Notes

Topic (in alphabetical order)

Circular Motion

Forces and Motion

Geometric Optics

Simple Harmonic Motion

Universal Gravitation

Topic	Notes
Circuits	What is a Circuit? A closed path through which charge can flow. Types of Circuits Series The charges have only one possible path to follow. Parallel The charges have multiple paths they can follow. Complex A circuit in which portions are wired in series and portions are wired in parallel. Most real circuits fall into this category. Current Current is the amount of charge that flows past a point in a given time interval. For current to flow certain conditions must be met: There must be a complete path for the current to flow through. There must be a potential difference present. Potential difference causes current to flow. Current is measured in amperes. Resistance Charge flows more easily through some substances than others. Substances through which it is more difficult for charge to flow are said to be more resistive. How much an object resists the flow of charge is measured by its resistance. Charge tends to follow the path of least resistance. i.e. more current flows through paths with less resistance. Resistance is measured in ohms. If multiple resistors are present in a circuit, one can find the equivalent resistance of the entire circuit. For series circuits, R_eq=R₁+R₂+R₃+... For parallel circuits, 1/R_eq=1/R₁+1/R₂+1/R₃+... Ohm's Law Ohm discovered that potential difference, resistance and current are related by the simple relationship V=IR. If one makes a graph of V as a function of I, a straight line with the slope being equal to R. Meters Current is measured by an ammeter. Ammeters are wired in series with the device one wishes to know the current through. Ammeters have very low resistance so they do not use up a significant amount of the circuit's electrical energy. Potential difference is measured by a voltmeter. Voltmeters are wired in parallel with the device one wishes to know the potential difference across. Voltmeters have large resistance so they do not have a significant amount of current flowing through them. Kirchoff's Laws Kirchoff's Loop Rule (Conservation of Energy in circuits) The sum of all changes in potential in a closed loop is 0. Kirchoff's Junction Rule (Conservation of Charge in circuits) The sum of all currents going into a junction equals the sum of all currents leaving a junction. Capacitance Capacitors are devices which store electrical energy by storing charge. Capacitance is charge stored per unit potential difference across the capacitor. The capacitance of a device depends solely upon geometry.
Circular Motion	Centripetal Force Centripetal force is a net force. To find a centripetal force, sum all forces (as vectors!) pointing towards or away from the center of the circle.
Electrostatics	Electric Fields Charge distributions produce electric fields. Electric fields exert a force on charge. Electric fields are vectors. Electric fields are illustrated using electric field lines. Electric field lines always point from positive charge towards negative charge. Stronger fields have more field lines per unit area. Electrostatic Force The electric force on a charge is equal to the charge multiplied by the electric field acting on it. The force on a negative charge always points in a direction opposite the electric field. The force on a positive charge always points in the same direction as the electric field. Electrostatic forces are conservative. Potential Difference When a charged particle is moved through an electric field, work is done on it. There is a change in electrostatic potential energy associated with this work. Potential difference is defined as the change in electrostatic potential energy per unit charge. Potential difference is a scalar. Two points in space with 0 potential difference between them are said to be equipotential. The entire surface of a conductor is considered an equipotential.
Forces and Motion	Notes on Specific Forces Here is a Force Fact Sheet listing information on many common forces. Remember a normal force only exists when there are two surfaces in contact with one another. The force due to a string is not a normal force, but tension; the force acting on the bottom of an airplane in flight is not a normal force, but lift.
Geometric Optics	Sign Convention Image distance is positive (negative) when the rays converge (diverge) as they leave an optical element. The focal length of an optical element is positive (negative) when incident parallel rays leaving the element converge (diverge). Object distance is positive (negative) when rays diverge (converge) as they approach an optical element. (Yes, you can have negative object distance!) Real vs. Virtual Images Real images have positive image distance, are inverted, have negative magnification, and can be projected onto a screen. Real images form where light rays converge. Virtual images have negative image distance, are upright, have positive magnification, and cannot be projected onto a screen. Virtual images form where light rays WOULD converge if they existed at that point. Magnification As the distance between the object and an optical element changes, so does the magnification of the image. Magnification as a function of object distance for elements of both positive focal length (concave mirrors and biconvex lenses) and negative focal length (convex mirrors and biconcave lenses) is plotted here.
Kinematics	Rule of Thumb If an object is slowing down, then the direction of the acceleration is opposite the direction of the velocity. If an object is speeding up, then the direction of the acceleration is the same as the direction of the velocity. Graph Relationships Velocity is the slope taken from a displacement-time graph. Displacement is the area under a velocity-time graph. Acceleration is the slop taken from a velocity-time graph. Velocity is the area under a acceleration-time graph. Tutorial This link will take you to a tutorial on kinematics.
