Organic Chemistry Common Names

Formyl Group

Formaldehyde

Formic Acid

Acetyl Group

Acetaldehyde

Acetic Acid

Acetone

Acetylacetone

Acetophenone

Benzyl Group

Benzaldehyde

Benzoic Acid

Benzoin

Styrene

Acryl Group

Acrolein

Acrylic Acid

Carboxyl Group

Carboxylate Ion

Carbonate Ion

Carbonic Acid

The Heart Oxygen Transport

The Heart and Oxygen Transport

Anatomy of the Heart

Blood Flow Through the Heart

Electrical Conduction Through the Heart

Hemoglobin

Found in blood. It has four polypeptide chains (tetramer), each combined with an iron-containing heme group. Most oxygen transport takes place through the use of hemoglobin. A small amount of oxygen will still dissolve in the plasma and be transported on its own.

Each RBC contains 2.7 × 108 hemoglobin molecules.

Cooperative Binding: When an O2 binds to one of the four binding sites, it becomes more likely that the remaining sites will bind to O2.

CO2 and H+ Inhibition: Allosterically inhibits hemoglobin. That means CO2 and H+ will trigger the heme group to release its O2.

The process starts when CO2 enters the RBC where carbonic anhydrase resides (the enzyme for the bicarbonate buffer). The CO2 combines with H2O to make H2CO3 which dissociates into H+ and HCO3. The H+ allosterically inhibits hemoglobin, e.g. changes the shape of hemoglobin, so it can’t hold onto the O2. Since CO2 initiates this process, the result is O2 is released near lots of CO2, which is where respiration is happening and O2 is needed.

↓pH ⇒ ↓Heme affinity for O2, curve shifts RIGHT (Bohr shift).

2,3-BPG Inhibition: Another allosteric regulator. It places itself in the center of the tetramer and causes α and β subunits to release their O2. Note, fetal hemoglobin has α and γ (gamma) subunits. γ subunits do not respond to 2,3-BPG, so HbF ends up with more O2 than HbA. 2,3-BPG causes a RIGHT shift on the dissociation curve, like CO2 and H+.

↑2,3-BPG means your body needs more oxygen.

CO2 Transport: After delivering O2 to a muscle, the CO2 that triggered the release of O2 will remain in the hemoglobin. The RBC then travels back to the lung, bringing the CO2 with it.

Fetal Hemoglobin: HbF has a higher affinity for O2 compared to adult hemoglobin (HbA). This is because its tetramer contains γ subunits, which don’t respond to 2,3-BPG. HbF dissociation curve has a LEFT shift, as if 2,3-BPG levels are low.

p50: Oxygen pressure when 50% of hemoglobin has an O2 bound. P50 is LOWER for HbF due to the high affinity HbF has for oxygen.

Sickle Cell Anemia: A disease that affects hemoglobin. Caused when Val replaces Glu. Hemoglobin aggregates into insoluble fibers. Glu ⇒ Val

Hypoxia: Oxygen deprivation.

Binding of Oxygen to a Heme Prosthetic Group

Without O2, the Fe atom sits below the plane. When O2 binds, the electrons in the Fe atom rearrange so it fits in the hole and becomes level with the plane; also pulls His up towards the plane.

Myoglobin

Found in muscle tissue, it stores and releases oxygen. It is a monomer and contains only 1 heme group. Myoglobin is NOT pH sensitive.

O2 Affinity: Myoglobin has a much HIGHER oxygen affinity than hemoglobin. This means it can bind more securely to the oxygen.

Heme Group: Myoglobin has only 1 heme group. This is why it cannot exhibit cooperative binding and it has a hyperbolic curve.

2,3-BPG: 2,3-BPG has NO AFFECT on myoglobin.

Hemoglobin and Myoglobin Dissociation Curves

Brain

The Brain
Cerebrum

Higher brain function such as though and action.

Cerebral Cortex: Layer of grey matter on the outside of the Cerebrum.
Primary Cortex: Basic motor and sensory functions.
Associative Cortex: Associates different types of information to do more complex processing and functions.

Prefrontal Cortex: Located at the front of the brain, behind the forehead. It is part of the Cerebral Cortex. Associated with “cerebral” activities. Ex: If your instinct is to attack someone, your prefrontal cortex will think about it and tell you to walk away.

Frontal Lobe: Reasoning, planning, speech production (Broca’s Area), movement, emotions, and problem solving.

