Question

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

Answer 1

`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"`