×

# The length if an arc traversed by minute hand of a watch 1 cm long after 15 minute as?

Mar 8, 2018

This should be the radius times the angular displacement in radians, written as $\frac{\pi}{2}$ cm.

#### Explanation:

It can be defined that Arc length = Angle(rad)*Radius. Radians are dimensionless, so we don't need to do any conversion!

We know the radius to be 1 cm, but we don't know the angle explicitly.

What we do know is that a full revolution of a minute hand means the hand rotated $2 \pi$ radians, in 1/60 increments (1 increment for each minute in an hour)

Therefore, we can use a basic ratio to figure out the number of radians 15 minutes gives

$\frac{15}{60} = \frac{x}{2 \pi}$

$\frac{1}{4} \cdot 2 \pi = x$

$\frac{\pi}{2} = x$

Now that we know the angular displacement, we can calculate the arclength:

$1 c m \cdot \frac{\pi}{2} = \frac{\pi}{2} c m$