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.