Prove that there is no work done by the Coriolis pseudoforce acting on a particle moving in a rotating frame. If the Coriolis pseudoforce were the only force acting on a particle, what could you conclude about the particle’s speed in the rotating frame?

I. With external gravitational field In this second part you are asked to analyze rocket propulsion with the present of gravitational field g. This appears for instance when the rocket is launching from the surface of a planet. (1) Describes why you are not allowed to use the momentum conservation here. (2) Evaluate the speed of the rocket measure by inertial observer on the ground as a function of time v(t) if the speed of the gas propulsion with respect to the rocket is vret and the burning rate is constant constant! dm dt (3) Plot v(t) that you obtained from point (2) above, for three different values of gravitational field (assuming similar initial mass), which is: Imoon = 1.62 m/s? • Gearth = 9.81 m/s? Ijupiter = 24.79 m/s? in a single plot, if the burn dm ate is constant = 1500 kg/s. Analyze your result and dt describes how the speed increases for each situation! 20:18 Ai 11/03/2022

We have two spheres (m and M) that are separated by a small distance; m is to the left of M. A sphere of mass m (identical to one of the two initial spheres) is moving towards m at a speed V0. Show that when M is smaller than or equal to m, there will be 2 collisions and calculate the final speeds. Show that when M is larger than m, there will be three collisions and calculate the final velocities.

I am given an equation (attatched image) and am told that G = newtons gravitational constant, m1 is the mass of the first object, m2 is the mass of the second object, and r is the distance separating them. Consider m1 to be stationary with m2 undergoing uniform circular motion around m1 at a distance r. How do I show that GPE = -2KE for any gravitational circular orbit (where KE is the kinetic energy of object 2).