Physics

frequency

# rotations/second f = 1/T hertz (Hz)

period

(T) the time required for one cycle, a complete motion that returns to its starting point T = 1/f

Newton's Third Law

(The law of action and reaction) To every action, there is always an opposed but equal reaction.

Newton's First Law

(The law of inertia) "A body in motion will stay in motion, and a body at rest will stay at rest, unless acted upon by an external force." F=ma=0

Newton's Second Law

(ΣF=ma) No acceleration of an object with mass "m" will occur when the vector sum of the forces results in a cancellation of those forces (vector sum equals zero) When the resultant force upon an object is zero, the object will not accelerate. Its motional behavior will be constant

mean free path

(λ) The average distance a molecule travels between collisions with other molecules.

mean free time

(τ) The average time between the collisions of a molecule. Is the mean free path divided by a typical speed, and the usual choice is the rms speed: τ = kB T / 4√2πr^2 PVrms

gravitational constant

6.67E-11 N*m²/kg²

completely inelastic collision

A collision in which the colliding objects stick together. Conservation of momentum as long as the vector sum of any forces (friction) is zero. mavai+mbvbi = (ma+mb)vf

Isotherm

A curve showing p as a function of V with the number of molecules and the temperature fixed. Then, for an ideal gas, pV = constant. For example, the volume of the gas decreases as the pressure increases. The resulting graph is a hyperbola.

friction force

A electromagnetic force that opposes motion between two surfaces that are in contact Ff = µFn

centripetal force

A force that acts on a body moving in a circular path and is directed toward the center around which the body is moving. In uniform circular motion, the tangential force is zero (a=0) because there is no change in the speed of the object. *Acceleration points towards the center, not tangent to the path. Remember, acceleration is always in the same direction of the resultant (sum or difference) force. Thus, the resultant (sum or difference) force is the radial (center-seeking) force, i.e. the centripetal force.

Carnot cycle

A hypothetical working cycle with the highest possible efficiency between the same two reservoirs. An engine operating in this cycle is called a Carnot engine.

Temperature

A measure of the average kinetic/mechanical energy of the particles in a system.

monatomic gas

A monatomic gas consists of single atom molecules (He), have no energy except their translational kinetic energy, and have neither rotational nor vibrational energy.

Scalar

A physical quantity that has magnitude only. Distance, speed, energy, pressure, and mass.

Maxwell-Boltzmann distribution

A predictable distribution of molecular speeds. With a finite number of molecules, the probability that a molecule will have exactly a given speed is 0. The most probable speed (peak speed) Vp is less than the rms speed Vrms . Although very high speeds are possible, only a tiny fraction of the molecules have speeds that are an order of magnitude greater than vrms.

reversible process

A process in which the system and environment can be restored to exactly the same initial states that they were in before the process occurred. A process that can be made to retrace its path by differential changes in the environment. Such a process must therefore also be quasi-static. Note, however, that a quasi-static process is not necessarily reversible, since there may be dissipative forces (friction) involved. It is quite easy to restore a system to its original state; the hard part is to have its environment restored to its original state at the same time. Both isothermal and adiabatic processes sketched on a pV graph are reversible in principle because the system is always at an equilibrium state at any point of the processes and can go forward or backward along the given curves. There is no net change in the entropy of a system undergoing any complete reversible cyclic process.

heat

A process of energy transfer, not itself energy. Heat is energy transferred spontaneously from a hotter to a colder system or body. Heat is energy in transfer, not a property of any one system, or 'contained' within it. Heat and work depend on the way in which an energy transfer occurred. Heat transfer "quantity of heat" (Q) is the change in the internal energy, which is the total energy of the molecules, and is typically proportional to the change in temperature and to the number of molecules, N. Q = mcΔT Q is expressed in J or kcal c is expressed in J/kg · °C or kcal/kg · °C

quasi-static process

A process that takes place in infinitesimally small steps, keeping the system at thermal equilibrium. Quasi-static processes are done slowly enough that the system remains at thermodynamic equilibrium at each instant, despite the fact that the system changes over time. In a quasi-static process, the path of the process between A and B can be drawn in a state diagram since all the states that the system goes through are known. An isothermal process is quasi-statically performed, since to be isothermal throughout the change of volume, you must be able to state the temperature of the system at each step, which is possible only if the system is in thermal equilibrium continuously.

