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Solid sphere of mass m and radius r R R 13 Before After Problem 3...

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Solid sphere of mass m and radius r R R 13 Before After Problem 3 A solid sphere of mass m and radius r rolls without slipping v rw along the track shown in the figure above on the left It starts from rest with the lowest point of the sphere at height h above the bottom of the loop of radius R much larger than r What is the minimum value of h in terms of R such that the sphere completes the loop The moment of inertia of a sphere is I 2 5 mr2 Hint You will need to draw a free body diagram of the ball at the top of the loop and you will need to find the minimum speed the ball needs to complete the loop Recall that the centriperal acceleration is a 2 Answer h 27 10 R 2 7R Problem 4 A disk with moment of inertia I rotates about a frictionless vertical axle with angular speed wi A second disk this one having moment of inertia 12 and initially not rotating drops onto the first disk see figure above on the right Because of friction between the surfaces the two eventually reach the same angular speed wf a Calculate wj Answer 1 wi h Colorleto KE the ratio of the final to the initial rotational energy Answer

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