A solid cylinder of mass `20 kg` and radius `0.12 m` rotating wit initial angula speed of `125 rad//s` is placed lightly (i.e. without any translational push) on a horizontal table with coefficient of kinetic friction `mu_(k) = 0.15` between the cylinder and the table.
(a) After how long does the cylinder start rolling ?
(b) What is the initial translational energy, rotational energy and total energy of the cylinder ?
(c) What is the final (i.e. after rolling begins) translational energy, rotational energy and total energy of the cylinder ? (d) Is the finl total enrgy equal to the initial total energy of motion of the cylinder ? If not, where does the difference of energy disappear ?
(e) Account for the loss of total energy of motion in the following way : find the work done by friction on the body its translational motion. Show that net work done by friction on the body is negative, equal in magnitude to the loss of total energy calculated in (d) above.