Consider a spacecraft orbiting Earth. At an instant in time, the angular velocity of the spacecraft relative to Earth is = 1.6b +0.52bz+0.21b3z (in rad/s). Now consider a top spinning in the spacecraft with an angular velocity relative to the spacecraft of wr = 5.86, +0.19ôg+0.15bg (in rad/s). What is the magnitude of the angular velocity (in rad/s) of the spinning top relative to the Earth reference frame. Note b1, b2, bz are unit vectors fixed in the spacecraft reference frame.
Q: 3. The Earth moves in an almost perfectly uniform circular orbit with the Sun at its center, 1.5 ×…
A: Radius of the orbit is given to be R=1.5*108km=1.5*1011m, Mass of the sun is around M=2*1030kg and…
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Q: Now we have a rod-shaped space station of length 682 m and mass 4.04 x 10^6 kg, which can change its…
A: Initial length of the space station, l1=682 m Mass of the space station, m=4.04×106 kg (mass of…
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A: Solution:-
Q: A star has a mass of 1.5 x 10^30 kg and is moving in a circular orbit about the center of its…
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Q: Planet A is located 1.81 x 10^10 [m] away from its parent star. What is the radial acceleration of…
A: The objective of this question is to calculate the radial acceleration of Planet A, which is…
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Q: Now we have a rod-shaped space station of length 572 m and mass 6.59 x 10^6 kg, which can change its…
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Q: A spaceship orbits earth from a distance of 2.656 × 10^4km with a centripetal acceleration of 7.962…
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Q: A star has a mass of 1.87 x 1030 kg and is moving in a circular orbit about the center of its…
A: mass of star (m) = 1.87×1030 kg radius of orbit (R) = 2.3×104 light years = 2.3×104×9.5×1015 m =…
Q: Calculate the angular momentum (in kg · m2/s) of Mercury in its orbit around the Sun. (The mass of…
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Q: QB3c. A satellite is moving with the constant angular velocity (see sketch below) and its…
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Q: A certain triple-star system consists of two stars, each of mass m = 6.7×1030 kg, revolving in the…
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A: Given Data: Length (L1) = 1282 m.Mass (m) = 7.89×106 kg.Initial rate of rotation (ω1) = 2.90…
Q: QB3a. A satellite is moving with a constant angular velocity (see sketch below). Write down an…
A: Step 1:Step 2:
Q: Suppose one of the Global Positioning System satellites has a speed of 4.34 km/skm/s at perigee and…
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Q: A disk with velocity v= 10m/s, mass m=4 kg, and radius r=.3 m. Find the total kinetic energy.
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Q: (a) Calculate the angular momentum (in kg · m2/s) of Mercury in its orbit around the Sun. (The mass…
A: (a) I = moment of inertia of mercury around sun = Mr2 = (3.3 x 1023) (5.79 x 1010)2 = 1.11 x 1045…
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A: This problem can be solved using basic formula for orbital velocity of the satellite.
Q: A star has a mass of 1.03 x 1030 kg and is moving in a circular orbit about the center of its…
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Q: (1 light-year = 9.5 x 1015 m), and the angular speed of the star is 1.6 x 10-15 rad/s. (a) Determine…
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- need asistance with number 711. Two satellites are in circular orbits around a planet that has radius 9.00 × 106 m. One satellite has mass 68.0 kg, orbital radius 5.00 × 107 m, and orbital speed 4800 m/s. The second satellite has mass 84.0 kg and orbital radius 3.00 × 107 m. What is the orbital speed of this second satellite? Answer: m/s (orbital speed of the second satellite)A space station consists of two donut-shaped living chambers, A and B, that have the radii shown in the figure. As the station rotates, an astronaut in chamber A is moved 369 m along a circular arc. How far along a circular arc is an astronaut in chamber B moved during the same time if r_a = 266 m and r_b = 165 m? Note: Express your answer in whole numbers. No unit is required for the final answer. Set your calculator in radians. ra A rB B.
- 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.a) What is the period of rotation of Venus in seconds? (The period of rotation of Venus in hours is 5,832.5 hr.) Answer in seconds (b)What is the angular velocity (in rad/s) of Venus? (Enter the magnitude.) Answer in rad/s (c) Given that Venus has a radius of 6.1 ✕ 106 m at its equator, what is the linear velocity (in m/s) at Venus's surface? (Enter the magnitude of the linear velocity at the equator.) Answer on m/sYou are a visitor aboard the New International Space Station, which is in a circular orbit around the Earth with an orbital speed of vo = 2.72 km/s. The station is equipped with a high velocity projectile launcher, which can be used to launch small projectiles in various directions at high speeds. Most of the time, the projectiles either enter new orbits around the Earth or eventually fall down and hit the Earth. However, as you know from your physics courses at the Academy, projectiles launched with a sufficiently great initial speed can travel away from the Earth indefinitely, always slowing down but never falling back to Earth. With what minimum total speed, relative to the Earth, would projectiles need to be launched from the station in order to "escape" in this way? For reference, recall that the radius of the Earth is RE = 6370000 m, the mass of the Earth is MẸ = 5.98 × 1024 kg, the acceleration due to gravity on the surface of the Earth is g = 9.81 m/s and the universal…
- A star with mass M and radius R collides head-on with another star of mass ¾*M and radius 4/5*R, and they coalesce to form a new start at rest whose radius is 6/5*R. Assume that initially the colliding stars had angular velocities with opposite directions but the same magnitude w. What is the magnitude and direction of the final’s stars angular velocity? (Express the magnitude as a fraction of w.)I don't understand why B would be the correct answer? Shouldn't the potential energy be decreasing as Mars gets farther, since the gravitational force decreases? And why is angular momentum the same?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 years.
- Now we have a rod-shaped space station of length 1296 m and mass 1.43 x 10^6 kg, which can change its length (kind of like an old-fashioned telescope), without changing its overall mass. Suppose that the station is initially rotating at a constant rate of 1.83 rpm. If the length of the rod is reduced to 1.83 m, what will be the new rotation rate of the space station? 1. 3.01 rpm 6.27 rpm 3 3.76 rpm 4 9.41 rpmSaturn orbits the Sun at an average distance of 1.43 × 10⁹ km with an orbital period of 29.46 yr. The Moon, which is one of the satellites of the Earth, orbits its parent at an average distance of 3.84 × 105 km with an orbital period of 0.07481 yr. (a) Use the above information to find the orbital speeds of Saturn around the Sun and of the Moon around the Earth. m/s m/s V Saturn VMoon = M = = (b) What is the expression for the mass M of the parent in terms of the orbital speed v of the satellite, the orbital radius R of the satellite and the gravitational constant G? (Do not substitute numerical values; use variables only.) (c) Now use your answers from parts (a) and (b) to find the ratio of the mass of the Earth to that of the Sun. ME MsA star has a mass of 1.03 x 1030 kg and is moving in a circular orbit about the center of its galaxy. The radius of the orbit is 2.4 x 104 light-years (1 light-year = 9.5 x 1015 m), and the angular speed of the star is 1.0 x 10-15 rad/s. (a) Determine the tangential speed of the star. (b) What is the magnitude of the net force that acts on the star to keep it moving around the center of the galaxy?