The oldest artificial satellite still in orbit is Vanguard I, launched March 3, 1958. It mass is 1.60 kg. Neglecting atmospheric drag, the satellite would still be in its initial orbit, with a minimum distance from the center of Earth of 7.02 Mm and a speed at this perigee point of 8.23 km/s. For this orbit, find (a) the total energy of the satelliteEarth system and (b) the magnitude of the angular momentum of the satellite. (c) At apogee, find the satellites speed and its distance from the center of the Earth. (d) Find the semimajor axis of its orbit. (e) Determine its period.

A roller coaster has mass 3000.0 kg and needs to make it safely through a vertical circular loop of radius 50.0 m. What is the minimum angular momentum of the coaster at the boom of the loop to make it safely through? Neglect friction on the track. Take the coaster to be a point particle.

The perihelion of Halley’s comet is 0.586 AU and the aphelion is 17.8 AU. Given that its speed at perihelion is 55 km/s, what is the speed at aphelion ( IAU=1.4961011m )? (Hint: You may use either conservation of energy or angular momentum, but the latter is much easier.)

Figure 13.24 shows a particle with momentum p. Using the coordinate systems shown, determine the direction of the angular momentum of the particle around the origin in each case, and write expressions for L, using symbols defined in Figure 13.23. FIGURE 13.24

If the torque acting on a particle about an axis through a certain origin is zero, what can you say about its angular momentum about that axis?

A buzzard (m = 9.29 kg) is flying in circular motion with aspeed of 8.44 m/s while viewing its meal below. If the radius ofthe buzzards circular motion is 8.00 m, what is the angularmomentum of the buzzardaround the center of its motion?

Stars originate as large bodies of slowly rotating gas. Because of gravity, these clumps of gas slowly decrease in size. What happens to the angular speed of a star as it shrinks? Explain.

Two particles of equal mass travel with the same speed in opposite directions along parallel lines separated by a distance d Show that the angular momentum of this two- particle system is the same no matter what point is used as the reference for calculating the angular momentum.

If a particle is moving with respect to a chosen origin it has linear momentum. What conditions must exist for this particle’s angular momentum to be zero about the chosen origin?