MCAT Physics-FULL Guide PDF

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Physics Final Exam Review with MCAT guide...

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Translational Motion •

Dimensions (length or distance, time)

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Vectors, components

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Vector addition

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Speed, velocity (average and instantaneous)

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Acceleration

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Freely falling bodies

Force and Motion, Gravitation •

Center of mass

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Newton's first law, inertia

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Newton's second law (F = ma)

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Newton's third law, forces equal and opposite

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Concept of a field

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Law of gravitation (F = Gm1m2/r^2)

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Uniform circular motion

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Centripetal Force (F=mv2/r)

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Weight

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Friction, static and kinetic

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Motion on an inclined plane

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Analysis of pulley systems

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Force

Equilibrium and Momentum •

Equilibrium o

Concept of force, units

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Translational equilibrium (Sum of Fi = 0)

Equilibrium •

When something is in equilibrium, the vector sum of all forces acting on it = 0.

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Another way to put it: when something is in equilibrium, it is either at rest or moving at constant velocity.

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Yet another way to put it: when something is in equilibrium, there is no overall acceleration.

Concept of force, units •

Force makes things accelerate, change velocity or change direction.

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In the MCAT, a force is indicated by an arrow.

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The direction of the arrow is the direction of the force.

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The magnitude of the force is often labeled beside the arrow.

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F=ma, so the unit for the force is kg·m/s2

Translational equilibrium (Sum of Fi = 0)

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When things are at translational equilibrium, the vector sum of all forces = 0.

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Things at translational equilibrium either don't move, or is moving at a constant velocity.

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If an object is accelerating, it's not in equilibrium.

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Deceleration is acceleration in the opposite direction.

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At translational equilibrium:

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An apple sitting still.

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A car moving at constant velocity.

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A skydiver falling at terminal velocity.

NOT at translational equilibrium: o

An apple falling toward the Earth with an acceleration of g.

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A car either accelerating or decelerating.

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A skydiver before he or she reaches terminal velocity.

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Rotational equilibrium (Sum of Torque = 0)

Rotational equilibrium (Sum of Torque = 0) •

When things are at rotational equilibrium, the sum of all torques = 0.

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Conventionally, positive torques act counterclockwise, negative torques act clockwise.

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When things are at rotational equilibrium, they either don't rotate or they rotate at a constant rate (angular velocity, frequency).

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You cannot have rotational equilibrium if there is angular acceleration.

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Deceleration is acceleration in the opposite direction.

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At rotational equilibrium:

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Equal weights on a balance.

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Propeller spinning at a fixed frequency.

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Asteroid rotating at a constant pace as it drifts in space.

NOT at rotational equilibrium: o

Unequal weights in a balance such that the balance begins to tilt.

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Propeller spinning faster and faster.

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Propeller slowing down.

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Analysis of forces acting on an object

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Draw force diagram (force vectors).

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Split the forces into x, y and z components (normal and parallel components for inclined planes).

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Add up all the force components.

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The resulting x, y and z components make up the net force acting on the object.

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Use Pythagoras theorem to get the magnitude of the net force from its components.

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Use trigonometry to get the angles.

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Newton's first law, inertia

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Torques, lever arms

Torque

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Torque is the angular equivalent of force - it makes things rotate, have angular acceleration, change angular velocity and direction.

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The convention is that positive torque makes things rotate anticlockwise and negative torque makes things rotate clockwise.

Lever o

The lever arm consists of a lever (rigid rod) and a fulcrum (where the center of rotation occurs).

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The torque is the same at all positions of the lever arm (both on the same side and on the other side of the fulcrum).

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If you apply a force at a long distance from the fulcrum, you exert a greater force on a position closer to the fulcrum.

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The catch: you need to move the lever arm through a longer distance.

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Weightlessness

Weightlessness •

There are two kind of weightlessness - real and apparent. o

Real weightlessness: when there is no net gravitational force acting on you. Either you are so far out in space that there's no objects around you for light-years away, or you are between two objects with equal gravitational forces that cancel each other out.

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Apparent weightlessness: this is what "weightlessness" really means when we see astronauts orbiting in space. The astronauts are falling toward the earth due to gravitational forces (weight), but they are falling at the same rate as their shuttle, so it appears that they are "weightless" inside the shuttle.

Momentum o •

Momentum

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Momentum = mv, where m is mass, v is velocity and the symbol for momentum is p.

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Impulse = Ft, where F is force and t is the time interval that the force acts.

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Impulse = change in momentum:

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Conservation of linear momentum

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Total momentum before = total momentum after.

