The earth spins on its axis once a day and orbits the sun once a year (365 1/4 days). Determine the average angular velocity (in radians/second) of the earth as it (a) spins on its axis and (b) orbits the sun. In each case, take the positive direction for the angular displacement to be the direction of the earth's motion.

These simply require converting rotational speed from revolutions per day or year to radians per second. For example for (a) you need to divide 1 rev/day by the number of seconds in a day to determine rev/sec, then multiply by 2 \pi radians/rev to get it in radians per second.