Prepping for AP Exams

The Physics AP Exam is Monday, May 10, with mechanics at noon, E&M at 2 pm.

A class motto has been: 'A problem a day keeps the 1, 2, 3's away.' You should know by now the topics and types of problems that cause you headaches, so do those problems each day (takes about 20 or so minutes to try the problem and then check the solution) to fix your understanding or to develop the right question to ask me or another student at school, and you will be set for the real thing. There are LOTS of resources and practice problems, so take advantage of them, and just dedicating 20-30 minutes per night gets you away from having to cram all weekend. Try to have some fun with it, as you try to apply all that we have learned through the year to figure out some challenging, neat problems!

Good luck over the next week and a half, and see you at school!!

How to Handle Real Pulley in a Tension Problem

This is our old favorite - a couple masses tied together, string going over a pulley. In the good ol' days, the pulley was frictionless, and we simply could say that the tensions at the two ends of the (massless) string were the same, and set up F = ma for the system to get the acceleration. Worked out well.

But, in reality the pulley accelerates, too. How do we handle this? This means there has to be a net torque on the pulley in order to cause an angular acceleration. The only way for this to happen is if the tensions on the sides of the pulley, due to the hanging masses, are different. Here we see how to deal with this new situation, and apply F = ma on the two blocks, and torque = I*alpha on the pulley. We will assume there is no slipping between the string and the pulley, so we can relate linear motion of the blocks to the rotational motion of the pulley. Check it out.

List of How to Videos on the blog

Below are links to specific “How To” videos that are relevant to 3 and 4 Chem-Phys. These show how to access programs perhaps, or how to do certain problems. It has a voice-over and screencast from Doc V’s tablet computer, so it is similar to being in class as we model how to do certain problems or run certain programs. These can be useful if you were gone the day we covered the topic, or need more examples with explanations, or want to review things from class prior to quizzams.


Student Independent Science Research
http://docvphysics.blogspot.com/2009/12/how-to-start-science-research-in-high.html


Mechanics

Air Friction – the math
http://docvphysics.blogspot.com/2009/10/how-to-deal-with-air-friction.html

Binary Orbits
http://docvphysics.blogspot.com/2009/12/how-to-find-basics-of-binary-orbits.html

Derivatives! What are they and how to do them.
http://docvphysics.blogspot.com/2009/10/how-to-define-and-find-derivatives.html

General Relativity and the Principle of Equivalence - Why does Gravity Bend Light?
http://docvphysics.blogspot.com/2010/11/basic-principle-of-general-relativity.html

Gravitational Potential Energy and Space Launches
http://docvphysics.blogspot.com/2009/12/how-to-find-gravitational-u-and-basics.html

Momentum Conservation – Why?
http://docvphysics.blogspot.com/2010/02/why-is-momentum-conserved-for-colliding.html

Momentum Conservation - How to do Inelastic Collisions
http://docvphysics.blogspot.com/2010/11/how-to-do-inelastic-collisions-where.html

Moment of Inertia Using the Integral – Disks
http://docvphysics.blogspot.com/2010/04/how-to-find-moment-of-inertia-for-solid.html

Moment of Inertia Using the Integral – Sticks
http://docvphysics.blogspot.com/2010/04/how-to-calculate-moments-of-inertia.html

Parallel Axis Theorem (finding moments of inertia)
http://docvphysics.blogspot.com/2010/03/how-to-use-parallel-axis-theorem-to.html

Pendulum: Simple Harmonic Motion for small angles
http://docvphysics.blogspot.com/2010/04/how-to-get-simple-harmonic-motion.html

Potential Wells
http://docvphysics.blogspot.com/2009/12/how-to-interpret-potential-wells.html

Quantum Numbers: Using Simple Harmonic Motion to help see where these come from
http://docvphysics.blogspot.com/2010/04/where-do-those-quantum-numbers-come.html

Rotations: Both Linear and Rotational Motion Simultaneously
http://docvphysics.blogspot.com/2010/03/how-to-handle-rotations-and-linear.html

Rotations: Collisions and Conservation of Angular Momentum
http://docvphysics.blogspot.com/2010/03/how-to-apply-conservation-of-angular.html

Rotations: NON-Constant Acceleration
http://docvphysics.blogspot.com/2010/03/how-to-do-rotational-motion-for.html

