Propagation of Uncertainty in labs

 In our physics classes, one experiment we do is finding speed of rolling objects. This requires us to make two different measurements, distance and time, and then calculate the speed result, v = d/t. On top of this, we normally would measure the time with a stop watch, and do multiple trials at a given distance. 

The questions becomes, knowing we are using imperfect measurements that have uncertainty, and divide them to get a result, how in the world can we combine those measurement uncertainties to get the uncertainty in the speed result??? Hmmm....

The process is called propagation of uncertainty. This video will show how to do this with a speed example, but the formula and thinking can be used in any experiment where one multiplies or divides multiple measurements! Keep in mind that if we do time trials in this example, then the uncertainty in the average time is the standard deviation of those time trials. 

How to find and use Standard Deviation in lab work

 Many believe the most important piece of a lab experiment is the result. While of course important, the most important part of experimentation is often not taught in high school - how to do an error analysis! That is, how believable and reliable are your data? If there is some huge spread in measurements with all sorts of uncertainty, then how good can results and conclusions possibly be? 

It reminds me of polling results before big elections. Suppose A is up on B in polling 51% - 49%. If this is all your given in a newscast, and it's the day before, you might cheer that A is going to win!! However, how does this conclusion change when you are informed the uncertainty of the polling is plus or minus 3%? Suddenly, we cannot reach any real conclusion about the result...it is statistically a tie, a tossup, and we'll have a nail-biter waiting for the results to come in! 

The standard way to handle uncertainty for measurements where we do multiple trials is the standard deviation. Check out how to calculate it, and how to interpret it.

Reviewing Constant Acceleration (Kinematics equations)

 Constant acceleration is the primary type of motion studied in first-year physics classes. Things like free fall with gravity (g = 9.8 m/s^2), and cars and runners starting races, or things moving down hills, can all be approximated as having constant acceleration. Keep in mind that it is a rarity to have constant acceleration in real life, but this is still a valid approximation to use. 

Check out a couple of examples to review the use of kinematics equations. This will not go away, even as we get into NON-constant forces and accelerations using the calculus. 

Using Derivatives: Redefining velocity and acceleration using motion graphs

 Calculus is one of the greatest discoveries in STEM history, and I would say in human history. Isaac Newton developed it in his studies of motion and gravity, and it is a 'tool' we will use from here on out once we get some understanding of derivatives (and later 'anti-derivatives', which will allow us to use integrals). 

Motion graphs like position vs time, velocity vs time, and acceleration vs time, are common features used to analyze motions of objects. And from last year, you may have even related velocity and acceleration to slopes of other graphs. But remember, derivative just means slope, too, only of tangent lines. 

We will now define v = dx/dt, and a = dv/dt...using slopes of tangent lines of strange curves, to determine the motion of object. This takes us to ANY MOTION, not just constant acceleration like last year!! 

Check this out to start getting some understanding. 

Introduction to Derivatives! Let's do some Calculus!

 Calculus is the mathematics of changing quantities. And one of the primary 'tools' for doing this is something called a Derivative. As usual, this is just the fancy name for a certain type of slope - the slope of a tangent line to a curve. 

It will seem weird, perhaps, to talk about slopes of curves. But this is just what we can do. And it might not seem like much at first, but the applications of this idea are vast, and we will figure some of that out over time. 

Keep in mind as you watch the video, that as far as the math goes, we are only using the normal slope equation, slope = rise/run. And then, the single step that changes a normal slope into a derivative, is a limit of two points on the curve getting unimaginably close to each other! 

But let's first define slope and see how to figure it out for a simple curve, a basic parabola. Check it out! 

The Earth's Magnetic Field weakening in certain areas, a potential reversal coming??

 The earth's magnetic field is necessary for life as we know it. It protects us from charged particles from outer space. But we know that the field has gone through dozens of reversals - there have many times when a compass needle pointed south, instead of north! Computer simulations are starting to reveal how and why this occurs, and signs of it have been observed for the past decade or two. A new 'dent' in the earth's magnetic field around one of the well known anomalies in the South Atlantic Ocean seems to fit into the continuation weakening of the field, and follows characteristics revealed and predicted in simulations leading up to reversals. 

We'll see what happens over the next couple centuries. We are actually 'overdue' for a reversal, the last one happened around 800,000 years ago. Check out a good NOVA episode on the earth's magnetic field. 

3 Chem/Phys Summer Camp

The new school year is almost upon us. And let's not hide the fact that everyone - students, teachers, parents, administrators - are some combination of nervous, scared, angry, confused, anxious, depressed, relieved, and fill in your own emotion. 

Our approach is more along the lines of developing a mindset that we are not just a class, but a learning team. We are more than classmates, we are teammates. We support each other, help each other, cheer for each other. We feel bad when another is having a bad day and try to help. We feel good when everyone 'gets it' and does well. 

This is a challenging time for everyone, so let's help each other not because some teacher wants you to...let's all actually want to help each other on our own! Let's be caring, thoughtful, compassionate and empathetic human beings who find meaning and joy in helping others through challenges. 

Class Information

You will be getting Google Classroom course numbers to sign in by the time school begins. In fact, all of your teachers will have a Google Classroom when school begins. In Physics, we will not only use Classroom, but Doc V also has the key class and unit documents housed on his school website (with Unit folders on the 3 Chem-Phys page), as well as this class blog. Check out the various pages on both the website and this blog, where there is all sorts of information not only used or class, but dozens of academic teams and extracurricular options each of you will be able to pursue if interested the next two years. 

TODAY - MONDAY, AUG. 3

We are going to break off in the Summer Camp and give you a bit of time to try a couple things asynchronously! Get used to this, because that combination of 'synchronous' Zoom class sessions and 'asynchronous' independent work will be the norm in every one of your classes. By the way, this is more like a college or adult work schedule than what you are used to in school. 

This means you have more individual control over your schedule, but also more individual responsibility for your own learning! 

To Try:

• Spend about 10 minutes to skim through the Physics website and the Physics blog. Begin to get a sense of resources, topics, activities, history, and so on. Perhaps something will already jump out at you and seem interesting! Make note of anything like this, and we can chat about it later. 

• At any time, post questions and what has been effective and not effective for you during elearning to this Google Sheet. Or you can email us separately if you don't want to share publicly. 

• Try a basic at home lab about rotational speed. You need to be logged into your eths202 account to access. We will try some of these throughout the year when we are remote. For this one, you can find any kind of sphere, any kind of disk or cylinder (like a full can of something), and if possible, a ring or hollow cylinder (like an empty can with both ends cut out). These are all objects that can roll, and you can do experiments to see if they all make it down a ramp in the same time and have the same speed at the bottom of the ramp. You did not do rotational motion last year, so this will be a new set of discoveries for you based on experimental information! 
• Our first website recommendation for the year! Check out a 3D version of the Powers of 10 video, which shows the range of smallest things to the largest! Very cool! 

Thank you for joining us today, and I cannot wait to get to know you and work with you!!