A hollow sphere (I=2/3mr^2) of radius R rotates about a diameter with an angular speed ω. The sphere then collapses (magically) under the action of internal forces to a final radius of R/2 with no change in its mass. What is the final angular speed of the sphere?   The answer is 4ω but I'm not sure how to get there.

In a satellite model for a science project, given the masses of the three satellites mA=1.4 kg, mp=2.8 kg, and mc =4.6 kg that are connected with massless rods, joined at the point the rotation axis is passing through. The satellites have the distances RA=1 m, RB rad = 0.9 m, and Rc =1.5 m, from the rotation axis. The system rotates with an angular speed w = 2.3 mA RA RB Rc MB 1. Calculate the moment of inertia /; for this model: /; = kg m² 2. Calculate the magnitude of the angular momentum L; = m2 kg 3. Calculate the rotational kinetic energy K;= 4. As the system is rotating counter-clockwise the direction of the vector is The mass mc was not properly glued and breaks away during the rotation. 1. Calculate the moment of inertia If for this model now. If= kg m2 2. Using the conservation of angular momentum, calculate the angular speed wf after the mass mc has broken away during rad the rotation. Wf= 3. Calculate the rotational kinetic energy in this situation: K=

A package of mass 5 kg sits at the equator of an airless asteroid of mass 3.0 x 1040 kg and radius 6.3 × 105 m. We want to launch the package in such a way that it will never come back, and when it is very far from the asteroid it will be traveling with speed 237 m/s. We have a large and powerful spring whose stiffness is 1.8 x 105 N/m. How much must we compress the spring? |compression| (a positive number) = %3D Additional Materials leBook