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Question: a solid cylinder of radius r and mass m rolls...

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A solid cylinder of radius r and mass M rolls without slipping up an inclined plane of angle e, see Figure 3. Please, make sure all symbols you are using are defined and explained. Do the following a) Draw an appropriate inertial coordinate system (X, Y, Z) and a coordinate system (x.y,z) fixed on the body. Which of the two coordinate systems is more appropriate to consider the dynamics of the rolling cylinder and why (max. two-sentence answer, preferably one, please) b) In the inertial coordinate system (X, Y, Z) please state in component formm velocity of the centre of mass, angular velocity of the cylinder, momentum of the cylinder, angular momentum of the cylinder, external forces acting on the cylinder, extemal moments acting about the cylinders centre of mass. Give numerical values where you can, using values from Section d) (i.e. velocity c) State the equation for the kinetic energy of the cylinder. Make sure that the no- slip rolling condition is accounted for in the equation. Give numerical value using numbers from Section d) (i.e. velocity 2 [m/s]). d) Calculate the friction force acting on the cylinder, express it in component form in the inertial (X, Y, Z) coordinate system and plot its absolute value as ns using symbols. In the final substitution please use the following numerical values: 0.3 [m], M-10 [kg]. 6-30 [degl initial velocity of the centre of mass of the cylinder at the bottom of the inclined a function of time. Conduct derivatio plane vo-2 [m/s] Mg Figure 3. Cylinder going up the slope

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