hand side. (c) A particle is released by the person riding on the platform, at a distance r from the center. Its initial velocity in the rotating frame is zero. Describe its subsequent trajectory in both reference frames. 2. A rocket in space is accelerating at 9.8 m/s 2 in the direction of its motion. (a) Repeat Problem 1 (a) and (b) for an observer on the rocket and an inertial observer which is instantaneously moving with the rocket at time t . (b) Use this result to complete Exercise 1.13. 3. Solve the following problems using Maple or Mathematica: (a) 2 + 2 = (b) ∫ e x dx = (indefinite integral) (c) ax 2 + bx + c = 0; solve for x (use the ‘solve’ function). (d) Plot y = sin(10 x ) exp(-x 2 ). (e) Plot a sample trajectory for problem 1(c), in the rotating frame....
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