Question

The angular velocity of earth around the sun increase when it comes closer to the sun. Why?

Answer 1

Another way of understanding this is by Kepler's 3rd law:

"The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit."

That means:

the larger the axis of orbit, the larger the orbital period

Which is the same as:

the larger the axis of orbit, the smaller the speed

Which is the same as:

the smaller the axis of orbit, the larger the speed (and, therefore, the larger the angular speed).