Scientists can now measure the mass of individual molecules

A new nanodevice is able to measure the mass of a single molecule.  The way this works is the device has a certain vibrational frequency.  This is like a spring that is oscillating at some frequency (simple harmonic motion).  But what we learn about springs is that the frequency depends on the mass that is attached to the spring.  What happens with this device is that when a molecule lands on the device, the frequency changes.  It is the change in frequency that determines the mass.

So this is a wonderful example of taking a basic physics principle and applying it in a new environment.  The engineering of the device is, of course, tricky, but the principle can be understood with the physics we study in class.  Very cool!

Special Relativity: From energy to particle-wave duality

In 1905, Einstein published what is now called special relativity.  We have the famous E = mc^2 as well as some other results: time slows down with speed, lengths get shorter with speed, and mass increases with speed.  If it helps, the idea of mass increasing makes sense straight from E = mc^2.  If an object moves faster, the total energy increases since there is more kinetic energy.  So the left side increases.  This means the right side must increase as well, but c cannot change (it is a constant, the speed of light).  This means the only thing that can and does change is the mass increases.

Einstein united space and time into a single 'fabric' we call the space-time continuum. Keep in mind that he also united mass and energy.  They aren't just related to each other, they are equivalent to each other!  It is sort of like saying they are two forms of the same stuff.  I like to think of ice and steam - there is no reason at all to think they are related just by looking at them, but with closer inspection they are both two forms of the same stuff, water.

In this video we will focus on the mass equation, and see what Einstein's energy equation is, where the notion of antimatter comes from, and where the idea of 'matter waves' comes from!  These are some of the foundations of modern science, and we can derive them in just a few minutes.  Check it out!!

Motion Graphs and the Meaning of Slope on These Graphs

Here we take a look at a more visual way of analyzing motion, motion graphs.  These refer to those graphs of position vs time, velocity vs time, and acceleration vs time.  What is cool about these is that when you get good at reading the graphs, you can picture the motion of the object the graphs are describing.  We will use one of the ActivPhysics simulations (1.2) to help connect the initial conditions, the actual motion of a car, and the motion graphs to each other.  I recommend playing with these simulations on your own (1.2, 1.3), and you will find yourself getting better and better of making all the connections.

Now, for us we will include the calculus.  Specifically, slopes of the motion graphs are important.  And we now know that derivatives are really just slopes of graphs, even if they are curves.  This is what we are after in this video lesson.

velocity = slope of position graphs = dx/dt
acceleration = slope of velocity graph = dv/dt

Focus on these definitions as you watch.

How to do Vector Addition to get Net Force

One basic skill we use over and over in physics and engineering is adding vectors to find the total, or resultant or net, vector.  Vectors are those quantities with BOTH magnitude and DIRECTION, such as forces.  Obviously, gravity has a direction of 'down' and is therefore a vector.

The easiest problem is when there are two vectors on the same line, called colinear vectors.  These we just add, if in the same direction, or subtract, if in opposite directions.  The trickier problems are when forces are pulling in multiple dimensions.  This is where the rules for right triangles are needed.  We can use sine, cosine, and tangent to figure out how much of each individual force is in the x and y directions.  We can also use these functions to determine the direction of the net force, and therefore the direction the object will actually start moving.  Remember Chief SOH-CAH-TOA for the definitions of these trig functions!

Check out this example with three force vectors.  Keep in mind to use a table of x and y components in all your problems to keep things organized - it will help.