APhys-HH02-RotDyn_001 - Advanced Physics HH#2 Rotational...

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Advanced Physics HH#2 Rotational Dynamics/Energetics For Part (a) of Problems 1-5, solve each using energy methods. Later, we will revisit Part (b) of these problems and find the acceleration using dynamics and Newton’s Second Law. 1. A massless, stretchless cord is wrapped around a uniform solid cylinder with a mass of 50 kg and a radius of 0.06 m. A constant force of 9.0 N is exerted for a distance of 4.0 m. a. Calculate the angular velocity of the cylinder and the final speed of the rope. b. Determine the angular acceleration of the cylinder. 2. A massless, stretchless cord is wrapped around a uniform solid cylinder with a mass of M and a radius of R. A block of mass m is hung from the cable and released from rest at a height, h, above the floor. a. Calculate the velocity of the block when it hits the floor. b. Determine the linear acceleration of the mass, m. 3. A solid cylinder and a solid sphere, each of mass M and radius R, are released from the top of an inclined plane. If released from rest, a. Calculate the velocity of each of the bottom of the incline (no slipping) in terms of M, R, g, L and θ . b. Determine the acceleration of each in terms of M, R, g, L and θ . h m M L θ R F = 9.0 N
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4. A solid uniform disk with a mass M and a radius R is pivoted around a horizontal axis through its center, and a small object with mass M is attached to the rim of the disk. If the disk is released from rest with the small object at the end of a horizontal radius, a. Find the angular velocity of the small object at the bottom. b. Determine the acceleration of the small object the instant it is released from rest.
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