Show that in the CM frame of two particles, the angular momentum / of particle 1 is related to the total angular momentum L by I-(m₂/M) L and likewise (m/M) L.
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- V 1 c²r The time dilation a distance from Earth's center is 3 = 2GM. The speed of a satellite in a stable circular orbit is v= GM due to the speed of a satellite + dilation due to gravity exactly equal the dilation experienced by a person at Earth's surface where 3 = two clocks run at the same rate? At what height above Earth's surface will the dilation 2GM? In other words, at what height will the V C² REThe center of our Milky Way galaxy is about 23000 ly away. (a) To eight significant figures, at what constant speed parameter would you need to travel exactly 23000 ly (measured in the Galaxy frame) in exactly 25 y (measured in your frame)? (b) Measured in your frame and in lightyears, what length of the Galaxy would pass by you during the trip?Two manned satellites approaching one another at a relative speed of 0.450 m/s intend to dock. The first has a mass of 3.00 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg. Assume that the positive direction is directed from the second satellite towards the first satellite. (a) Calculate the final velocity after docking, in the frame of reference in which the first satellite was originally at rest. m/s(b) What is the loss of kinetic energy in this inelastic collision? J(c) Repeat both parts, in the frame of reference in which the second satellite was originally at rest. final velocity (m/s) loss of kinetic energy (J)
- The center of our Milky Way galaxy is about 23000 ly away. (a) To eight significant figures, at what constant speed parameter would you need to travel exactly 23000 ly (measured in the Galaxy frame) in exactly 25 y (measured in your frame)? (b) Measured in your frame and in lightyears, what length of the Galaxy would pass by you during the trip? (a) Number (b) Number I Units UnitsAs measured in our frame, the horizontal component of the ball's velocity is 2v, while the vertical compenent of the ball's velcolity is √(v02 - v2). How long will it take the ship-clock to tick once (a.k.a, for the ball to bounce once back and forth)?Two manned satellites approaching one another at a relative speed of 0.100 m/s intend to dock. The first has a mass of 5.00 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg. Assume that the positive direction is directed from the second satellite towards the first satellite. (a) Calculate the final velocity after docking, in the frame of reference in which the first satellite was originally at rest.m/s(b) What is the loss of kinetic energy in this inelastic collision?J(c) Repeat both parts, in the frame of reference in which the second satellite was originally at rest.final velocitym/sloss of kinetic energyJ
- 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.)1) Calculate the interval As 2 between two events with coordinates (x1 = 50 m, y1 = 0, z1 = 0, t1 = 1 us) and (x2 = 120 m, y2 = 0, z2 = 0, t2 = 1.2 µs) in an inertial frame S. 2) Now transform the coordinates of the events into the S0 frame, which is travelling at 0.6c along the x-axis in a positive direction with respect to the frame S. Hence verify that the spacetime interval is invariant.An unstable particle is at rest and suddenly breaks up into two fragments. No external forces act on the particle or its fragments. One of the fragments has a velocity of +0.837c and a mass of 1.77 × 10-27 kg, and the other has a mass of 5.29 × 10-27 kg. What is the velocity of the more massive fragment (as a multiple of c)? (Hint: This problem is similar to Example 6 in Chapter 7.) Unstable particle at rest Number i V2 m2 Units m1 V1 Recoiling fragments
- An unstable particle is at rest and suddenly breaks up into two fragments. No external forces act on the particle or its fragments. One of the fragments has a velocity of +0.811c and a mass of 1.57 × 10-27 kg, and the other has a mass of 5.98 × 10-27 kg. What is the velocity of the more massive fragment (as a multiple of c)? (Hint: This problem is similar to Example 6 in Chapter 7.) Unstable particle at rest V2 m2 m1 V1 Recoiling fragmentsNiloConsider a binary star system that has bright lines at 656.72 and 656.86 nm,56.46-nm hydrogen line in the rest frame, estimate the speed V of the center of mass of the binary system is 151km/s how do I determine the mass of each star, they orbit in a circular motion.