Temporal Lobe: Perception of auditory stimuli, memory, and language comprehension (Wernicke’s Area).

Parietal Lobe: Movement, orientation, proprioception, recognition and perception of stimuli.

Occipital Lobe: Visual processing.

Hemispheres and Functions:

Left: Language, logic, math and science, analytic thought, written, right-hand control.

Right: Creativity, 3-D forms, imagination, intuition, art & music, left-hand control.

Hemispheres and Emotion:

Left: Positive emotions, more sociable, joyful, enthusiastic.

Right: Negative emotions, socially isolated, fearful, avoidant, depressed.

Cerebellum

Motor control. Regulation and coordination of movement, posture, and balance. The cerebellum does not initiate mvmt, it helps control and smooth out the mvmt.

Movement Control: The cerebellum receives a motor plan from the Cerebrum and compares it to position sense information from Somatosensory Neurons. It then determines if corrections are necessary. If needed, the cerebellum will tell the cerebrum to adjust the mvmt.

Speech Control: Cerebellum coordinates the mouth muscles that produce speech.

Damage: Damage to the cerebellum produces disorders in fine movement, equilibrium, posture, and motor learning. The damage could also impair speech enunciation or eye movement.

Limbic System

Sits on top of the brain stem.

Hypothalamus: “Below the thalamus”. Regulates the autonomic nervous system via the endocrine system. The four Fs.

Amygdala: Aggression center. Fear and anxiety. Stimulation causes more fear & anxiety. Damage causes mellow mood, and less fear; hypersexuality, disinhibition. Kluver-Busy Syndrome is the destruction of the amygdala.

Thalamus: Sensory relay station.

Hippocampus: Converts STM → LTM. If damaged, new memories fail to form.

Brain Stem

Connects all parts of the nervous system together, including cranial nerves.

Pons: Regulates waking and relaxing.

Reticular Formation: Alertness and motivation. Controls autonomic functions such as circulation, respiration and digestion. Also plays a role in higher cognition functions.

Medulla: Regulates the autonomic activity of the heart and lungs.

Long Tracts: Collections of axons connecting the cerebrum to the spinal cord, passing through the brainstem. Upper motor neurons signaling down and somatosensory long tracts signaling up.

Endocrine Organs and Hormones

Hypothalamus

“Below the thalamus”. Regulates the autonomic nervous system via the endocrine system. The four Fs.

GnRH: Gonadotropin-Releasing Hormone. Stimulates the release of FSH and LH.

GHRH: Growth Hormone-Releasing Hormone. Stimulates the release of GH.

TRH: Thyrotropin-Releasing Hormone. Stimulates the release of TSH.

CRH: Corticotropin-Releasing Hormone. Stimulates pituitary synthesis of ACTH.

PIF or Dopamine: A catecholamine. As a neurotransmitter, most rewards will increase the level of dopamine.

ADH: Produced in the hypothalamus; released from the posterior pituitary.

Anterior Pituitary

Anterior lobe of the pituitary gland. It regulates several physiological processes including stress, growth, reproduction, and lactation.

FSH: Follicle-Stimulating Hormone. A gonadotropin. In males it promotes spermatogenesis. In females it stimulates growth of ovarian follicles.

LH: Luteinizing Hormone. A gonadotropin that induces ovulation.

ACTH: Adrenocorticotropic Hormone. Stimulates the production and release of cortisol.

TSH: Thyroid-Stimulating Hormone. Stimulates the Thyroid to produce Thyroxine (T4) and Triiodothyronine (T3), which stimulates metabolism.

Prolactin: Stimulates milk production.

Endorphins: ↓Pain

Growth Hormone: Also known as somatotropin. Stimulates growth and cell reproduction.

Pancreas

A large gland behind the stomach. It secretes digestive enzymes into the duodenum. Embedded in the pancreas are the islets of Langerhans which secrete insulin and glucagon into the blood.

Insulin: Peptide hormone secreted by β-islet cells. Its function is to help glucose enter the cells. ↑Glucose triggers insulin secretion. Inhibited by norepinephrine.

Glucagon: Peptide hormone secreted by α-islet cells. Its function is to help glucose enter the blood stream. ↓Glucose triggers glucagon secretion.

Somatostatin: Growth Hormone-Inhibiting Hormone. A peptide hormone (GHIH) secreted by δ-islet (delta) cells. Inhibits GH and also leads to ↓Insulin and ↓Glucagon.

