Question
You are a first-year physics student attempting to solve a problem about a solid cylinder of mass m and radius r rolling down an inclined plane of angle theta relative to the ground. For 10 points each:
[10e] You begin by constructing one of these diagrams for the cylinder consisting of all the forces acting on it.
ANSWER: free-body diagram
[10m] You have been told that the cylinder rolls without slipping, which means that this quantity must be at least one-third times the tangent of theta. The angle of repose is equal to the arctangent of this quantity.
ANSWER: coefficient of static friction [prompt on coefficient of friction; prompt on mu or mu sub s]
[10h] You conclude that the cylinder's acceleration equals g times sine theta over this fraction. The moment of inertia for a cylinder about a parallel axis that lies on the cylinder’s edge equals m r-squared times this fraction.
ANSWER: three-halves [or 3/2] (The moment of inertia through the cylinder’s center is ½ m r-squared and the parallel axis theorem adds another m r-squared term.)
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Summary
| 2023 ACF Winter @ Columbia | 11/11/2023 | Y | 3 | 10.00 | 67% | 33% | 0% |