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In this lesson, we will learn how to use the angular acceleration, angular speed, and Newton's second law equations of a particle to analyze circular motion.

Q1:

A particle is held at a point π΄ on a smooth solid hemisphere of radius 3 m and centre π . The particle is released and slides down the hemisphere under gravity before leaving the hemisphere at point π΅ . Given that π π΄ makes an angle of 2 6 β with the upward vertical, find the angle that π π΅ makes with the upward vertical. Take π = 9 . 8 / m s 2 and give your answer correct to one decimal place.

Q2:

A bead π΅ 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 π , about which the rod can freely rotate in a vertical plane. The bead was at rest vertically below π when it was pushed horizontally at a speed of 14 m/s. Taking π = 9 . 8 / m s 2 , find the beadβs speed when it passed the point vertically above π . Give your answer in metres per second correct to one decimal place.

Q3:

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 π = 9 . 8 / m s 2 , 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.

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