(a) Calculate the angular momentum (in kg · m2/s) of Neptune in its orbit around the Sun. (The mass of Neptune is 1.020 x 1026 kg, the orbital radius is 4.497 x 109 km and the orbital period is 165 y.) kg · m2/s (b) Compare this angular momentum with the angular momentum of Neptune on its axis. (The radius of Neptune is 2.476 x 104 km and the rotation period is 16.11 h.) Lorbital Lrotation

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.

Uranus has a mass of 8.68 x 1025 kg and a radius of 2.56 x 10 m. Assume it is a uniform solid sphere. The distance of Uranus from the Sun is 2.87 x 10¹2 m. (Assume Uranus completes a single rotation in 17.3 hours and orbits the Sun once every 3.08 x 104 Earth days.) (a) What is the rotational kinetic energy of Uranus on its axis? J (b) What is the rotational kinetic energy of Uranus in its orbit around the Sun? J

a) Calculate the angular momentum (in kg · m2/s) of Mercury in its orbit around the Sun. (The mass of Mercury is 3.300 ✕ 1023 kg, the orbital radius is 5.790 ✕ 107 km and the orbital period is 0.241 y.)  kg · m2/s (b) Compare this angular momentum with the angular momentum of Mercury on its axis. (The radius of Mercury is 2.440 ✕ 103 km and the rotation period is 1408 h.) Lorbital Lrotation  =

The angular momentum of a sphere is given by , ?=(―4.59?^3)? + (6.01―1.19?^2)? + (6.26?)? where L has units of kg·m2/s when t is in seconds. What is the net torque on the sphere as a function of time?

A kid's merry-go-round in a park is a thin 150 kg disk (I = ½ MR2) with a radius of 3 m mounted to rotate freely about a central axis. On the edge of %3D the disk is an essentially massless bar. A 25 kg child jumps onto the bar (tangentially to the outer rim of the disk) at a speed of 12 m/s and a distance of 3 m from the rotation axis. If we think of the child as being essentially a point mass, what is the angular velocity of the system after the collision?

In the figure, two satellites, A and B, both of mass m = 36.1 kg, move in the same circular orbit of radius r = 7240 km around Earth (mass ME = 5.98×1024 kg) but in opposite senses of rotation and therefore on a collision course. (a) Find the total mechanical energy Е+ ЕÅ of the two satellites + Earth system before the collision. (b) If the collision is completely inelastic so that the wreckage remains as one piece of tangled material (mass = 2m), find the total mechanical energy immediately after the collision. (c) Just after the collision, is the wreckage falling directly toward Earth's center or orbiting around Earth? (a) Number Units (b) Number (c) Units A B Earth

An asteroid has a mass of m = 2.6 x 106 kg and is approaching Earth. When the asteroid is exactly 3 radii away from the Earth's centre,  it's speed relative to the Earth's centre is u = 8.7 x 103 ms-1. The asteroid then falls to the Earth's surface, but remains intact without dissipating any energy as it passes through the Earth's atmosphere. If the rotation of the asteroid and the Earth is ignored, what is the kinetic energy of the asteroid just before it hits the ground?  The Earth has mass ME = 5.98 x 1024 kg and a radius of 6.38 x 106 m. To find the relevant potential energies, you must use G = 6.67 x 10-11 N m2 kg-2

Let's consider the three atoms composing the molecule now have different masses and coordinate, while the axis of rotation is still y axis. The first atom has a mass of 9.199 kg, with x coordinate at 3.655 m and y coordinate at 8.442 m. The second atom has a mass of 41.619 kg, with x coordinate at 76.902 m and y coordinate at 57.706 m. The third atom has a mass of 39.818 kg, with x coordinate at 39.495 m and y coordinate at 25.9 m. What is the moment of inertia in unit of kg m2 with respect to the y axis?

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?