A disk of mass 4m and radius R rolls without slipping down a plane inclined by...

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A disk of mass 4m and radius R rolls without slipping down a plane inclined by 30°. It is restrained by a cord that wraps around the outer rim and wraps around another pulley of mass m and radius r. Assume that the disk and the pulley can be modeled as circular disks and that R = 2r. (a) (10 points) Find a relationship between the angular acceleration of the large disk and the angular acceleration of the small pulley (it is the same relationship as the ratio of angular velocities.) (b) (15 points) Find the equations which, when solved, will yield the angular acceleration of the large disk, the friction force, and the normal force at the instant when the system is released from rest. g 4m, R B A m, r R 30⁰ A disk of mass 4m and radius R rolls without slipping down a plane inclined by 30°. It is restrained by a cord that wraps around the outer rim and wraps around another pulley of mass m and radius r. Assume that the disk and the pulley can be modeled as circular disks and that R = 2r. (a) (10 points) Find a relationship between the angular acceleration of the large disk and the angular acceleration of the small pulley (it is the same relationship as the ratio of angular velocities.) (b) (15 points) Find the equations which, when solved, will yield the angular acceleration of the large disk, the friction force, and the normal force at the instant when the system is released from rest. g 4m, R B A m, r R 30⁰

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