hw1 - Florida State University Department of Physics PHY...

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Florida State University Department of Physics PHY 5246 Assignment # 1 (Due Wednesday, September 9th, 2009) (1) (10 points) A massless string is placed over a masssless pulley, and each end is wound around and fastened to a vertical hoop. The hoops have masses M 1 and M 2 , and radii R 1 and R 2 . The apparatus is placed in a uniform gravitational Feld g and released with each end of the string aligned along the Feld. (a) Show that the tension in the string is τ = gM 1 M 2 / ( M 1 + M 2 ). (b) Show that the acceleration of the center of mass of hoop 1 is a 1 = M 1 ( M 1 M 2 ) - 1 a point 1 , where a point 1 is the acceleration when both hoops are replaced with point masses. (2) (10 points) (a) Starting from Newton’s second law m ¨ r = F for a central force F = f ( r r , show that the equations of motion in two-dimensional polar coordinates become m r r ˙ φ 2 ) = f ( r ) and m (2˙ r ˙ φ + r ¨ φ ) = 0 . (b) Integrate these equations explicitly; hence relate them to the treatment of central-force
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hw1 - Florida State University Department of Physics PHY...

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