- Good morning.
Billy, could you please read the problem
and Bo could you please translate?
♫ Flipping Physics ♫
- The wheel of a bike rotates exactly three times
in 12.2 seconds.
- Please stop.
So, theta equals three revolutions.
- [Mr. P] Actually Bo, three revolutions
is not just the angular position
but rather it is the change in angular position.
- Yeah, so change in theta equals three revolutions
and change in time equals 12.2 seconds.
- Mr. P, are we really supposed to use one significant digit
for three revolutions?
- Okay, sometimes physics problems use this word exactly
when referring to a number
and we interpret that to mean the number
has as many significant digits as we need it to.
Hopefully you recognize this is not possible,
however, you will probably see the word "exactly" in problems,
so I thought I would include it.
- Thanks Mr. P.
- Billy, could you please keep reading?
- What is the average angular velocity of the wheel
in a, radians per second and b, revolutions per minute?
- Average angular velocity equals question mark
in both radians per second and revolutions per minute.
- [Mr. P] Bo, what is the symbol for angular velocity?
- It's like a curly w.
- Omega.
- Bobby, please solve part a.
- Okay, the equation for average angular velocity
is omega equals change in angular position
over change in time,
so three revolutions over 12.2 seconds
but that would give us revolutions per second
and we need radians per second.
- One revolution equals 360 degrees
equals two pi radians.
- Right, so
multiply by two pi radians over one revolution
to cancel out revolutions
and we get 1.54505
or 1.55 radians per second with three significant digits.
- Billy, could you please do part B?
Please convert the angular velocity from radians per second
to revolutions per minutes.
- Well, we can multiply the angular velocity
by 60 seconds over one minute to convert to minutes
and multiply by one revolution over two pi radians
to convert to revolutions
and that is 145.617
or no wait, actually, that doesn't make any sense.
- I got 14.8 pi.
- Actually it's 46.351.
- Unfortunately you are all wrong.
There are three common mistakes
when converting from radians per second
to revolutions per minute and you each made one of them.
Before we discuss your mistakes,
let's get the correct solution on the board.
When we do this correctly,
the answer is 14.8 revolutions per minute.
Now, Bobby, you added pi to your answer
even though you had already divided by pi.
I do not understand why students do this,
however, sometimes they do,
so realize when you include pi
in your calculator calculations,
which you should always do when finding an answer in physics
then you no longer have pi in your answer.
- Okay, that makes sense.
- [Mr. P] Bo, where Bobby added an extra pi,
you simply ignored it.
That's correct.
You forgot to multiply by the number pi.
Please remember to multiply by pi.
You cannot simply ignore it.
- Right.
- [Mr. P] Billy, your mistake is actually in the use
of your calculator and is the most common student mistake.
When you divide by 2 pi on your calculator,
you need to be careful to put parentheses around two pi.
If you do not put parentheses around two pi,
then you are, according to the order of operations,
telling your calculator to divide by two
and then multiply by pi.
To make matters worse, this is not true of every calculator
so please check to make sure you know
how to divide by two pi on your calculator, okay.
- Yeah, that's not how my calculator works.
- Mr. P, for part B could we not just go back
to the equation for average angular velocity
and divide three revolutions by 12.2 seconds
and then convert by multiplying by 60 seconds
over one minute to get the same 14.8 revolutions per minute?
- [Mr. P] Absolutely, Bobby.
We could solve it that way
and in the future you certainly should.
However, if we had, we would not have made those mistakes
and I find students learn more by making mistakes
than by doing everything correctly.
That is why I intentionally led you to toward the mistakes,
the mistakes you made on your own.
- That's great.
Letting us make mistakes is a great teaching strategy.
- Please, do your best to avoid these common mistakes
when converting from radians per second
to revolutions per minute.
Thank you very much for learning with me today.
I enjoyed learning with you.