Energy

A property or characteristic of a system to do work or more broadly, to make something happen SI unit is the joule (J) kg(m^2/s^2) 4.184 J = 1 cal

Momentum

A quality of an objects motion. The product of an object's mass and velocity. p = mv Has magnitude and direction and thus is a vector quantity.

Speed

A scalar quantity. The rate of actual distance traveled in a given unit of time. The instantaneous speed of an object will always be equal to the magnitude of the object's instantaneous velocity, which is a measure of the average velocity as the change in time (delta t) approaches 0.

electric field

A vector field (an assignment of a vector to each point in a subset of space) surrounding an electric charge that exerts force on other charges, attracting or repelling them. A field, in physics, is a physical quantity whose value depends on (is a function of) position, relative to the source of the field. A continuous, immaterial substance that surrounds the source charge, filling all of space—in principle, to ±∞ in all directions. The electric charge on an object alters the space around the charged object in such a way that all other electrically charged objects in space experience an electric force as a result of being in that field. The electric field, then, is the mechanism by which the electric properties of the source charge are transmitted to and through the rest of the universe. The direction of any electric field vector is the same as the direction of the electric force vector that the field would apply to a positive test charge placed in that field. It is independent of the test charge. Notice that the calculation of the electric field makes no reference to the test charge. It only depends on the configuration of the source charges. The units of the electric field: From F = QE , the units of E are newtons per coulomb, N/C, that is, the electric field applies a force on each unit charge. The value of E (both the magnitude and the direction) depends on where in space the point P is located, measured from the locations ri of the source charges qi.

Displacement

A vector quantity (magnitude and direction) that connects (in a straight line) the object's initial position and its final position. Describes an object's change in position from the starting point.

Velocity

A vector quantity that includes the speed and direction of an object. Its magnitude is measured as the rate of change of displacement in a given unit of time. v = 2πr/t = wr

state variables

A well-defined quantity that depends only on the current state of the system, rather than on the history of that system. Temperature and internal energy are state variables. Heat and work are not state variables

centripetal acceleration

Acceleration of an object toward the center of a curved or circular path. Both force and acceleration are vectors and the acceleration is always in the same direction as the resulting force. Thus, it is this acceleration generated by the centripetal force that keeps an object in its circular path. ac = v2/r

degree of freedom

An independent possible motion of a molecule, such as each of the three dimensions of translation. A diatomic ideal gas, such as N2 and O2, has more degrees of freedom than a monatomic gas. In addition to the three degrees of freedom for translation (d=3), it has two degrees of freedom for rotation perpendicular to its axis (d=5), and the molecule can vibrate along its axis (d=7). Note: Vibrational motion has both kinetic and potential energy. Each of these forms of energy corresponds to a degree of freedom, giving two more.

PV diagram

An isotherm plot, which is a curve showing p as a function of V with the number of molecules and the temperature fixed (pV = constant). The resulting graph is a hyperbola. At high temperatures, the curves are approximately hyperbolas, representing approximately ideal behavior at various fixed temperatures. At lower temperatures, the curves look less and less like hyperbolas—that is, the gas is not behaving ideally.

torque

Application of force at some distance from the fulcrum, along the lever arm. Torque depends on: 1) magnitude of the force 2) the angle at which the force is applied against the lever arm 3) the distance between the fulcrum and the point of force application t = rFsinθ Torques that generate clockwise rotation are conventionally negative. Torques that generate counterclockwise rotation are positive. sin90=1, thus the torque is greatest when the force applied is 90 degrees (perpendicular) to the length of the lever arm. sin0=0, thus there is no torque when the force applied is parallel to the lever arm.

