(a) Calculate the angular momentum (in kg · m2/s) of Jupiter in its orbit around the Sun. (The mass of Jupiter is 1.898 ✕ 1027 kg, the orbital radius is 7.783 ✕ 108 km and the orbital period is 11.9 y.) kg · m2/s (b) Compare this angular momentum with the angular momentum of Jupiter on its axis. (The radius of Jupiter is 7.149 ✕ 104 km and the rotation period is 9.925 h.) Lorbital Lrotation
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- Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star. A star with a of mass of 2.0x1032 kg and radius 7.0x108 m is initially rotating at a rate of once every 30 days. The star collapses into a neutron star with the same mass but a new radius of 16,000 m. What is the angular speed of the star? (Give your answer in rotations per second.) Assume the star is a solid sphere: Isphere = 2/5 MR2. The Crab Nebula (shown below) formed from a nearby supernova (6000 light years away). Chinese astronomers observed the event in the year 1054 and since that time the nebula has been expanding into what it appears like today. The Crab Pulsar is a neutron star at the center of the nebula and the remains of the original supernova.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 7.281 kg, with x coordinate at 6.769 m and y coordinate at 9.989 m. The second atom has a mass of 61.310 kg, with x coordinate at 39.549 m and y coordinate at 25.180 m. The third atom has a mass of 49.316 kg, with x coordinate at 35.553 m and y coordinate at 31.216 m. What is the moment of inertia in the unit of kg m2 with respect to the y axis?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 rpmUranus 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? JA planet is at a position of r→=3.0×10^12mx̂ − 4.0×10^12mŷ as it moves in an elliptical orbit around a large star at the origin (x=0, y=0). If the planet has a mass of 6.0 ×1026 kg and is moving with a velocity of v→=9.5km/sx̂, what is its angular momentum vector? (give magnitude and direction)
- 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 =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 EarthAn 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
- 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 rpmWe 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 rpmBy how many newtons does the weight of a 191-lb person change when he goes from sea level to an altitude of 10.0 miles if we neglect the earth's rotational effects? (The mean radius of the Earth is 6.38 × 10^6 m, G = 6.67 × 10^ - 11 N ∙ m^2/kg^2.)