A spherical satellite of approximately uniform density with radius 5.4 m and mass 300 kg is originally moving with velocity <2600, 0, 0>m/s, and is originally rotating with an angular speed 2 rad/s, in the direction shown in the diagram. A small piece of space junk of mass 5.1 kg is initially moving toward the satellite with velocity <−2200, 0, 0>m/s. The space junk hits the edge of the satellite as shown in the figure below, and moves off with a new velocity <−1300, 480, 0>m/s. Both before and after the collision, the rotation of the space junk is negligible. What is the rise in the internal energy of the satellite and space junk combined?

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

A 4,600 kg open train car is rolling on frictionless rails at 21.1 m/s when it starts pouring rain. A while later the car's speed is 19.5 m/s. What mass of water has collected in the car? Provide your answer in appropriate units of meters (m), seconds (s), kilograms (kg), radians (rad) or combinations thereof, such as m/s or m/s^2. Use at least three significant figures in your answer, do not use scientific notation. Using more significant figures will not be considered incorrect; using fewer may lead to errors due to rounding.

Consider a spacecraft orbiting Earth. At an instant in time, the angular velocity of the spacecraft relative to Earth is = 1.9bh +0.82b2+0.34b3 (in rad/s) and the angular acceleration of the spacecraft relative to Earth is a = 0.0561 +0.19bz+0.22bg (in rad/s?). What is the moment (in N.m) being applied on the spacecraft in the b2. Assume the moment of inertia of the spacecraft is given by: Г5000 0.0 0.0 0.0 10000 0.0 kg.m? 0.0 13000 Note b1, b2, bz are unit vectors fixed in the spacecraft reference frame.

This time we have a non-rotating space station in the shape of a long thin uniform rod of mass 8.40 x 10^6 kg and length 1137 meters. Small probes of mass 8057 kg are periodically launched in pairs from two points on the rod-shaped part of the station as shown, launching at a speed of 2897 m/s with respect to the launch points, which are each located 400 m from the center of the rod. After 10 pairs of probes have launched, how fast will the station be spinning? (1) 2.36 rpm 2 1.11 rpm 3) 1.97 rpm 4 1.58 rpm

We have a non-rotating space station in the shape of a long thin uniform rod of mass 2.60 x 10^6 kg and length 769 meters. Small probes of mass 8303 kg are periodically launched in pairs from two points on the rod-shaped part of the station as shown, launching at a speed of 2888 m/s with respect to the launch points, which are each located 196 m from the center of the rod. After 11 pairs of probes have launched, how fast will the station be spinning?     3.70 rpm     7.71 rpm     4.63 rpm     10.02 rpm

A horizontal solid circular plate of mass 60 kg rotates about a vertical axis passing through its center at period of T = 6 s. A block of mass 60 kg is placed on the edge of the plate and rotating with the plate. Now, let’s move the block from the edge of the plate to the center of the plate. What is the velocity of rotation now? (Hint: You may consider angular momentum conservation.)

How fast, in rpm, would a 129 g, 44.0 cm diameter beach ball have to spin to have an angular momentum of 0.115 kg*m2/s?

Modeled after the triatomic molecule problem that is let's consider the three atoms composing the molecule have different masses and coordinate, while the axis of rotation is still y-axis. The first atom has a mass of 6.778 kg, with x coordinate at 2.814 m and y coordinate at 9.967 m. The second atom has a mass of 48.003 kg, with x coordinate at 47.145 m and y coordinate at 17.003 m. The third atom has a mass of 43.312 kg, with x coordinate at 44.89 m and y coordinate at 22.657 m. What is the moment of inertia in the unit of kg m2 with respect to the y axis?