completely elastic collision

Both total momentum and total kinetic energy are conserved (nothing lost). Objects do not stick together No energy of motion was transformed in the instance of the collision into another form, such as thermal, light, or sound. Objects will almost always experience changes in their velocity (magnitude and/or direction); It is the TOTAL kinetic energy, not the individual velocities or even the individual kinetic energies of the objects, that remains constant. mavai+mbvbi = mavaf+mbvbf (conservation of momentum in a completely elastic collision) 1/2mav^2ai+1/2mbv^2bi = 1/2mav^2af+1/2mbv^2bf (conservation of kinetic energy in a completely elastic collision)

Impulse

Change in momentum Vector quantity When net force acts on an object, thus changing its motion (a=nonzero #), the object's momentum also changes. For a constant force applied through a period of time: I = FΔt = Δp= mv2-mv1, F = Δp/Δt If impulse is constant, there is an inverse relationship between force magnitude and time I/t=F. The longer the period of time through which this impulse is achieved, the smaller the force necessary to achieve the impulse

Acceleration

Change in velocity divided by the time it takes for the change to occur The only manner by which an objects motion can change is when there is a net force acting on it to cause it to accelerate. Vector quantity

Molar heat capacity of an ideal gas under constant pressure (Cp)

Cp = Cv + R The derivation of Cp was based only on the ideal gas law. Consequently, this relationship is approximately valid for all dilute gases, whether monatomic like He, diatomic like O2, or polyatomic like CO2 or NH3.

Dalton's law of partial pressures

Dalton's law states that the total pressure is the sum of the partial pressures of all of the component gases present, assuming ideal gas behavior and no chemical reactions between the components. For any two gases (labeled 1 and 2) in equilibrium in a container: p1/n1 = p2/n2

Gravitational potential energy

Depends on a body's position with respect to some level identified as "ground" or the zero potential energy position. U = mgh (the U is in a direct linear relationship with all three of the variables)

Efficiency

Efficiency = Wout/Win Efficiency of this ideal gas Carnot engine: e = 1 - Tcold/Thot

first law of thermodynamics

Energy can be transferred and transformed, but it cannot be created or destroyed. A change in the internal energy of a system comes from changes in heat or work. The first law is a statement of energy conservation. It tells us that a system can exchange energy with its surroundings by the transmission of heat and by the performance of work. The net energy exchanged is then equal to the change in the total mechanical energy of the molecules of the system (i.e., the system's internal energy). Thus, if a system is isolated, its internal energy must remain constant. Although Q and W both depend on the thermodynamic path taken between two equilibrium states, their difference Q − W does not.

Entropy

Entropy, like internal energy, is a state function. This means that when a system makes a transition from one state into another, the change in entropy ΔS is independent of path and depends only on the thermodynamic variables of the two states. ΔS for a system undergoing a reversible process at a constant temperature: ΔS = Q/T There is no net change in the entropy of a system undergoing any complete reversible cyclic process. the entropy change of a system undergoing a reversible process between two given states is path independent. When the process is irreversible, we expect the entropy of a closed system, or the system and its environment (the universe), to increase. In any irreversible process, the universe becomes more disordered.

gravitational force equation

F = Gm1m2/r^2

centripital force equation

F = mv^2 / r

Conservative forces

Forces that have potential energies associated with them. a) If the net work done to move a particle in any round tip path is zero b) If the net work needed to move a particle between two points is the same regardless of the path taken Most popular on MCAT: gravitational and electrostatic When work done by nonconservative forces is zero, or when there are no nonconservative forces acting on the system, the total mechanical energy of the system remains constant: ΔE=ΔU+ΔK=0.

