Earth orbits the sun once every 365.25 days. Find the average angular speed of earth about the sun. Answer in units of rad/s.

2.0x10-7 rad/s.

Explanation:

Calculating the angular velocity of the Earth is a deceptively easy task. The reason for this is simple - the angular velocity is defined as the angle subtended in a certain time.

We know the Earth goes round the Sun, all the way around is 2 radians (360 degrees). We also know that it takes a year (approx 365 days) which is therefore about 3.2x107 secs.

Therefore = 2 / 3.2x107 = 2.0x10-7 rad/s. We have calculated the angular velocity.

However, if we can measure the distance to the Sun we can also calculate the velocity of the Earth relative to the Sun. Although unless we define a direction this is more technically known as the speed. This can be done by looking at the definition of the radian. The radian is a unit which conects the radius of an arc, the length of the arc and the angle subtended by the arc. The formula for this is s = r x (where s is the length of the arc, r is the radius and the angle). So if we know the radius of the Earth's orbit (1.5x10¹¹m) we can substitute the angular velocity from our previous equation to give v = x r (where v is the velocity, the angular velocity and r the radius).

So, the Earth travels through space (relative to the Sun) at: v = 2.0x10-7 x 6.4x106 = 3.0x104m/s