T2 A dumbbell with mass 3M, radius R, and moment of inertia MR² is on an incline of angle 0. There is sufficient friction on the incline so that the dumbbell rolls without slipping. The dumbbell is connected by a massless cord passing over a pulley of mass M and radius R (I = ½MR²) to a hanging mass M as shown 3M M

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M,R
A dumbbell with mass 3M, radius R, and moment of inertia - MR2 is on an
3M
incline of angle 0. There is sufficient friction on the incline so that the dumbbell
rolls without slipping. The dumbbell is connected by a massless cord passing
over a pulley of mass M and radius R (I = ½MR²) to a hanging mass M as shown
below. The system starts from rest.
M
Draw free-body diagrams for the dumbbell (including one for torques), the pulley, and the
(а)
hanging mass, noting the coordinates used and the positive direction for torque, if applicable.
Write down the translational and/or rotational forms of Newton's Second Law for the
(b)
three objects in the system.
What is the acceleration of the system?
Transcribed Image Text:M,R A dumbbell with mass 3M, radius R, and moment of inertia - MR2 is on an 3M incline of angle 0. There is sufficient friction on the incline so that the dumbbell rolls without slipping. The dumbbell is connected by a massless cord passing over a pulley of mass M and radius R (I = ½MR²) to a hanging mass M as shown below. The system starts from rest. M Draw free-body diagrams for the dumbbell (including one for torques), the pulley, and the (а) hanging mass, noting the coordinates used and the positive direction for torque, if applicable. Write down the translational and/or rotational forms of Newton's Second Law for the (b) three objects in the system. What is the acceleration of the system?
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