# Thread: hour hand/ angular velocity question

1. ## hour hand/ angular velocity question

This question states "determine the angular velocity in radians per minute of the hour hand of a clock."

This problem does not involve conversions since it wants the answer in minutes. This I know.

Now, looking at the back of the book, I know the answer is pi/360 rad/min. Looking at this, I know that the 360 is perahps coming from the 360 degrees that the hour hand travels in one revolution.

2. Originally Posted by xdem713o

… I know the answer is pi/360 rad/min. Looking at this, I know that the 360 is perahps coming from the 360 degrees … in one revolution.

You've jumped to a false conclusion; it's only a coincidence that the denominator matches the number of degrees in one revolution.

Whenever an exercise gives angle measurement units in radians, forget about degree units (unless, of course, the exercise also makes some statement regarding degrees).

We want to multiply revolutions by 2Pi, so how many revolutions does an hour hand make in one minute? In other words, you need to determine the fractional part of a single revolution that an hour hand moves in one minute.

If this seems daunting, then try (1) realizing that an hour hand revolves once in 12 hours, and (2) calculating the corresponding number of minutes. Use the total number of minutes to determine the fractional part of one revolution (in one minute).

For example, if something takes 9000 minutes to complete one revolution, then that thing completes 1/9000th of a revolution per minute, and the angular velocity is (2 Pi)(1/9000) radians/minute.

MY EDIT: Fixed incorrect number of hours for one revolution of an hour hand.

3. ## Re: hour hand/ angular velocity question

I'm still confused.

I understand that you have to multiply the number of revolutions by 2pi. I'm not sure though, how many revolutions an hour hand makes in a minute. 1/60th? 60 minutes in an hour. I'm puzzled.

4. ## Re:

Originally Posted by mmm4444bot
Originally Posted by xdem713o

… I know the answer is pi/360 rad/min. Looking at this, I know that the 360 is perahps coming from the 360 degrees … in one revolution.

If this seems daunting, then try (1) realizing that an hour hand revolves once in 24 hours, and (2) calculating the corresponding number of minutes. Use the total number of minutes to determine the fractional part of one revolution (in one minute).

What do you mean by saying an hour hand revolves once in 24 hours?

5. Originally Posted by xdem713o

What do you mean by saying an hour hand revolves once in 24 hours?

Oops!
My previous statement is wrong, due to a transient brain infarct in my head.

An hour hand makes one revolution in 12 hours.

(I apologize for the resulting confusion.)

So, how many minutes elapse in 12 hours?

MY EDIT: Replaced misleading pronoun "that" with explitict noun phrase

6. ## Re: Re:

Originally Posted by xdem713o
Originally Posted by mmm4444bot
Originally Posted by xdem713o

… I know the answer is pi/360 rad/min. Looking at this, I know that the 360 is perahps coming from the 360 degrees … in one revolution.

If this seems daunting, then try (1) realizing that an hour hand revolves once in 24 hours, and (2) calculating the corresponding number of minutes. Use the total number of minutes to determine the fractional part of one revolution (in one minute).

What do you mean by saying an hour hand revolves once in 24 hours?
Actually, I think the hour hand revolves once in 12 hours.

For example, if the hour hand is on 1, it will be back there again in 12 hours (if we are dealing with a standard clock...not a military clock).

So, the hour hand moves through one revolution in 12 hours.

12 hours is 12*60 minutes, or 720 minutes.

If the hour hand makes 1 revolution in 720 minutes, then it makes 1/720 revolutions per minute.

Now, does that make sense? Suppose you think about the movement of the hour hand in ONE hour. If the hour hand is on 1, it will be on 2 one hour later, right? The hour hand will have moved 1/12 of the way around the circular clock. And, if we've determined that the hour hand moves 1/720 revolutions per minute. Ok...in 1 hour (60 minutes) how far would the hour hand move? Well, it would be 60/720 revolutions, or 1/12 revolutions...which would put the hour hand ONE HOUR past where it was to begin with.

If you want radians per minute, then remember that 2 pi radians = 1 revolution.

So 1/720 revolutions per minute = (1 revolution/720 minutes)*(2 pi radians/revolution) = 1 pi radian / 360 minutes

7. ## Re: hour hand/ angular velocity question

Ok, this makes alot of sense!! I understand it now.. that the hour hand makes one revolution in 12 hours. And in order to get the amount of minutes, you must multiply 12 hour by 60 minutesper hour. Thank you!

8. Originally Posted by Mrspi

Actually, I think the hour hand revolves once in 12 hours.

Could I have gotten away with blaming my mistake on the prevalence of digital timepieces, instead of my brain?

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