What is the angular displacement by minute's hand of a clock after 5 minutes?

1 Answer
Jun 13, 2018

theta=pi/6 color(white)(l) "rad"

Explanation:

It takes an hour (60 minutes) for the minute's hand to turn a full circle or achieve an angular rotation of 2pi color(white)(l) "rad".

There are 60/5=12 periods of five minutes in an hour. Meaning that the five-minute rotation accounts for 1/12 of 2pi, the rotation of the minute's hand in an hour.

2 pi * 1/12=pi/6 color(white)(l) "rad" so the minute's hand shall see an angular displacement of pi/6 radians.

Dimensional analysis:

(2pi color(white)(l) "rad")/(60 color(white)(l) color(red)(cancel(color(black)("minutes"))))*5 color(white)(l) color(red)(cancel(color(black)("minutes")))=pi/6 color(white)(l) "rad"