Second Law of Thermodynamics (Clausius statement)

Heat never flows spontaneously from a colder object to a hotter object. The word "spontaneously" here means no other effort has been made by a third party, or one that is neither the hotter nor colder object.

intensive variables

Independent of the size of the system (pressure and temperature).

internal (thermal) energy

Internal energy is a state function that depends on only the temperature of an ideal gas. In an ideal gas, the internal energy is the statistical mean of the gas particles' kinetic energy. The sum of the mechanical energies of all of the molecules in a thermodynamic system. Internal energy can be increased or decreased by heat transfer or by doing work on it. The increase in internal energy is equal to the total heat added plus the work done on the system by its surroundings. The equation for the internal energy of a monatomic ideal gas: Eint = (3/2)NkBT Eint = (3/2)nRT In an ideal monatomic gas, each molecule is a single atom. Consequently, there is no rotational or vibrational kinetic energy. The molecules' only energy is their translational kinetic energy secondary to its monatomic nature. Furthermore, there are no interatomic interactions (collisions notwithstanding), so Ui = constant. The internal energy of a given quantity of an ideal monatomic gas depends on just the temperature and is completely independent of the pressure and volume of the gas. An increase in internal energy can often be associated with an increase in temperature.

conservative system

Is a system that does not loose energy through work The sum of the kinetic and potential energies will be constant KE1+PE1=KE2+PE2

Second Law of Thermodynamics (Kelvin statement)

It is impossible to convert the heat from a single source into work without any other effect. All reversible engine cycles produce exactly the same efficiency

inelastic collision

Momentum is conserved, but the total kinetic energy of a system is decreased (transformed/"lost"). The change in kinetic energy will be equal to the amount of energy released from the system in the form of heat, light, or sound. The final kinetic energy will be less than the initial kinetic energy. 1/2mav^2ai+1/2mbv^2bi > 1/2mav^2af+1/2mbv^2bf

conservation of momentum

Momentum of a system remains constant when there are no net external forces acting on it, or if external forces are present, the vector sum of the external forces acting on that system is zero. ***Think of the 3 types of collisions: -Completely elastic -Inelestic -Completely inelastic Momentum is concerved in an idealized collision (instintanious and in a specific location) as long as no net external forces act on the objects. The vector sum of the momenta is constant: the total momentum after the collision is equal to the total momentum before the collision. Indivigual changes in momentum may occure (objects may expereince changes in velocity as a result of the collision), but total momentum is conserved. pai+pbi=paf+pbf mavai+mbvbi=mavaf+mbvbf

Carnot's Principle

No engine working between two reservoirs at constant temperatures can have a greater efficiency than a reversible engine.

mechanical equilibrium

Occurs when the vector sum of the forces or torques acting on an object is zero; that is, when all of the force vectors or torque vectors cancel out.

Supercritical gas

PT diagram: At sufficiently high pressure above the critical point/temperature the gas has the density of a liquid but will not condense. PV diagram: At sufficiently low pressure above the critical temperature (Tc), the gas has the density of a liquid but will not condense. At higher pressure, it is solid. Carbon dioxide is supercritical (PT diagram) and has no liquid phase (PV diagram) at a temperature above 31.0 ºC (the critical temperature)

Boyle's Law

PV=k For a given mass of gas at constant temperature, pressure times volume always equals the same number (volume and pressure are inversely proportional).

nonconservative forces

Path dependent. The work done is not stored as potential energy Causes dissipation of mechanical energy from a system. The total energy of a system is conserved, but nonconservative forces such as friction or drag (due to a fluid such as air or water) convert some mechanical energy (U+K) into thermal energy (the energy contained within a system that is responsible for its temperature) as heat. When nonconservative forces (friction or drag) are present, total mechanical energy is not conserved: W'(work of nc forces)=ΔE=ΔK+ΔU.

Vectors

Quantities that have both a magnitude and a direction. Displacement, velocity, acceleration, and force.

Resultant vector

Sum or difference of two or more vectors.

