1. A rocket ( initial mass m0) needs to use its engines to hover stationary, just above the ground. a) If it can afford to burn no more than a mass lamda m0 of its fuel, for how long cAN it hover (taking v(ex) to be constant)? b) if v(ex) roughly equals 3000 m/s and lamda roughly equals to 10%, for how long could the rocket hover just above the earth's surface?
2. consider a rigid body rotating with angular velocity omega about a fixed axis 9 e.g. a door rotating about the axis defined by its hinges.) Take the axis of rotation to be the z axis and use cylindrical polar co ordinates RHO ALFA, PHI ALFA, Z ALFA TO SPECIFY THE POSITIONS OF THE PARTICLES ALFA= 1,.., N THAT UP THE BODY. A) SHOW THE VELOCITY OF THE PARTICLE ALFA IS RHO ALFA OMEGA in the phi direction.
b) Hence show that the z component of the angular momentum l alfa of particle alfa is m alfa rho^2 alfa omega. c/ show total z component angular momentum can be written as Lz=I omega where I is the moment of inertia (for axis in question). I = SIGMA alfa=1 to N m alfa rho^2 alfa