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Momentum is a vector, so be sure to assign one direction as positive and another as negative when adding individual momenta in calculating the total momentum.

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The momentum of a bomb at rest = the vector sum of the momenta of all the shrapnel from the explosion.

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Total momentum of 2 objects before a collision = total momentum of 2 objects after a collision.

Elastic collisions o

Perfectly elastic collisions: conservation of both kinetic energy and

momentum.

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Conservation of kinetic energy: total kinetic energy before = total kinetic energy after.

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Kinetic energy is scalar, so there are no positive / negative signs to worry about.

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If you drop a ball and the ball bounces back to its original height - that's a perfectly elastic collision.

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If you throw a ball at a wall and your ball bounces back with exactly the same speed as it was before it hit the wall - that's a perfectly elastic collision.

Inelastic collisions o

Conservation of momentum only.

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Kinetic energy is lost during an inelastic collision.

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Collisions in everyday life are inelastic to varying extents.

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When things stick together after a collision, it is said to be a totally inelastic collision.

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Work and Energy •

Work o

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Derived units, sign conventions

F is force, d is the distance over which the force is applied, and θ is the angle between the force and distance. o

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Work is energy, and the unit is the Joule.

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Joule = N·m = kg·m/s2·m = kg·m2/s2

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For a non-rotating system, friction always does negative work because it acts against the direction of motion.

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If the force is acting in one direction, but the object moves in a perpendicular direction, then no work is done.

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The classic example is that no work is done by your arms when you carry a bucket of water for a mile. Because you are lifting the bucket vertically while its motion is horizontal. o o

Amount of work done in gravitational field is path-independent

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Mechanical advantage

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Mechanical advantage = little input force (effort) -> large output force.

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Using the lever arm can achieve mechanical advantage.

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Using pulleys can achieve mechanical advantage. o o

Work-kinetic energy theorem

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When you pushing on an object, it will move: Fd = ½mv2

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When gravity does work on an object, it will move: Fweighth = mgh = ½mv2 o

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A moving object can slide up an inclined plane before coming to a stop: ½mv2 = mgh

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A moving object can slide against friction for a while before coming to a stop: ½mv2 = Ffrictiond o o

Power

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Power is the rate of work, or work over time: P = W/t

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The unit for power is the Watt, or W (don't confuse this W with the shorthand of work).

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Watt = Joule / second o

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Energy (Work is just like energy)

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Kinetic energy: KE = 1/2 mv^2; units

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KE = ½mv2

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Unit = Joule = kg·m2/s2 o o

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Potential energy

PE = 1/2kx^2 (spring) o

x is distance of the end of the spring from its equilibrium position.

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k is the spring constant.

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Stiff springs have a larger k because they are harder to stretch (it takes more energy to stretch them).

PE = -GmM/r (gravitational, general) o

This is the general formula for gravitational potential energy.

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r is the distance between the center of the two attracting objects.

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G is the universal gravitation constant - it is the same for everything.

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m and M are the mass of the two attracting objects.

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Conservation of energy

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Conservative forces

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If a force doesn't dissipate heat, sound or light, then it is a conservative force.

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Work done by conservative forces are path independent.

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Conservative forces are associated with a potential energy.

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For example, the force from a spring can be stored as spring potential energy.

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Gravitational force can be stored as gravitational potential energy.

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Electromagnetic forces are also conservative.

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non-conservative include frictional forces and human exertion. When friction acts on an object, the heat and sound released cannot be recovered. When you flex your arm, you lose heat that cannot be recovered (you cannot re-absorb the heat you lost).

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Power, units (How fast )

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Power is the rate of energy use.

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The unit for power is the Watt, or Joule per second.

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Lifting a crate in one minute requires more power than lifting the same crate in an hour. o

Waves and Periodic Motion •

Periodic motion o

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Amplitude, period, frequency

Amplitude (A): how high the peaks are or how low the troughs are, in meters. o

The displacement is how far the wave vibrates / oscillates about its equilibrium (center) position.

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The amplitude is the maximum displacement.

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Amplitude is correlated with the total energy of the system in periodic motion. Larger amplitude = greater energy.

Period (T): the time it takes for one cycle, in seconds.

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T = 1/f

Frequency (f): the rate, or how many cycles per second, in Hertz (cycles per second). o

f = 1/T

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Sometimes, frequency is in rpm (revolutions per minute). rpm = cycles per second x 60.

Angular frequency (w): the rate, in how many radians per second. o

w = 2πf

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w is also called angular velocity.

