Please answer the following questions:

Section 2 |Rotary Mechanics | 25 Marks Q4. (a) A shiny coin is on a rough horizontal turntable at a distance 0.8 m from its centre. The turntable rotates at a constant angular speed. The coefficient of friction between the shiny coin and the turntable is 0.3. Find the maximum angular speed, in radians per second, at which the turntable can rotate if the shiny coin is not going to slide. (4) (b) The turntable is stopped, and the shiny coin is removed. An old coin is placed on the turntable at a distance 0.15 m from its centre. The turntable is made to rotate at a constant angular speed of 45 revolutions per minute. (i) Find the angular speed of the turntable in radians per second. (2) (ii) The old coin remains in the same position on the turntable. Find the least value of the coefficient of friction between the old coin and the turntable needed to prevent the old coin from sliding. (4) (Total 10 marks) Q5. A particle of mass m is suspended from a fixed-point O by a light inextensible string of length /. The particle hangs in equilibrium at the point P vertically below O. The particle is then set into motion with a horizontal velocity U so that it moves in a complete vertical circle with centre O. The point Q on the circle is such that