ONE PAGE REVIEW OF KINEMATICS
Displacement – A change of position in particular direction. Unit: m
Average Velocity = Unit: m/s
(Instantaneous) Velocity – Value of velocity at a particular time. Unit: m/s
Acceleration = Unit: m/s2
Acceleration can cause: 1. change in speed (speeding up: v and a in the same direction;
slowing down: v and a in the opposite direction)
2. changing direction
3. both
Motion with constant velocity(including horizontal component of projectile motion)
v =
Motion with constant acceleration a (including free fall and vertical component of projectile motion)
vf = vi + at x = vit + at2 vf2 = vi2 + 2ax
For free fall and vertical component of projectile motion g = 9.8 m/s2
Tricks and Key words:
- Stop / dropped / at rest / rolled off means v = 0
- If something is ‘thrown horizontally’ then its initial vertical velocity is 0.
- vertical v at highest point in projectile / free fall is zero
- Free fall is symmetrical (i.e. vi = -vfif thrown and landed at same height)
- You never have to use the quadratic formula (unless you love it). You can always do a two step problem to find anything you need.
Projectile Motion: treat vertical and horizontal motion separately. They do not affect one another in any way! Vertical motion uses accelerated motion equations; horizontal motion has no force acting, so uses v = x/t only.
Graphs for:
ONE PAGE REVIEW OF FORCES
Inertia is resistance an object has to a change of velocity
Mass is numerical measure of the inertia of a body / is a measure of the amount of matter in the object unit: kg
• doesn’t depend on the location of the object . Object of mass of 1 kg here on earth would have the mass
of 1 kg on the moon, even though it would weigh only one-sixth as much.
Weight is the gravitational force acting on an object . • W = mg unit: Newton (N)
Net force, Fnet, is the vector sum of all forces acting on an object
Free Body Diagram/ Force diagram is a sketch of a body and all forces acting on it.
Newton’s first law: An object continues in motion with constant speed in a straight line (constant velocity)
or at rest unless acted upon by a net external force.
If net force is zero, acceleration is zero, velocity is constant (or zero).
The object is in equilibrium. Any force acting on it is balanced.
Newton’s second law: If a net force is acting on an object of mass m, object will acquire acceleration proportional to the net force and inversely proportional to the mass of the object. Direction of acceleration is direction of the net force.
Newton’s third law:
Whenever object A exerts a force on object B, object B exerts an equal in magnitude but
opposite in direction force on object A
FA - force object A exerts on object B
FB - force object B exerts on object A
Tension isa force that the end of the rope exerts on whatever is attached to it.
Direction of tension is along the rope.
Normal force is the force which is preventing an object from falling through the surface of another body .
That’s why normal force is always perpendicular (normal) to the surfaces in contact.
Friction force is the force that opposes slipping (relative motion ) between two surfaces in contact;
it acts parallel to surface in direction opposed to slipping.
Friction depends on type and roughness of surfaces and normal force.
Ffr = μ Fn μ is called coefficient of friction
• μ has no units
• it is a measure of surface-to-surface roughness
• depends on characteristics of both surfaces
• different values for static and kinetic coefficient of friction (tables)
• kinetic μ is smaller than static μ. You probably noticed that once you moved
something from rest it becomes easier to push around.
Newton’s Law of Universal Gravitation: Forcebetween masses m1 and m2 that are at distance r from each other
attract each other with the force
F = G
ONE PAGE REVIEW OF WORK, ENERGY, AND MOMENTUM
Momentum, p ismass times velocity:p = m v vector! unit: (p) = kg m/s
Impulse F∆t will produce change in momentum Δp: F∆t = ∆p Δp = mvf - mvi
Example: You want to throw a ball (m=0.5 kg) over a tree. You hit it at 60o so it leaves your hand at the speed of 10 m/s. Unfortunately that was not enough. Your ball is now stuck in the tree. It was just at its maximum height. What impulse did you impart on the ball. What impulse did the tree exert on the ball?
you: impulse = change in momentum = 5 kg m/s.
tree: at the top speed is equal to the horizontal component of the velocity = 10 cos 600 = 5 m/s impulse = change in momentum = 2.5 kg m/s
Law of conservation of momentum:
In collision pafter = pbefore m1vi1 + m2vi2 = m1vf1 + m2vf2
WORK and ENERGY (measured in Joules)
Work done by external force changes potential energy (when net force is zero, so there is no acceleration).