Third Law of Thermodynamics

The absolute zero temperature cannot be reached through any finite number of cooling steps. In other words, the temperature of any given physical system must be finite, that is, T > 0. A system becomes perfectly ordered when its temperature approaches absolute zero and its entropy approaches its absolute minimum. If there could be a reservoir at the absolute zero temperature, we could have engines with efficiency of 100% , which would, of course, violate the second law of thermodynamics.

kinetic theory

The average kinetic energy of a molecule is directly proportional to its absolute temperature: K = (1/2)mv^2 = (3/2)kBT The equation K=(3/2)kBT is the average kinetic energy per molecule. This equation does NOT depend on any property of a gas (molecular mass, pressure, etc.) except for the temperature. At the same temperature, any molecules have the same average kinetic energy. The energy of (3/2)kBT is the sum of contributions of (1/2)kB T from each of the three dimensions (V^2x, V^2y, V^2z) of translational motion. For a monatomic ideal gas, the molecules' only energy is their translational kinetic energy. The internal energy is the sum of the mechanical (kinetic) energies of all of the molecules in it. Therefore, denoting the internal energy by Eint, we simply have Eint = NK. Eint = (3/2)NkBT Eint = 3nRT/2

Kinematics

The branch of Newtonian mechanics that deals with the description of motion

Coulomb's Law

The electric force F on one of the charges is proportional to the magnitude of its own charge and the magnitude of the other charge, and is inversely proportional to the square of the distance between them: F ∝ (q1q2)/r^2 1on2 This proportionality becomes an equality with the introduction of a proportionality constant.

Kinetic energy

The energy of motion. K = 1/2 mv^2 The SI unit is joule (J) kg(m^2/s^2) *Kinetic energy is a function of the square of the velocity. So if the velocity doubles, the kinetic energy will quadruple (assuming the mass is constant) The average kinetic energy of a molecule is: K=(3/2)KbT

Potential energy

The energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors. Energy that could be used to do work (not potentially energy, its potential work!) -Gravitational potential energy -Electric potential energy -Mechanical potential energy (compressed spring Fs=kx) -Chemical potential energy (between the covalent and ionic bonds holding atoms together in molecules)

Second Law of Thermodynamics (Entropy statement)

The entropy of a closed system and the entire universe never decreases.

Ideal Gas Law

The equation of state of an ideal gas. The ideal gas law describes the behavior of any real gas when its density is low enough or its temperature high enough that it is far from liquefaction. Most gases are nearly ideal unless they are close to the boiling point or at pressures far above atmospheric pressure. *(boiling point = vapor pressure approx 1 atm = increased density of gas) *(pressure > 1atm = decreased volume = increased density) PV=NkB T, PV=nRT Where p is the absolute pressure of a gas in pascals (Pa) (the sum of gauge pressure and atmospheric pressure), V is the volume it occupies (m^3), N is the number of molecules in the gas, or n is the number of moles, T is its absolute temperature, kB = Boltzmann Constant 1.38x10^-23 J/k, and R = universal gas constant, R = NA kB, 8.31 J/mol K. The term (NkB T) is roughly the total translational kinetic energy (the energy of translation of a molecule, not that of vibration of its atoms or rotation) of N molecules at an absolute temperature T. Pressure multiplied by volume (PV) has units of energy (Joule), (kg)(m^2/s^2). The energy of a gas can be changed when the gas does work as it increases in volume, and the amount of work is related to the pressure (gasoline or steam engines and turbines).

kinetic friction

The force that opposes the movement of two surfaces that are in contact and are moving over each other.

Newton

The international unit of measure for force. One newton is equal to 1 kilogram meter per second squared. The force required to accelerate an object with a mass of 1 kilogram 1 meter per second per second.

vapor pressure

The partial pressure of a vapor at which it is in equilibrium with the liquid (or solid, in the case of sublimation) phase of the same substance. At any temperature, the partial pressure of the water in the air cannot exceed the vapor pressure of the water at that temperature, because whenever the partial pressure reaches the vapor pressure, water condenses out of the air.

critical point/temperature-PT diagram

The point at which the boiling point curve ends. The point at which the liquid and gas phases cannot be distinguished; the substance is called a supercritical fluid. The point on the PV diagram at the critical pressure and temperature is the critical point.

partial pressure

The pressure a gas would create if it occupied the total volume available. Partial pressure is the pressure a gas would create if it existed alone. In chemistry, it functions as the concentration of a gas in determining the rate of a reaction.

critical pressure

The pressure of the critical point. The maximum pressure at which the liquid can exist.

