m T2 m Problem IV: A twirly-twirly consists of two equal masses m attached to a massless cord of total length 31. Each m

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M T2 M Problem Iv A Twirly Twirly Consists Of Two Equal Masses M Attached To A Massless Cord Of Total Length 31 Each M 1 (257.8 KiB) Viewed 49 times

m T2 m Problem IV: A twirly-twirly consists of two equal masses m attached to a massless cord of total length 31. Each mass moves on a frictionless horizontal plane. The planes are attached by a small frictionless hollow tube of length l on which the cord can slide such that if you pull outward on mass 2 then mass 1 gets pulled inward and vice versa. Establish a polar coordinate system on each plane for each mass: (11,01) and (r2,02). Hint: in polar coordinates the radial component of the acceleration is ar = - rº2 and the angular component is ap = rö + 2ro. = + 1. What is the relationship satisfied by r1,72, and l? 2. Write down the radial and the angular component of the equations of motion for each mass. 3. Is the angular momentum of mass 1 conserved? How about mass 2? Explain. Write down the angular momentum of each mass in polar coordinates. 4. Show that the quantity E given below is conserved: E = m ( +r?) + m (i? +r36) 5. The initial conditions are such that both masses are given the same angular momentum L = Lz2. Show that there is a stable circular orbit for both masses and determine the radius for each mass. One mass is now displaced radially, determine the frequency for small oscillations around the circular orbit.