Gravitational Potential energy, PE = mgh
Work done by net force changes kinetic energy (net force gives acceleration, therefore changes velocity).
the change in the kinetic energy of the object is equal to the net work done on the object.
W = ∆KE = KEf – KEi = ½ mvf2 – ½ mvi2
Example: Firework explodes into three pieces of equal mass. They all move in three different directions each with the speed v.
What work was done on firework?
W = ∆KE = 3(½ mvf2) In addition remember that momentum must be conserved !!!!!
Conservation of energy law
For the system that has only mechanical energy (ME = PE + KE)
and there is no frictional force acting on it, so no mechanical energy
is converted into heat, mechanical energy is conserved
ME1 = ME2 = ME3 = ME4
mgh1 + ½ mv12 = mgh2 + ½ mv22 = • • • • • •
ONE PAGE REVIEW OF STATIC ELECTRICITY
Charge, q: Comes in two forms + and -; opposite charges attractive, same charges repel; measured in units of Coulombs (C)
The only type of charge that can move around is the negative charge, or electrons. The positive charge stays in the nuclei. So, we can put a NET CHARGE on different objects in two ways
◊ Add electrons and make the object negatively charged.
◊ Remove electrons and make the object positively charged.
Electrical conductors, insulators, semiconductors and superconductors
-distinction based on their ability to conduct (transfer between materials) electric charge.
-Conductorshave loosely bound electrons, allows them to conduct heat and electricity.
Examples: human body, metals, tap water
-Insulatorshave tightly bound electrons, which makes them poor conductors of heat and electricity.
Examples: rubber, plastic, dry air
-Semiconductorssometimes act as conductors, sometimes as insulators. Useful as switches. Can easily adjust the amount of resistance.
Examples: silicon, germanium
-Superconductorshave virtually no resistance, which means they can transmit current with no energy loss.
Examples: metals or ceramics at exceptionally cold temperatures (between 0 – 100 K)
Polarization occurs when charge becomes separated on a neutral object (one side becomes positively charge, one side becomes negatively charged). Objects can become polarized if they are brought close to a charged object.
Electrostatic Force between TWO POINT charges q1 and q2 at distance r from each otheris proportional to the product of the amount of the charges on each one, and inversely proportional to the square of the distance between them.
Force is a vector, therefore it must always have a direction.
ONE PAGE REVIEW OF CIRCUITS
OHM’S LAW: Current through resistor is proportional to potential difference
across the resistor and inversely proportional to resistance
of that resistor.
Electric power, P, is the rate at which energy is supplied to or used by a device in which electric energy is
converted into another form such as mechanical energy, thermal energy, or light.
Power dissipated in a resistor: P = I V P =
Power of the source = ε I
Electric energy is:
Electromotive force, , is the voltage generated by battery (how much energy per unit charge is available for
the circuit including internal resistance)
Resistors in Series
• connected in such a way that all components have the same current through them.
Resistors in Parallel
• Electric devices connected in parallel are connected to the same two points of an electric circuit, so all components have the same potential difference across them.
• The current flowing into the point of splitting is equal to the sum of the currents flowing out at that point:
The greater resistance, the smaller current.
A device that transforms mechanical energy into electrical energy is called a generator.
A device that transforms electrical energy into mechanical energy is called anelectric motor.
A transformer is a device that transforms/change voltage.
ONE PAGE REVIEW OF MAGNETISM
The direction of a magnetic field line is defined as the direction in which the north pole of a compass points when it is placed in the magnetic field.
Outside the magnet, the field lines emerge from the magnet at its north pole and enter the magnet at its south pole.
Inside the magnet, there are no isolated poles on which field lines can start or stop, so magnetic field lines always travel inside the magnet from the south pole to the north pole to form closed loops.
Magnetic field is measured in Tesla 1 T(Tesla) =
- An electric charge experiences a magnetic force when moving in a magnetic field.
Magnetic force acting on a charge q
in a magnetic Field B: F = qvB sin
q = charge [C]
v = velocity [m/s]
B = magnetic field [Tesla T]
= angle between v andB
- RHR 1: The direction of the magnetic force on a charge/current is given by the right-hand rule 1:
Outstretch fingers in the direction of v (or current I).
