The 6.50-cm-long second hand on a watch rotates smoothly. what is its angular velocity? what is the speed of the tip of the hand?

The seconds hand of a clock completes one full revolution around
the face of the clock every minute.

One full revolution = 360 degrees.

The hand revolves  (360 degrees / 60 seconds) = 6 degrees per second.

The tip of the hand travels in a circle, and covers the circumference
of the circle every minute.  The circumference of a circle is

                           (2π) x (radius of the circle).

The length of the hand is the radius of the circle that it travels in,
so the circumference of the circle is

                            (2π) x (6.5 cm)  centimeters.

The tip of the hand covers this distance in 60 seconds,
so its speed is

                             (13π cm) / (60 seconds)  =  0.681 cm/sec.