The distance of the earth from the sun is 93 000 000 miles. if there are 3.15 * 107 s in one year, find the speed of the earth in its orbit about the sun.

The angular velocity of the orbit about the sun is:

w = 1 rev / year = 1 rev / 3.15 * 10^7 s

Now in 1 rev there is 360° or 2π rad, therefore:

w = 2π rad / 3.15 * 10^7 s

To convert in linear velocity, multiply the rad / s by the radius:

v = (2π rad / 3.15 * 10^7 s) * 93,000,000 miles

v = 18.55 miles / s = 29.85 km / s