Rotate wrist so that palm faces the magnetic field.
Magnetic force on a positive charge is in the direction of the thumb.
Magnetic force on a negative charge points in opposite direction.
- A moving charge produces a magnetic field.
A solenoid is a coil of wire with an electric current. The shape of the solenoid creates a strong uniform magnetic field within the center of the coil. You can find the direction of the magnetic field using RHR for solenoids.
RHR for solenoids:
Curve your fingers around coil so fingers point
in direction of current.
Thumb shows direction of magnetic field.
3. Electricity can be generated (induced) when a magnetic field and a conductor move past each other.
If you move a long conducting rod perpendicularly through a magnetic field, then
EMF = lvB EMF = voltage induced (units: V) v = velocity of conductor (units: m/s)
l = length of conductor (units: m) B = strength of magnetic field (T)
One Page Review of Waves
Wave variables
Amplitude, A – maximum displacement from equilibrium (units: m)
Wavelength, λ– of a wave is the distance from one point on a wave to the next corresponding point (e.g. from crest to crest, or from compression to compression) (units: m)
Period, T – time for one complete oscillation of a wave (units: s)
Frequency, f – of a wave is the number of complete cycles each second (units Hz)T = 1/f ; f= 1/T.
Speed, v - The speed with which wavefronts pass a given point. The speed of a wave depends upon the medium!
Types of Waves
Electromagnetic vs Mechanical – Electromagnetic waves (light waves) occur due to the oscillation of the electric and magnetic fields. They do not require a medium to travel, and all travel at the speed of light in a vacuum (c = 3.00 X 108 m/s). Mechanical waves occur due to the oscillation of atoms within a medium. Mechanical waves only propagate through a medium. (That’s why you wouldn’t hear sound in space!)
Longitudinal vs Transverse – In longitudinal waves, the particles oscillate parallel to the direction of the wave. Longitudinal waves create areas of high pressure (compressions) and areas of low pressure (rarefactions). Sound is an example of a longitudinal wave. In transverse waves, the particles oscillate perpendicular to the medium, creating crests and troughs. EM waves are transverse.
Wave behaviour
Reflection occurs when a wave bounces back after encountering a new medium.
Law of reflection: the angle of incidence = the angle of reflection
Refraction occurs when a wave bends as it transmits through a new medium. Refraction occurs because waves change speed when they enter a new medium.
Rule of thumb: The medium that has the bigger angle (angle of incidence or angle of refraction) has the greater speed.
Snell’s law: n1sin(θ1) = n2sin(θ2)
Index of refraction (n)
Diffraction occurs when a wave spreads out behind an obstruction or opening. Diffraction effects are big when the wavelength is big and the obstruction / slit is small. Audible sound diffracts (goes around obstacles) much better than visible light because sound has much larger wavelengths. Echolocation works because dolphins and bats produce small wavelengths of sound that reflect off objects rather than diffract around them.
Dispersion occurs when a wave separates into its component frequencies (such as the formation of a rainbow as light goes through a prism). It occurs because different frequencies diffract to different degrees as they enter a new medium.
Doppler Effectis the observed change in frequency of a wave that occurs when an observer and the wave source are in motion relative to each other. When the observer and the source are moving closer together, the apparent frequency is higher. When the observer and the source and moving farther apart, the apparent frequency is lower.
Interference occurs when two waves occupy the same spot at the same time. When two waves meet, they do not affect each other in any way, but what we observe is the sum of the displacements from each wave.
Principle of Superposition: When two or more waves overlap, the resultant displacement at any point and at any instant is the sum of the displacements of the individual waves at that point.
Constructive interference: Occurs when waves are in phase / oscillate in the same direction at a given point. Results in an increase in amplitude / loud sounds / bright spots
Destructive interference: Occurs when waves are out of phase / oscillate in opposite directions at a given point. Results in a decrease in amplitude / quiet sounds / dark spots
Beats: Are variation in the loudness of sound (throbbing sound) that results from the interaction of two waves of slightly different frequency
Standing waves are the result of the interference of two identical waves traveling in opposite direction (such as a wave and its reflection).