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A thin plank of mass M is placed centrally across two solid cylindrical rollers each of mass m, and the system is allowed to move freely from rest without slip down a slope of angle θ as shown in the figure below.
(a) Derive expressions for the initial accelerations of the plank and the roller.
Your solution should include the following in a systematic way:
(i) free-body, kinematic and kinetic diagrams with an appropriate global axes system clearly shown
(ii) statements of relevant kinematic and kinetic relationships with reference to your chosen global axes system in (i), and
(iii) clear, logical, and systematic manipulations of the relationships you have stated in (ii) above to arrive at the desired results.
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