Posterior Pituitary

Posterior lobe of the pituitary gland.

ADH (Vasopressin): Antidiuretic Hormone. A peptide hormone synthesized in the hypothalamus and released by the posterior pituitary. It regulates the tonicity of body fluids. ADH is released in response to hypertonicity and causes the kidneys to reabsorb H2O. Results in concentrated urine and reduced urine volume. Can also ↑BP.

Oxytocin: A peptide hormone synthesized in the hypothalamus and released by the posterior pituitary. During childbirth, it increases uterine contractions and is released in response to cervix stretching. Also increases milk production and certain bonding behaviors.

Gonads

A gland that produces gametes (sex cells) and sex hormones. In males, the gonads are testicles, in females they are ovaries.

Testosterone: Produced by the testes in men and ovaries in women with a small amount produced by the Adrenal Cortex. In males, it is the primary sex hormone and an anabolic steroid.

Estrogen: Produced by the ovaries. It is the primary female sex hormone and leads to the development of secondary sexual characteristics. Estrogen also regulates the menstrual cycle. ↑Milk production.

Progesterone: Produced by the ovaries. Prepares the endometrium for potential pregnancy following ovulation. ↑Milk production.

Thyroid Gland

In the neck and below the Adam’s Apple. Secretes thyroid hormones that regulate metabolism. Also helps regulate calcium homeostasis.

T3 & T4: Thyroxine (T4) and Triiodothyronine (T3). T4 is a precursor to T3. Regulates metabolism. Created from Iodine and Tyrosine.

Calcitonin: Builds bone
↓Ca2+ in bone
↑Ca2+ excretion from kidneys
↓Ca2+ in blood
↓Ca2+ absorption in gut

Pineal Gland

Located in the epithalamus, tucked into a groove between the two thalamus halves.

Melatonin: Regulates sleep / wakefulness and controls the circadian rhythm.

Parathyroid Glands

A collection of 4 parathyroid glands located on the back of the thyroid. Primary function is to maintain the body’s Ca2+ and K+ levels so that the nervous and muscular systems can function properly.

PTH: Parathyroid Hormone. Bone breakdown.
↑Ca2+ in bone
↓Ca2+ excretion from kidneys
↑Ca2+ in blood
↑Ca2+ absorption in gut
Activates Vitamin D (Calcitriol)

Adrenal Cortex

Sits along the perimeter of the adrenal gland (top of kidney). Mediates stress response.

Glucocorticoids: Cortisol is released during stress.
↑Glucose in blood through gluconeogenesis
↓Immune system
↓Protein synthesis
Cortisone is similar to Cortisol.
↓Immune response to ↓inflammation and ↓allergic response

Mineralocorticoids: Aldosterone causes ↑Na+ in blood which ↑BP. It is regulated by K+ and angiotensin II which is derived from angiotensin I.

Androgens: Converted to Testosterone and Estrogen in the gonads.

Adrenal Medulla

Sits on top of the kidney. Adrenal Medulla is located at the center of the adrenal gland, surrounded by the adrenal cortex. It converts tyrosine into catecholamines.

Epinephrine: ↑HR and ↑BP. Primarily a hormone. Also an anti-histamine.

Norepinephrine: ↑HR and ↑BP. A hormone and a neurotransmitter; inhibits insulin.

Dopamine: The adrenal medulla secretes a small amount of dopamine.

Lab Techniques

Gel Electrophoresis

Separates macromolecules (proteins, DNA, or RNA). For proteins and small molecules the gel is polyacrylamide. For larger molecules (>500 bp), the gel is agarose. Negatively charged molecules travel toward the anode at the bottom. Large molecules will move SLOWER. Coomassie Blue stain can be used for visualization.

Southern Blotting: Detection of a specific DNA sequence in a sample.

Northern Blotting: Detection of a specific RNA sequence in a sample.

Western Blotting: Detection of a specific PROTEIN in a sample.

Chromatography

Separates two or more molecules from a mixture.

Stationary Phase: Typically polar. Polar molecules elute slower.
Mobile Phase: Typically nonpolar. Nonpolar molecules elute faster.

Gel electrophoresis

Sanger DNA Sequencing

Chain termination method. Uses dideoxy nucleotides. The ddNTP lacks a hydroxyl group on the 3’ carbon of the sugar ring. With the 3’ hydroxyl group missing, no more nucleotides can be added to the chain. The chain ends with the ddNTP, which is marked with a particular color of dye depending on the base that it carries.

