**Q1: **

A uniform circular hoop of mass 1.2 kg and radius 0.6 m is rotating in a horizontal plane about a smooth vertical axis through point of its circumference.

Calculate the kinetic energy of the hoop when it is rotating at 5 rad/s.

A particle of mass 0.4 kg is now fixed to the hoop at point , where is a diameter. The hoop continues to rotate at 5 rad/s. Calculate the total kinetic energy of the hoop and the particle.

**Q2: **

A uniform circular disc of mass 1.5 kg and radius 0.4 m is free to rotate in a horizontal plane about a fixed smooth vertical axis through the centre of the disc. Particles of masses 0.5 kg, 0.8 kg, and 1.2 kg are attached to points on the circumference of the disc. The loaded disc is rotating at 100 revolutions per minute. Calculate the angular momentum of the loaded disc to the nearest decimal place.

**Q3: **

A uniform square lamina has sides of length 0.8 m and a mass of 4 kg. It is free to rotate about a fixed axis which coincides with one of its sides. Calculate the change of angular momentum when the angular speed of the lamina is increased from 2 rad/s to 5 rad/s.