He then asked us, what causes a change in velocity? (answer: unbalanced force)

What direction must the force be? (answer: towards the center*)

What direction is the acceleration? (answer: towards the center)

*Chris showed us a demo we can do if the class doesn't agree that the force/acceleration is towards the center. He grabbed the bowling ball (yes, the bowling ball, again) and a broom, and asked one of the students to make the ball move in a circle. She first started out inside the circle of the ball and was constantly pulling the ball towards herself. Chris then had her stand outside the circle and put a cup as a reference point for the center of the circle. She again had to constantly push the ball towards the cup.

From there, Jon led us to derive an equation for the average speed of an object in circular motion:

$\large \overline {v} = \frac {\Delta x}{\Delta t} = \frac {2 \pi r}{\Delta t}$

From there, we walked through the tradition questions for paradigm labs:

What do you notice?

What can you measure?

What can you manipulate?

Then Jon helped us to create the purpose:

To determine the graphical and mathematical relationships that exist between the speed of the stopper and the amount of mass hanging on the string.

{We did not study the mass rotating, however you could have part of the class investigating this, and the radius if you want to "kick it up a notch"

**- Bam!**}

We found that this lab was very tricky and had lots of error. A couple points to minimize the error:

- Have the lab members keep one job: timer, recorder, twirler
- Make marks on the string to help see where it needs to be to keep a constant radius
- This is huge!
- Possibly use a force sensor held against the table.
- Possibly use video analysis to determine the actual radius
- as the ball drops, the length of the string is no longer the true radius
- cut a slit in a tennis ball and squeeze over stopper to make a more visible point.

If the students didn't already, have them create graphs of $F_{hanger}$ vs $v^2$ instead of $m_{hanger}$ vs $v^2$. When they do so, ask what the slope represents. If they aren't sure, ask what the units of the slope are (kg/m). Since the slope is constant, what mass and distance are staying constant? To which, they should reply the mass of the stopper and the radius of the circle. From there you should be able to derive the centripetal force equation:

$\large F_c = \frac {m v^2}{r}$

When we came back from lunch, Jon again attempted to shoot his ping pong launcher. See the results in this blog post.

After that, we began work on Unit VIII worksheet 1 & worksheet 2

A couple great ideas from one of our cohort to help students "see" circular motion:

- Cut a wedge out of a disposable pie pan, then roll the ball roulette style
- ball will come out in a straight line
- Have student's run down multiple flights of stairs as fast as they can
- may need to make this a "mental" experiment not an actual one.
- ask students what they must do to turn from one flight to the next while at a landing

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