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"#