Question

A plastic disk initially rotates freely and without friction on an icy surface, as shown in the figure. The disk completes 1.0 revolution every 0.75 seconds., The disk has a radius 0.035 m, a thickness o 0,0070 m, and a mass of 0.15 k seolution esery eled Bool Square face is 0.060 m by 0.060 m. 0.012 m rotating plastic icy surface (a) Calculate the initial angular velocity of the plastic disk in units of radians per second. (b) Calculate the moment of inertia of the plastic disk about its axis of rotation. A table of angular momenta for certain objects and axes is given on page 314 of the textbook. (c) Calculate the initial angular momentum of the disk. ) Calculate the initial rotational kinetic energy of the disk. inued on other side.)

Answer 1

Given that radius (r) = 0.035 m The thickness = 0.0070 m The mass (m) = 0.15 kg The initial angular velocity of the plastic disk in units of radians per second w = 1 rev/0.75 s = 2 pi rad/0.75s = 2 rimes 3.14/0.75 = 0.28/0.75 = 8.37 rad/s the moment of inertia of the plastic disk about its axis rotation I = MR^2/2 = (0.15) (0.035)^2/2 = 9.1875 times 10^-5 kg - m^2 \r\n the initial angular momentum of the disk L = I w = 9.1875 times 10^-5 times 8.37 L = 7.6899 times 10^-4 the initial rotational kinetic energy of the disk KE = 1/2 Iw^2 = 1/2 9.1875 times 10^-5 (8.37)^2 = 3.22 times 10^-3