Q.In a Circus, a motor-cyclist having mass of 50 kg moves in a spherical cage of radius 3 m. Calculate the least velocity with which he must pass the highest point without losing contact. Also calculate his angular speed at the highest point.

The 'sphere of death' is a circus act in which motorcyclists ride inside a large hollow sphere, starting with small, nearly horizontal circles (governed by the same dynamics as a conical pendulum) and building up to full vertical circles. Once performing genuine vertical circles, the dynamics are identical, point for point, to a bob tied to a string undergoing vertical circular motion under gravity -- with exactly one substitution: since there is no string, the role played elsewhere by string tension is instead played by the sphere wall's normal reactio …