Simple Harmonic Motion: General Derivation of sine, cosine solutions
http://docvphysics.blogspot.com/2010/03/how-to-find-solutions-for-simple.html

Simple Harmonic Motion: Solving with specific initial conditions using phase angle
http://docvphysics.blogspot.com/2010/03/how-to-solve-simple-harmonic-motion.html

Special Relativity – mass and energy, where E = mc2 comes from
http://docvphysics.blogspot.com/2009/12/how-to-play-einstein-for-day-mass-and.html

Springs and Energy
http://docvphysics.blogspot.com/2010/11/spring-problems-and-use-of-energy.html

Tension problems with rotating pulleys: http://docvphysics.blogspot.com/2010/04/how-to-handle-real-pulley-in-tension.html

Tension problems with systems of objects: http://docvphysics.blogspot.com/2009/10/how-to-do-tension-problems.html



E&M

Ammeters and Voltmeters - How they work
http://docvphysics.blogspot.com/2010/12/wussup-with-ammeters-and-voltmeters.html

Ampere’s law applications
http://docvphysics.blogspot.com/2010/03/how-to-apply-amperes-law.html

Capacitance – how to find capacitance for the 3 types of capacitors
http://docvphysics.blogspot.com/2009/12/how-to-find-capacitance-for-each-type.html

Capacitor Circuits – How to find stored charge
http://docvphysics.blogspot.com/2009/12/how-to-find-charge-on-capacitors-in.html

Electric Circuit analysis
http://docvphysics.blogspot.com/2009/11/how-to-analyze-resistor-circuits.html

Electromagnetic Induction – how Induced Currents turn on (includes circulating E-field)
http://docvphysics.blogspot.com/2010/04/how-to-find-circulating-induced.html

Faraday’s law – Changing area with constant B-field
http://docvphysics.blogspot.com/2010/04/how-to-do-faradays-law-for-changing.html

Faraday’s law – Changing B-field with constant area
http://docvphysics.blogspot.com/2010/04/how-to-use-faradays-law-for-cases-where.html

Gauss’s law with conductors
http://docvphysics.blogspot.com/2009/10/how-to-do-gausss-law-with-conducting.html

Gauss’s law with NON-conductors: charge density
http://docvphysics.blogspot.com/2009/10/how-to-do-gausss-law-with-non.html

Gauss’s law with NON-uniform charge densities
http://docvphysics.blogspot.com/2010/04/how-to-do-gausss-law-with-non-uniform.html

Integration of E-fields to get Potential
http://docvphysics.blogspot.com/2009/11/how-to-integrate-and-find-electric.html

LC Circuit – similar to simple harmonic motion
http://docvphysics.blogspot.com/2010/04/how-to-do-math-of-lc-circuits.html

Magnetic Flux – Rectangular loop next to straight wire with current
http://docvphysics.blogspot.com/2010/04/how-to-find-magnetic-flux-straight-wire.html

Magnetic force between two current carrying wires
http://docvphysics.blogspot.com/2010/03/how-to-find-magnetic-forces-between.html

Mass Spectrometers and Velocity Selectors – magnetic forces, F = qv x B
http://docvphysics.blogspot.com/2010/04/how-to-think-about-mass-spectrometers.html

Point Charge Systems – finding total electric fields and potentials
http://docvphysics.blogspot.com/2010/04/how-to-find-electric-fields-and.html

Projectile Motion of Electric Charges
http://docvphysics.blogspot.com/2010/04/how-to-do-electrical-projectiles.html

RC Circuits – Charging Capacitor (series RC)
http://docvphysics.blogspot.com/2009/12/how-to-solve-charging-rc-circuit.html

RC Circuits – Discharging Capacitor (series RC)
http://docvphysics.blogspot.com/2009/12/how-to-solve-discharging-rc-circuit.html

RC Circuits – Resistor and capacitor in parallel
http://docvphysics.blogspot.com/2010/01/how-to-do-rc-circuit-with-r-and-c-in.html

RL Circuits – Current as functions of time
http://docvphysics.blogspot.com/2010/04/how-to-analyze-rl-circuits.html



