d)A fixed solid disc pulley is acted upon by a torque of 12 Nm. If the mass of the disc is 0.6 Kg, calculate the acceleration of the pulley if the radius of the pulley is 0.2 m (5 Marks) e) A rod of diameter 4 cm, length 48 cm and mass 1.2 kg rotates through its centre with axis parallel to its length Find the Moment of inertia (5 Marks) f) Define a couple of force (2 Marks) g) For a solid cylinder of radius 24 cm and mass 3.2 kg find the radius of gyration (5 Marks)

d) To calculate the acceleration of the pulley, we can use the formula:<br /><br />Torque = Moment of Inertia * Angular Acceleration<br /><br />The moment of inertia for a solid disc is given by:<br /><br />Moment of Inertia = (1/2) * Mass * Radius^2<br /><br />Given:<br />Torque = 12 Nm<br />Mass = 0.6 kg<br />Radius = 0.2 m<br /><br />Substituting the values in the formula:<br /><br />12 Nm = (1/2) * 0.6 kg * (0.2 m)^2 * Angular Acceleration<br /><br />Solving for Angular Acceleration:<br /><br />Angular Acceleration = 12 Nm / ((1/2) * 0.6 kg * (0.2 m)^2)<br />Angular Acceleration = 100 rad/s^2<br /><br />Therefore, the acceleration of the pulley is 100 rad/s^2.<br /><br />e) The moment of inertia for a rod rotating about its center is given by:<br /><br />Moment of Inertia = (1/12) * Mass * Length^2<br /><br />Given:<br />Diameter = 4 cm<br />Length = 48 cm<br />Mass = 1.2 kg<br /><br />Radius = Diameter / 2 = 2 cm<br />Length = 48 cm<br /><br />Substituting the values in the formula:<br /><br />Moment of Inertia = (1/12) * 1.2 kg * (0.48 m)^2<br />Moment of Inertia = 0.0288 kg*m^2<br /><br />Therefore, the moment of inertia of the rod is 0.0288 kg*m^2.<br /><br />f) A couple of force refers to a pair of forces that are equal in magnitude but opposite in direction, resulting in a net force of zero. These forces cause a rotation or torque without causing a linear acceleration.<br /><br />g) The radius of gyration for a solid cylinder is given by:<br /><br />Radius of Gyration = sqrt((2/3) * Radius^2)<br /><br />Given:<br />Radius = 24 cm<br />Mass = 3.2 kg<br /><br />Substituting the values in the formula:<br /><br />Radius of Gyration = sqrt((2/3) * (0.24 m)^2)<br />Radius of Gyration = 0.24 m<br /><br />Therefore, the radius of gyration for the solid cylinder is 0.24 m.