Prove that the acceleration of a solid cylinder rolling without slipping down an inclined plane is 2g sin 3 .
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Using the conservation of mechanical energy: 1/2 Mv2 + 1/2 I w2 + Mgh = 1/2Mv2 + 1/2 Iw2 + Mgh ***Note: w = angular velocity, I'm just not sure how to insert the symbol v2 = v20 + 2a(x-x0) I=1/2MR2
In this equation, 1/4v2 + gh = 1/2v2 + 1/4v2, the v on the left side is not the same as the v on the right side. If v on the left is initially zero, i.e. the cylinder is at rest, then the equation becomes gh = 1/2v2 + 1/4v2 and then using v2=2a(d) gh = 1/2(2ad) + 1/4(2ad).
Reference https://www.physicsforums.com/threads/acceleration-of-a-solid-cylinder-on-an-incline.337029/
In this equation, 1/4v2 + gh = 1/2v2 + 1/4v2, the v on the left side is not the same as the v on the right side. If v on the left is initially zero, i.e. the cylinder is at rest, then the equation becomes gh = 1/2v2 + 1/4v2 and then using v2=2a(d) gh = 1/2(2ad) + 1/4(2ad).
Reference https://www.physicsforums.com/threads/acceleration-of-a-solid-cylinder-on-an-incline.337029/
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