Define the moment of inertia. b) A uniform rod of mass $m$ and length L is rotating about an axis AB passing through its one end and perpendicular to…

Define the moment of inertia. 

b) A uniform rod of mass $m$ and length L is rotating about an axis AB passing through its one end and perpendicular to the length. Calculate the moment of inertia of the rod about the axis AB. 

c) A fly wheel of moment of inertia \( 0.32\text{ kgm}^2 \) is rotated steadily at 120 rad/sec by a 50 watt electric motor. Calculate: 

      i) the kinetic energy of the fly wheel.

      ii) the frictional couple opposing the rotation.

           OR

a) One end of a light spring having spring constant 18 N/m is attached to a rigid support. A mass of 0.15kg is suspended from other end of the spring. A student pulls down it such that extension of spring increases by 4cm. The student now releases it, as a result, the mass performs SHM.

i) Define simple harmonic motion.

ii) Calculate the maximum acceleration and time period of SHM. 

b) Write an expression for total energy of a particle executing SHM. Also draw a graph showing the variation of K.E. and P.E. of it.