Magnetism
Simple Harmonic Motion	Mass-spring System Basic model for all SHM. This applet demonstrates how the motion can be considered harmonic in nature. Notice that the displacement-time graph is a sinusoid. The velocity-time and acceleration-time graphs will also be sinusoids. The total energy in a mass-spring system is 1/2kA². Simple Pendulum This applet demonstrates how the motion can be considered harmonic in nature. Resonance This applet demonstrates resonance. Examine what happens when the frequency of oscillation approaches the resonant frequency.
Thermodynamics	Sign Convention Our sign convention for thermodynamics is essentially a bookkeeping system. Energy put into the system is like a credit. Energy taken out of the system is like a debit. Work done by a system is negative (-). Work done on a system is positive (+). Heat transferred from a system is negative (-). Heat transferred to a system is positive (+). If a system loses internal energy over a process, the change in internal energy is negative (-). If a system gains internal energy over a process, the change in internal energy is positive (+). Zeroth Law of Thermodynamics If two systems are in thermal equilibrium with a third system, then they are in thermal equilbrium with each other. First Law of Thermodynamics The change in internal energy of a system is equal to the sum of the work done on/by that system and the heat transferred to/from that system. Second Law of Thermodynamics Heat flows naturally from "warmer" bodies to "cooler" bodies. This will not spontaneously happen in reverse. Thermodynamic Processes Isothermal The system remains at a constant temperature throughout the process. Pressure and volume must change to accommodate the constant temperature. This indicates that work must be done on/by the system. Applying the ideal gas law to a closed system, we see that for temperature to remain constant, the product of pressure and volume must remain constant as well. No temperature change means no change in internal energy. As such, if work is done on the system in an isothermal process an amount of heat equal to the work must be transferred from the system. Conversely, if work is done by the system in an isothermal process an amount of heat equal to the work must be transferred to the system. Heat must be exchanged. Adiabatic No heat is exchanged throught the process. Reversible adiabatic processes are isentropic - the entropy of the system does not change. Pressure, volume and temperature change. Applying the First Law of Thermodynamics, we see that the change in internal energy is equal to the work done on/by the system. This change in internal energy corresponds to a change in temperature. Isochoric The system remains at a constant volume throughout the process. Because there is no change in volume, there is no work done on/by the system. Applying the First Law of Thermodynamics, we see that the change in internal energy is equal to the heat transferred to/from the system. This change in internal energy corresponds to a change in temperature. Isobaric The system remains at constant pressure throughout the process. Work is done on/by the system. Heat is exchanged to/from the system. The internal energy of the system changes. This change in internal energy corresponds to a change in temperature.
Universal Gravitation	General Notes All masses exert a gravitational pull on other masses. This force is always attractive. The gravitational attraction between two masses acts along a line connecting their centers of mass. Consider two masses, A and B. The gravitational force that A exerts on B is equal in magnitude but opposite in direction to the gravitational force that B exerts on A. This fact is an illustration of Newton's Third Law. Gravitational Fields All masses produce a gravitational field that interacts with other masses. The gravitational force between two masses can be considered the gravitational field of one mass telling the other mass how to behave. Gravitational fields have the unit of acceleration (meters per second squared). The familiar formula for determining the force due to gravity acting on an object at Earth's surface (F_G=mg) can now be considered the Earth's gravitational field strength being mutliplied by the mass it is acting on.
Vectors	Vectors in Two Dimensions This powerpoint illustrates how to add vectors and resolve them into components. Here is a link to a web tutorial on vectors. This animation shows one way to define direction for a vector in two dimensions. Vector Addition This animation shows how to add multiple vectors in two dimensions. Notice that the resultant is the same regardless of the order in which the vectors are added. Vectors may be added graphically or analytically. For graphical addition, be sure that the tail of one vector touches the head of the other. In graphical addition, the resultant is always drawn from "start to finish". In graphical addition, we measure the magnitude of the resultant with a ruler. In graphical addition, we measure the direction of the resultant with a protractor. For anayltic addition, we must break each vector down into its components using trigonometry. Once the vector components are found, they may be added one dimension at a time, giving the components of the resultant. In analytic addition, the magnitude of the resultant is found by applying the Pythagorean Theorem to its components. In analytic addition, the direction of the resultant is found by taking the arctangent of the ratio of the two components. Resolving Vectors Into Components Any vector may be resolved into two perpendicular components. We find the components by applying the SOH, CAH, TOA rules learned in trigonometry. Once found, components may be treated as vectors in one dimension. Here is a link on how to find vector components.