Molar heat capacity at constant volume (Cv)

The properties of an ideal gas depend directly on the number of moles in a sample, so here we define specific heat capacity in terms of the number of moles (Q = nCvΔT), not the mass (Q = mcΔT). Q = nCvΔT, Q = 3/2nRΔT Cv = 3/2R for an ideal monatomic gas. Q = heat transfer Qhot + Qcold = 0 Using molar heat capacity at constant volume: ΔEint = Q = nCvΔT + mLf + mLv *(W not included due to no volume change or displacement) Using heat capacity by mass: ΔEint = Q - W = mcΔT + mLf + mLv The "3" in the formula reflects each of the three dimensions of translational motion, i.e. the number of degrees of freedom. Cv = d/2 R, d = 3. *Volume does not change, there is no overall displacement, so no work is done, and the only change in internal energy is due to the heat flow ΔEint = Q.

Extensive variables

The quantity associated with an amount of matter (volume and the number of moles). Variables dependent on the size or amount of the system. An extensive variable doubles its value if the amount of matter in the system doubles, provided all the intensive variables remain the same.

Power

The rate at which energy is transformed from one system to another P = W/t, W=work (measured in joules) P = (Fd)/t, V = d/t, thus P =FV The SI unit for power is the watt (W=J/s) The advertised power of various appliances is a measure of the rate at which these appliances transform ("consume") electrical potential energy into other forms such as thermal, light, sound, and kinetic energy.

Relative Humidity (RH)

The ratio of the moisture content of the air (partial pressure) to the maximum possible moisture content (vapor pressure) at given temperatures.

equation of state

The relationship between measurable properties of the system (pressure, volume, temperature, and the number of molecules or moles of the gas). The range of specific relevant variables depends upon the system. For example, the thermodynamic variables for a stretched rubber band are tension, length, temperature, and mass. Describes the state of matter under a given set of physical conditions. An example of an equation of state for an ideal gas, f(p, V, T) = pV − nRT = 0.

peak speed (Vp)

The speed at the peak of the velocity distribution. (In statistics it would be called the mode.) It is less than the rms speed Vrms.

root-mean-square (rms) speed

The square root of the average of the square of the speed v2. The rms speed is not the average or the most likely speed of molecules, but it provides an easily calculated estimate of the molecules' speed that is related to their kinetic energy. The rms speed is greater than both the most probable speed (Vp) and the average speed. *Note: A high value for rms speed is reflected in the speed of sound, which is about 340 m/s at room temperature. The higher the rms speed of air molecules, the faster sound vibrations can be transferred through the air. The speed of sound increases with temperature and is greater in gases with small molecular masses, such as helium.

cyclic process

The state of the system at the end is same as the state at the beginning. Therefore, state properties such as temperature, pressure, volume, and internal energy of the system do not change over a complete cycle: ΔEint = 0. The heat into the system equals the work done by the system over the cycle: Q = W (cyclic process)

Mechanical potential energy

The sum of an objects potential and kinetic energies is its total mechanical energy. E = U + K Constant in the absence of nonconservative forces such as frictional forces

irreversible process

The system and its environment cannot be restored to their original states at the same time. Because this is what happens in nature, it is also called a natural process. The sign of an irreversible process comes from the finite gradient between the states occurring in the actual process. For example, when heat flows from one object to another, there is a finite temperature difference (gradient) between the two objects. More importantly, at any given moment of the process, the system most likely is not at equilibrium or in a well defined state.

adiabatic process

The system is insulated from its environment so that although the state of the system changes, no heat is allowed to enter or leave the system (Q = 0). An adiabatic process can be conducted either quasi-statically or non-quasi-statically. When a system expands adiabatically, it must do work against the outside world, and therefore its energy goes down, which is reflected in the lowering of the temperature of the system. An adiabatic expansion leads to a lowering of temperature, and an adiabatic compression leads to an increase of temperature.