Interactive Physics
Interactive Physics is software where you can design and create your own simulations; mostly for mechanics, but there are some E&M topics you can also work on. This is on school computers.
http://docvphysics.blogspot.com/2009/08/how-to-access-interactive-physics.html



iLab
See how to access the radioactivity iLab:
http://docvphysics.blogspot.com/2009/08/how-to-access-radioactivity-ilab.html

How to do the Math of LC Circuits

Interesting things happen when you combine loops of wire and metal plates in series. Inductors and capacitors together create AC currents at tunable frequencies, which in principle is the essence of our wireless society. In classical physics, the easiest way to create electromagnetic radiation is to accelerate (such as by shaking) electric charges, and that is exactly what you have in an AC current. Check this out to remind you of the math, and how LC circuits are the equivalent of simple harmonic motion of masses on springs from mechanics.

How to Find Magnetic Flux - Straight wire next to a loop

This is a classic type of problem, where a current in a straight wire is next to a rectangular loop, and we need to find the total magnetic flux through the loop. We need to break the loop into skinny strips of area, and find the flux through those skinny strips, then add them all up, i.e. integrate! Check it out to remind yourself.

How to do Electrical Projectiles

When a charge flies between the plates of a parallel-plate capacitor that is charged up, the particle will essentially be in a uniform electric field. This means there is a constant electric force, F = qE, and therefore we have a condition similar to a ball rolling off a table. The charge will move in a parabolic path as if it were a projectile...it has a constant horizontal speed, and a constant vertical acceleration. Check this out to remind yourself how to do the mechanics of a projectile.

How to think about mass spectrometers

We know that electric charges moving in magnetic fields feel a force, called the Lorentz force, which is a cross product: F = qv x B.

This force is always perpendicular to the motion and B-field, and because of this particles get pushed into circular paths. This means the centripetal force is determined by the magnetic force. No work is done, as the energy is unchanged, but just the direction of the particle is changed.

In order to get a mass spectrometer to work, we also need to know the velocity of the particles. We can use electric fields to create a velocity selector. Keep in mind there is a good ActivPhysics simulation for mass spectrometers, 13.10, you may want to check out, too.

How to Analyze RL Circuits

An inductor is like a small solenoid in a circuit. It behaves like any loop of wire with currents, and follows the rules of em induction, such as Lenz's law. Conceptually, inductors resist changes in magnetic flux. This means they fight batteries when first connected, and therefore prevent current from flowing initially, and after a long time become nothing more than wires in a circuit, with steady current flowing.

The voltage across an inductor was derived from Faraday's law to be V = -L di/dt. Inductors with current flowing around the loops of wire also has a B-field in the tube, and this field stores energy, U = (1/2)Li^2. Check out this video to see how to do the mathematical derivations of current as a function of time when inductors are in series with a resistor.

How to find electric fields and potentials for systems of point charges

One of the most essential and basic systems we study includes systems of stationary point charges. These bring out the essence of what charges do, which is produce a vector quantity, electric field, and a scalar quantity, electric potential.

We need to remember that finding electric fields includes us forgetting about the sign of a charge when calculating the fields. Being a vector, let the picture tell you whether we are dealing with positive or negative directions of components. But for potentials, which are scalars, we DO need to include the signs of charges numerically since positive charges produce positive voltage, and negative charges produce negative voltage, and we just add up the values.

How to do Gauss's law with NON-uniform charge density inside a non-conducting material

The vast majority of Gauss's law problems we do deal with uniform charge densities for non-conductors/insulators. These are the cases where there is charge inside the material, and therefore an electric field, and our job is to find the electric field inside. When the charge density, rho, is constant/uniform, the classic result is the field is linear with r. That is the result whether we have a sphere or a cylinder, and would be the same for gravity, electric fields, or magnetic fields (using Ampere's law).

But what about NON-uniform charge density, where rho depends on radius, r? What do we do with Gauss's law to find the electric fields inside these type of materials and objects? This video is an example of how to handle it. The gist is we need to set up an integral where we add the charges within skinny, hollow spheres of charge. Each little sphere has its own charge density value, and so the charge of each hollow shell is rho x dV. The trick is the dV = (4*pi*r^2)(dr), at least for a sphere. The dr is the small thickness of the hollow shell. The same idea holds for cylinders, where dV = (2*pi*L*r)(dr). I hope this helps!