Two particles, each of mass 2.75 × 104 kg and speed 7.10 m/s, travel in opposite directions along parallel lines separated by 4.04 cm. (a) What is the magnitude L of the angular momentum of the two-particle system around a point midway between the two lines? (b) Is the value different for a different location of the point? If the direction of either particle is reversed, what are the answers for (c) part (a) and (d) part (b)?

A space of mass 120 kg is going to use a planet for a gravitational assist- that is, use the planet's gravity to change its direction of travel without expending any fuel. It is initially moving at a velocity of 280 m/s and at an angle of theta initial = 53 degrees, at a distance of 11500 km from the center of the planet. Given an expression for the angular momentum of the spacecraft using the coordinate system specified in terms of m, r0, v0, theta initial, and vector units i, j, k   If the spaceship whips around the planet to the other side so that the angle is theta 35 and is moving at 95 m/s, how far, in kilometers, from the planet is it?

A particle of mass m is dropped from rest near the Earth’s surface at time t = 0. Relative to an x-y coordinate system, where upward is the positive y direction and the x axis is horizontal, the initial position of the particle is (-d, 0). Neglect air resistance. Part (a)  Write an expression for the magnitude of the angular momentum of the particle about the origin as it falls. Your expression will be in terms of m, d, t, and g (the acceleration due to gravity).   Part (b)  Write an expression for magnitude of the the torque on the particle about the origin as it falls. Your expression will be in terms of m, d, and g (the acceleration due to gravity).  Part (c)  Write an expression for the magnitude of the rate of change of the angular momentum of the particle as it falls. Your expression will be in terms of m, d, and g (the acceleration due to gravity).

Two particles of mass m, = 2.06 kg and m, = 5.02 kg are joined by a uniform massless rod of length { = 1.80 m (see figure below). The system rotates in the xy plane about an axis through the midpoint of the rod in such a way that the particles are moving with a speed of 3.05 m/s. What is the angular momentum of the system? magnitude direction ]kg • m²/s |---Select-- V