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Homework Statement
There is an empty bottle described as an hollow cylinder, that lies on a paper. Now the paper is pulled with an acceleration a, so that the bottle starts rolling perfectly on the paper. (Have a look at the figure.)
Homework Equations
Calculate the acceleration of the center of mass.
The Attempt at a Solution
Moment of inertia in the center of mass: ##{I_C = 1/2 M R^2}##
Moment of inertia in the center of mass on the surface: ##{I_S = 3/2 M R^2}##
Torque: ##{|\bf{M}| = |\bf{R}| |\bf{F}|}##
Angular acceleration: ##{\alpha = \dfrac{M}{I_S} = \dfrac{F}{3/2 M R}}##
acceleration of the center of mass: ##{a_s = \alpha R = 2/3 \dfrac{F}{M}} ##I have the feeling that my answer isn't the intended of the question. Mistakes? More to do? I hope on your answers and thoughts.