The uniform cylinder of mass m = P.1) 100 kg and radius r = 0.5 m is released from rest on a sloped surface. The coefficient of friction between the cylinder and the sloped surface is µ. a. Determine whether the cylinder slips on the surface if µ = 0.1. b. Find the cylinder's angular and linear acceleration if u = 0.3. G. 30°

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3) A 50-lb spool with outer radius of 15 inches, inner radius of 9 inches, and moment of inertia of 0.8 slug-ft? is initially at rest. If a 10-lb force, P, is applied at the inner radius of the spool as shown. The coefficients of static and kinetic friction between the cylinder and the ground at point A are us = 0.3 and µk = 0.25 respectively. a) Draw the FBD and IRD of the system. b) Determine the acceleration of the center of mass, G, in ft/s². Assume the wheel is rolling without slipping. [Ans. to Check: a = -7.75 i ft/s²] c) Check the assumption of rolling without slip. Was this a valid assumption? %3D r = 1.25 ft P = 10 lbs r2 = 0.75 ft

The velocity of the 7.6-kg cylinder is 0.49 m/s at a certain instant. What is its speed v after dropping an additional 1.87 m? The mass of the grooved drum is m = 10.1 kg, its centroidal radius of gyration is k = 260 mm, and the radius of its groove is r; = 225 mm. The frictional moment at O is a constant 15.3 N-m. Assume r, = 345 mm. m Answer: v = i m/s

3/72 The small object is placed on the inner surface of the conical dish at the radius shown. If the coefficient of static friction between the object and the conical sur- face is 0.30, for what range of angular velocities w about the vertical axis will the block remain on the dish without slipping? Assume that speed changes are made slowly so that any angular acceleration may be neglected. (0 0.2 m m 30° CamScanner Lino izowall