QUESTION

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# A solid disk of radius 0.10 m is mounted on a vertical axis. A string of negligible mass is wrapped around the rim of the disk; passes over a small, lightweight, frictionless pulley; and is tied to a block of mass 0.050 kg. The system is released from rest, and a computer records the velocity of the falling block as a function of time, as shown below. A solid disk of radius $0.10 \mathrm{~m}$ is mounted on a vertical axis. A string of negligible mass is wrapped around the rim of the disk; passes over a small, lightweight, frictionless pulley; and is tied to a block of mass $0.050 \mathrm{~kg}$. The system is released from rest, and a computer records the velocity of the falling block as a function of time, as shown below. a) Using the graph above, calculate the acceleration of the falling block. b) Use your result from part (a) to calculate the rotational inertia of the disk. c) Calculate the angular momentum of the disk at time $t=0.45 \mathrm{~s}$. d) Calculate the kinetic energy of the disk at time $t=0.45 \mathrm{~s}$. e) The disk is removed and replaced with a hoop of the same mass and radius, but with all of its mass concentrated near the rim of the hoop and connected to the axis by lightweight spokes. The experiment is then repeated. Is the angular acceleration of the hoop greater than, less than or the same as that of the solid disk? Justify your answer.  