After mixing all components, it is virtually guaranteed that a ddNTP has incorporated at every single position of the target DNA strand. The strands are run through gel electrophoresis to separate them based on length. The colored dye is read and is used to establish the DNA sequence.

Polymerase Chain Reaction

Used to make many copies of a specific DNA region in vitro. The key ingredients of PCR are Taq polymerase, primers, template DNA, and nucleotides (DNA building blocks). The ingredients are assembled in a tube, along with cofactors needed by the enzyme, and are put through repeated cycles of heating and cooling that allow DNA to be synthesized.

Steps:

  1. Denaturation (96°C)
  2. Annealing (55 – 65°C)
  3. Extension (72°C)

Cycle is repeated until you have enough DNA.

Thin-Layer Chromatography

DNA and RNA

DNA

A polymer made up of monomers called nucleotides. Long strands form a double helix which runs antiparallel.

Charge: DNA is negatively charged due to its phosphate backbone.

Nucleotides:

Each nucleotide has three parts:

Note: A nucleoside lacks the phosphate group.

Example of a Nucleotide: Guanosine diphosphate (GDP)

Nucleotide Pairs:

Note: RNA has U instead of T.

Structural Bonds:

DNA backbone is held together via phosphodiester bonds that form between the sugar and the phosphate groups. Hydrogen bonds hold the nucleotide bases together inside the double helix.

Pyrimidines

Purines

Nitrogenous Bases

Pairing:

DNA Double Helix Width:

DNA double helix has a diameter of 20 angstroms.

RNA:

Also a polymer of nucleotides, but differs from DNA in three major respects:

  1. RNA is usually single stranded.
  2. The sugar in RNA is ribose, which is more reactive than deoxyribose.
  3. The nitrogenous base is Uracil (U), not thymine (T).
DNA vs. RNA

Proofreading:

DNA replication has proofreading while RNA transcription does not. This makes DNA replication more accurate than RNA transcription.

Stability:

RNA is less stable than DNA because it contains the sugar ribose compared to DNA’s deoxyribose. As a result, mRNA degrades rapidly in the cytoplasm.

DNA Structure

Levels of DNA Packaging

DNA Replication

Topoisomerase: Unwinds the DNA double helix.

Helicase: Breaks the hydrogen bonds between the nitrogenous bases in order to separate the DNA strands.

Single Strand Binding Protein (SSB): Binds to ssDNA and prevents annealing of ssDNA into double-stranded DNA.

DNA Primase: Catalyzes the synthesis of the RNA primer.

RNA Primers: Short RNA nucleotide sequences that are complementary to the ssDNA. They allow DNA replication to start.

DNA Polymerase: Adds nucleotides to the growing strand. It reads the template 3’ → 5’ and synthesizes the new strand 5’ → 3’.
DNA Polymerase also removes the RNA primer at the end of the strand. There are many varieties of DNA polymerase. Eukaryotes use Pol α, β, δ, ε etc. Prokaryotes use Pol I, II, III, IV, V.

Okazaki Fragment: Short, newly synthesized DNA fragments that are formed on the lagging template strand during DNA replication.

DNA Ligase: Joins DNA strands together by catalyzing the formation of phosphodiester bonds.

The Central Dogma
Amino Acids

Hydrophobic

Glycine, Gly, G
Alanine, Ala, A
Valine, Val, V
Leucine, Leu, L
Isoleucine, Ile, I
Methionine, Met, M
Proline, Pro, P
Phenylalanine, Phe, F
Tryptophan, Trp, W

Polar Neutral

Serine, Ser, S
Threonine, Thr, T
Tyrosine, Tyr, Y
Cysteine, Cys, C
Asparagine, Asn, N
Glutamine, Gln, Q

Basic, +, Hydrophilic

Lysine, Lys, K
Arginine, Arg, R
Histidine, His, H

Acidic, −

Aspartic Acid, Asp, D
Glutamic Acid, Glu, E

Indole Group
(Tryptophan)

Imidazole Group
(Histidine)

Guanidinium Group
(Arginine)

Enzyme Inhibition

Vmax: The maximum rate of the reaction

Km: The amount of substrate needed for the enzyme to work half as fast as it is capable of.

↑Km = ↓ enzyme-substrate affinity
↓Km = ↑ enzyme-substrate affinity

Competitive Inhibition

Vmax no change
Km

A competitive inhibitor binds at the active site and thus prevents the substrate from binding.Uncompetitive Inhibition

Vmax
Km

An uncompetitive inhibitor binds only to the enzyme–substrate complex.

