A particle is held at a point on a smooth solid hemisphere of radius 3 m and centre . The particle is released and slides down the hemisphere under gravity before leaving the hemisphere at point . Given that makes an angle of with the upward vertical, find the angle that makes with the upward vertical. Take and give your answer correct to one decimal place.
A bead of mass 0.9 kg is attached to one end of a light rod of length 0.3 m. The other end of the rod is fixed at a point , about which the rod can freely rotate in a vertical plane. The bead was at rest vertically below when it was pushed horizontally at a speed of 14 m/s. Taking , find the bead’s speed when it passed the point vertically above . Give your answer in metres per second correct to one decimal place.
A rough horizontal disc is rotating at a constant angular speed of 7 rad/s about a vertical axis through its centre. A rock resting on this disc is on the point of slipping. Taking , determine the coefficient of friction between the rock and the disc given that the rock lies 11 cm away from the centre of the disc.