Dew point

The temperature at which condensation occurs for a sample of air. The temperature seldom falls below the dew point, because when it reaches the dew point or frost point, water condenses and releases a relatively large amount of latent heat of vaporization.

critical temperature (Tc)-PV diagram

The temperature at which the PV curve has a point with zero slope. The isotherms above Tc do not go through the liquid-gas transition. Therefore, liquid cannot exist above that temperature. Below that temperature, the curves do not decrease monotonically; instead, they each have a "hump," meaning that for a certain range of volume, increasing the volume increases the pressure (completely unphysical). The curves "humps" are understood as describing a liquid-gas phase transition (boiling and condensation); when a substance is at its boiling temperature for a particular pressure, it can increase in volume as some of the liquid turns to gas, or decrease as some of the gas turns to liquid, without any change in temperature or pressure.

Inertia

The tendency of objects to resist changes in their motion and momentum. The resistance of any physical object to any change in its position and state of motion. This includes changes to the object's speed, direction, or state of rest

work-energy theorem

The work done on or by an object equals the change in kinetic energy of the object Wnet = ΔK = Kf - Ki Used to calculate work (when the magnitude or displacement through which the forces act on an object are unknown) through the change in kinetic energy.

Linear motion equations

V = V0 + at Δx = V0t + 1/2at^2 V^2 = V0^2 + 2aΔx Δx = vt

Work

W = Fd W = Fdcosθ (θ is the angle between the applied force vector and the displacement vector) SI unit is the joule (J) kg(m^2/s^2), same as energy! Not a form of energy, but a process by which energy can be transferred (a change in energy). The process by which a quantity of energy is moved from one system to another. When an external force is applied to a system and changes the energy of that system. A change in system energy means work is being done on it. Ex: pushing a box from rest over a distance changes its kinetic energy from 0 to a nonzero value. thermodynamic work is path dependent

circular motion

When a force causes an object to curve in a circular pathway. For circular motion at a constant speed, the instantaneous velocity vector is always tangent to the circular path.

rotational motion

When forces are applied against an object in such a way as to cause the object to rotate around a fixed pivot point (the fulcrum).

translational motion

When forces cause an object to move without any rotation about a fixed point in the object. May be linear or parabolic (of or like a parabola or part of one).

Translational Equilibrium

When the vector sum of all forces (the resultant force) acting on an object is zero, thus, the object will not accelerate. Its motional behavior will be constant (a=0). An object experiencing transnational equilibrium will have a constant speed a=0 (which could be zero or nonzero value) and a constant direction. Called the first condition of equilibrium

rotational equilibrium

When the vector sum of all the torques acting on an object is zero. Called the second condition of equilibrium All the positive torques exactly cancel out all of the negative torques

static friction

exists between a stationary object and the surface upon which it rests. 0≤fs≤µsFn The maximum value for the static friction will always be greater than the constant value for kinetic friction.

kinetic friction equation

f(k)= u(k)Fn f(k)=kinetic friction u(k)=coefficient of kinetic friction Fn=the normal force (no "≤ sign" like the static friction equation) The kinetic friction will have a constant value for any given combination of a coefficient of kinetic friction and normal force. *No matter how much surface area or even the velocity of the sliding object.

Van der Waals equation of state

used to improve the ideal gas law by taking into account two factors: intermolecular attractions and molecular volume. (a) Intermolecular attractions, i.e. the attractive forces between molecules, which are stronger at higher density and reduce the pressure, are taken into account by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. (b) The volume of the molecules is represented by a positive constant b, which can be thought of as the volume of a mole of molecules. This is subtracted from the total volume to give the remaining volume that the molecules can move in. In the limit of low density (small n), the a and b terms are negligible, and we have the ideal gas law, as we should for low density.

angular velocity

w = 2π(radians) / t(seconds) how quickly an object goes around something over a period of time.