The infamous 'Bowling ball' problem!! Rotations!!

 Things like bowling balls, hitting a billiard ball, and tires on an icy road, sees examples of motion we can label slipping, rolling AND slipping, or rolling WITH NO slipping. These are objects and situations where all three motions can be seen one after the other. The 2012 AP Physics C Mechanics problem #3 was this problem, with a ring doing it. 

A bowling ball type problem sees several key concepts from rotational motion make an appearance, and this video walks through the details about how to think about the situation. The concepts are not too difficult in their own right, but combining them tends to be where confusion and self-doubt enter into the psychology of the problem! Check it out, see if this makes sense. 

Rotational motion - some lab examples

 Here are a few examples of objects that rotate. Remember that rotational motion is NOT the same as circular motion of point masses moving on a circular path; instead it is where all points of a solid, rigid body moves together through an angle. 

Check these out, hopefully it will help reinforce things like moment of inertia and torque, as well as angular displacement or angular velocity. 

Simple harmonic motion (SHM) - Some lab examples

 Check out some examples we would see in the lab for Simple harmonic motion (SHM). A normal spring is the prime example of this motion, where the restoring force depends on the displacement from equilibrium. A spring is F = -kx. So check these out, and we'll figure out the math in class or in the following videos: 

SHM of a spring

SHM for a pendulum (small angle approximation)

SHM for a swinging stick (small angle approx.)

Interesting Stats on STEM employment by race, gender

 A recent update on data collected for STEM employment is broken down by both race and gender. While progress has been made, it largely varies from field to field. 

Check it out.

Faraday's law - The glider problem and heating, B dA/dt case

 Imagine a glider with a wire hoop (circuit) on it, and it slides into a constant B-field. As long as the loop is entering the B-field, and the flux is changing (increasing), an emf and current are induced. This is a case where emf = induced voltage = B dA/dt. 

This example walks us through step by step, but then has a focus on how the glider slows down in time, and how much heat energy is burned off due to current flowing through a resistance. 

Check it out. See if it makes sense. If the glider could have the braking force acting until the glider stops, the energy burned off should be equivalent to the initial KE. Let's see what Faraday's law and others say about this thought! 

Possible hint of new physics at Fermilab

 From my old stomping grounds of Fermilab, about an hour outside Chicago and Evanston, comes measurements of muon magnetic properties that deviate significantly from the Standard Model, the theory we have that explains everything we know about the particles and forces of Nature, with the exception of gravity. 

Muons are in the electron family (200 times more massive...a heavy electron, basically, but it also decays with a lifetime of around 2.2 microseconds), and therefore 'spin' like the electron does. When you put spinning charged particles in a magnetic field, they precess...like a spinning top does if it is slightly tilted while spinning, and its whole axis rotates in a cone shape. By measuring these gyrations of muons as they spin in magnetic fields, precise measurements of their behavior are made. And these behaviors differ from what is predicted in the Standard Model. Some of the only theoretical explanations for such a difference involves new types of particles/matter. 

Check out this article if interested. This is also a good example of how discovery claims need to hold up to standards in a field built around error analysis! There needs to be a large enough gap between the predicted and lab results, but also a large enough gap between their error bars, of 5 sigma (5 standard deviations). The experiments still need more data to shrink these error bars a little smaller before they can claim discovery of some new physics, but it is getting close, and therefore more and more convincing that something new is out there!! 

Faraday's law: Lab examples of AdB/dt

 Faraday's law says that there is an induced voltage (emf) created if you change the magnetic flux through a conductor. Mathematically, this is induced voltage = d(BA)/dt, since flux is magnetic field times the area it flows through. 

One way to cause a change is to change the B-field through an area, or emf = A dB/dt. To see the math for this case, check this video out. 

Here are some lab examples where we see this happening. By the way, the physical reason why and how this works is that whenever you change a magnetic field, it induces a circulating electric field! It is an E-field that is turning on the current in the loops of wire and metal! 

Faraday's law: Lab examples of induced voltage = B dA/dt

 Faraday's law is one of the most important discoveries in the history of physics, in my opinion. It is relatively simple in its mathematical form, but in terms of applications it is invaluable and tells us how to create 90-something percent of the world's electricity, from generators in power plants. 

Faraday's law is: emf = induced voltage = d(BA)/dt. Magnetic flux = (B)(A), where A is the area the magnetic field flows through. 

This video shows a few lab examples of what it looks like for the case of emf = B dA/dt, where the area is changing due to some type of motion of the conductor (loops of wire). To see the math for this case, check out this video.