The length if an arc traversed by minute hand of a watch 1 cm long after 15 minute as?
This should be the radius times the angular displacement in radians, written as
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
Therefore, we can use a basic ratio to figure out the number of radians 15 minutes gives
Now that we know the angular displacement, we can calculate the arclength: