A wheel rolls without slipping on a surface with a constant radius of curvature R. The...

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A wheel rolls without slipping on a surface with a constant radius of curvature R. The centre of curvature is located at point O. R 20 9 G m Assume the wheel can be approximated as a uniform disk (mass m, and radius r), with JG = mr. a) (4 pts) Determine the equation of motion of the disk in terms of g, R, and r, using 0 as your coordinate. Assume small oscillations. Leave your answer in standard form. b) (4 pts) The initial conditions of the system are given as 0 (0) = 0 and (0) = w. If instead, the no-slip condition is changed to perfect slip (ie. surface is frictionless), how much would the amplitude (A2) of 0 (t) change compared to the original amplitude (A) corresponding to rolling without slipping? (ie. determine A2/A). c) (2 pts) Even though friction (which is a non-conservative force) is acting on the wheel as it rolls without slipping, the wheel can still be considered as a conservative system in the absence of any external damping. Explain why. A wheel rolls without slipping on a surface with a constant radius of curvature R. The centre of curvature is located at point O. R 20 9 G m Assume the wheel can be approximated as a uniform disk (mass m, and radius r), with JG = mr. a) (4 pts) Determine the equation of motion of the disk in terms of g, R, and r, using 0 as your coordinate. Assume small oscillations. Leave your answer in standard form. b) (4 pts) The initial conditions of the system are given as 0 (0) = 0 and (0) = w. If instead, the no-slip condition is changed to perfect slip (ie. surface is frictionless), how much would the amplitude (A2) of 0 (t) change compared to the original amplitude (A) corresponding to rolling without slipping? (ie. determine A2/A). c) (2 pts) Even though friction (which is a non-conservative force) is acting on the wheel as it rolls without slipping, the wheel can still be considered as a conservative system in the absence of any external damping. Explain why.