This time we have a non-rotating space station in the shape of a long thin uniform rod of mass 4.23 x 10^6 kg and length 660 meters. Small probes of mass 9078 kg are periodically launched in pairs from two points on the rod-shaped part of the station as shown, launching at a speed of 3658 m/s with respect to the launch points, which are each located 235 m from the center of the rod. After 12 pairs of probes have launched, how fast will the station be spinning?

Planet X is a sphere where a 0.5 kg block weighs 36 N when sitting on the surface. If an object is dropped from rest at a distance 9R from X's center it is observed to impact the surface at a speed of 16,000 m/s. Find a value for the radius of planet X.

A meteoroid is moving towards a planet. It has mass m = 0.54×109 kg and speed v1 = 4.7×107 m/s at distance R1 = 1.6×107 m from the center of the planet. The radius of the planet is R = 0.78×107 m. The mass of the planet is M = 5.6×1025kg. There is no air around the planet.  a)Enter an expression for the total energy E of the meteoroid at R, the surface of the planet, in terms of defined quantities and v, the meteoroid’s speed when it reaches the planet’s surface. Select from the variables below to write your expression. Note that all variables may not be required.α, β, θ, d, g, G, h, m, M, P, R, R1, t, v, v1 b)Enter an expression for v, the meteoroid’s speed at the planet’s surface, in terms of G, M, v1, R1, and R. c)Calculate the value of v in meters per second.

This time we have a non-rotating space station in the shape of a long thin uniform rod of mass 4.07 x 10^6 kg and length 1052 meters. Small probes of mass 9923 kg are periodically launched in pairs from two points on the rod-shaped part of the station as shown, launching at a speed of 4148 m/s with respect to the launch points, which are each located 357 m from the center of the rod. After 10 pairs of probes have launched, how fast will the station be spinning?     7.48 rpm     2.99 rpm     8.98 rpm     2.09 rpm