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Phase

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In phase: the waves are 0 or 2π radians (0 or 360°) apart. The resulting amplitude (sum of the waves) is twice the original.

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Completely out of phase: the waves are π radians (180°) apart. The resulting amplitude is zero.

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Out of phase: resulting amplitude is between 0 and twice the original. o o

Hooke's law, force F= -kx

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F is the force that acts to restore the spring back to its equilibrium position, or restoring force.

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k is the spring constant. Stiffer springs have a higher k value.

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x is the displacement. The amplitude (A) is the maximum x value.

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Potential energy = PE = ½kx2

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Kinetic energy = KE = ½mv2

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At the equilibrium position x = 0, PE = 0, KE = maximum.

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At the maximum displacement (amplitude) x = A, PE = maximum, KE = 0.

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At any point, PE + KE = maximum PE = maximum KE = constant.

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constant = PEmax = ½kA2

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constant = KEmax = ½mv2 at x = 0

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Simple harmonic motion; displacement as a sinusoidal function of time

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x = A·sin(wt)

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x is displacement.

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A is amplitude.

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w is angular frequency (also called angular velocity).

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t is time.

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Examples of simple harmonic motion o

Oscillating spring.

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Pendulum.

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Things going around a circle at constant speed (when plot the x axis position against time).

Motion of a spring with mass attached to its end

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T is period, m is the mass of the attached mass, and k is the spring constant.

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A simpler way to express this is:

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w is the angular frequency. The spring vibrates faster if it's stiffer and if the mass attached to it is smaller

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Motion of a pendulum

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T is period, L is the length of the string, and g is 9.8.

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A simpler way to express this is:

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w is the angular frequency. The pendulum oscillates faster when gravity is large and when the string is short. o o

General periodic motion: velocity, amplitude

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At the equilibrium position, PE = 0, KE = maximum.

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At the maximum displacement (amplitude) x = A, PE = maximum, KE = 0.

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At any point, PE + KE = maximum PE = maximum KE = constant.

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constant = PEmax o

= ½kA2 for a spring.

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= mgA for a pendulum, where A is the maximum height that the pendulum can gain during a swing.

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constant = KEmax = ½mv2 at the equilibrium position.

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If you are given the velocity at the equilibrium position, then you should be able to find out the amplitude by setting maximum KE = maximum PE.

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If you are given the amplitude, then you should be able to find out the velocity at the equilibrium position by setting maximum PE = maximum KE. o

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Wave Characteristics o

Transverse and longitudinal waves

Transverse wave: wave displacement is perpendicular to the direction of motion. •

Light.

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Electromagnetic radiation.

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A standing wave by oscillating a string side ways. The speed for such a wave = square root of (string tension / mass per unit length of the string). For the MCAT, just know that tense, light strings can produce faster transverse waves.

Longitudinal wave: wave displacement is parallel to the direction of motion. •

Sound.

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Pressure wave.

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Earth quakes. o o

Wavelength, frequency, velocity

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v = fλ

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v is velocity, f is frequency, and λ is wavelength. o o

Amplitude, intensity

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Amplitude is correlated with the energy of the wave. Greater amplitude = greater energy of the wave.

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Intensity = energy per area per time = power per area.

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Thus, amplitude and intensity are correlated. Greater amplitude leads to higher intensity.

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Special note on electromagnetic waves: amplitude and intensity increases the overall energy of electromagnetic waves such as light. However, neither amplitude nor intensity changes the energy per photon. Energy per photon depends on wavelength. The shorter the wavelength (also the higher the frequency), the greater the energy. o o

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Superposition of waves, interference, addition

· · When waves superimpose on each other, they interfere. · Interference results from the addition of waves. · When in phase waves add, the resulting wave has a greater amplitude. · When out of phase waves add, the resulting wave has a smaller amplitude. · Constructive interference: addition of waves resulting in greater amplitude. · Destructive interference: addition (cancellation) of waves resulting in diminished amplitude. o o •

Resonance

Resonance is when things oscillate at its maximum amplitude.

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Resonance occurs at resonance frequencies. o o

Standing waves, nodes

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Standing waves vibrate at resonance frequencies.

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Standing waves do not propagate like other waves (that's why they're called standing waves).

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Node: point where there's no oscillation.

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Antinode: point where there's maximum oscillation. http://mcat-review.org/resonance-frequencies.gif

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Frequencies can be obtained by f = v/λ

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Both strings and tubes open at both ends have L = n/2λ

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Tubes with a closed end ha...