Beach sand and river sand?

Question

what is the main mineral of these sands?

and why are the grains appear rounded?

Answer 1

They are rounded because of abrasion with other mineral grains.

The mineral of which the grains are composed is determined by the parent rock.  In most rivers and on most beaches, the dominant mineral is quartz.  However, in many places, notably volcanic islands, the dominant mineral is olivine.

Sandstones are formed from river or beach sand that is compacted and cemented to form  rock.  There are three main types of sandstone, based on composition: quartz arenite, graywacke, and arkose.

Quartz arenite is dominantly composed of quartz grains.

Graywacke is dominantly composed of rock fragments the size of sand grains.

Arkose is a mixture of sand-sized grains having roughly the same composition as granite, i.e. orthoclase feldspar and quartz.

On some beaches, the sand is composed of shell fragments.  Since minerals must be inorganic, these sands are not composed of minerals.

Answer 2

Silica, and they're rounded because the edges are worn off due to being bounced against the other grains in the constantly moving water.