Noncompetitive Inhibition

Vmax
Km no change

A noncompetitive inhibitor binds at the allosteric site, away from the active site. It does NOT prevent the substrate from binding to the active site.

Lineweaver-Burk Plots

Lineweaver-Burk Plots

Michaelis-Menten Curves

Uninhibited

Competitive Inhibitor: Vmax no change, ↑Km

Uncompetitive Inhibitor: ↓Vmax, ↓Km

Noncompetitive Inhibitor: ↓Vmax, Km no change

[S] = substrate concentration

Metabolism Overview
Glycolysis

Occurs in cytoplasm

Glucose has 6 carbons

Pyruvate has 3 carbons. Glycolysis produces two Pyruvates

  1. Glucose
    Hexokinase
    Induced fit
    Regulated by G-6-P feedback
    ATP → ADP
  2. Glucose 6-phosphate
    Phosphoglucose isomerase
  3. Fructose 6-phosphate
    Phosphofructokinase (PFK)
    Committed step
    Regulated by ATP/AMP ratio and Citrate
    ATP → ADP
  4. Fructose 1,6-bisphosphate
    Aldolase
  5. Dihydroxyacetone phosphate ↔ Glyceraldehyde 3-phosphate
    Triose phosphate isomerase
  6. Glyceraldehyde 3-phosphate
    Glyceraldehyde 3-phosphate dehydrogenase
    Pi, NAD⁺ → NADH
  7. 1,3-Bisphosphoglycerate
    Phosphoglycerate kinase
    ADP → ATP
  8. 3-Phosphoglycerate
    Phosphoglycerate mutase
  9. 2-Phosphoglycerate
    Enolase
    → H₂O
  10. Phosphoenolpyruvate (PEP)
    Pyruvate Kinase
    Regulated by covalent modification.
    Phosphorylated = inactive
    ↑Alanine = inactive
    ADP → ATP
    Pyruvate

Note: PEP is high energy because the phosphoryl group traps PEP in its enol form. When the phosphoryl group is donated to ADP, making ATP, the enol converts to a more stable ketone (pyruvate), which releases a lot of energy.

Reactants → Products

The Fate of Pyruvate

Gluconeogenesis

Glucose

Glucose 6-phosphate
Glucose 6-phosphatase
Found only in liver.

Glucose 6-phosphate
Phosphoglucose isomerase

Fructose 6-phosphate
Fructose 1,6-bisphosphatase
Control point of gluconeogenesis
Activated by ATP, inhibited by AMP and fructose 2,6-bisphosphate.

Fructose 1,6-bisphosphate
Aldolase

Dihydroxyacetone phosphate ←→ Glyceraldehyde 3-phosphate
Triose phosphate isomerase

1,3-Bisphosphoglycerate
Glyceraldehyde 3-phosphate dehydrogenase
Pi, NAD⁺ → NADH

3-Phosphoglycerate
Phosphoglycerate kinase
ADP → ATP

2-Phosphoglycerate
Phosphoglycerate mutase

Phosphoenolpyruvate (PEP)
Enolase
→ H₂O

Oxaloacetate
Phosphoenolpyruvate Carboxykinase (PEPCK)
Activated by glucagon and cortisol.
GDP, CO₂ → GTP

Pyruvate
Pyruvate Carboxylase
Activated by Acetyl-CoA. Begins in mitochondria and uses malate as intermediate to exit the mitochondria.
ATP, HCO₃⁻ → ADP + Pi

The combination of Pyruvate Carboxylase and PEPCK is used to circumvent the action of Pyruvate Kinase.

Citric Acid Cycle
StepRegulatory EnzymeInhibitors / Activators
1Citrate SynthaseInhibitors: ATP, NADH, Citrate, Succinyl-CoA
Activator: ADP
3Isocitrate dehydrogenase (Rate limiting enzyme)Inhibitors: ATP and NADH
Activators: ADP and NAD+
4α-Ketoglutarate dehydrogenase complexInhibitors: Succinyl-CoA, NADH, ATP
Activator: ADP

Reactants: 1 Acetyl CoA, 3 NAD+, 1 FAD, 1 ADP, 1 Pi, 3 H2O

Products: 2 CO2, 3 NADH, 1 FADH2, 1 ATP, 3 H+

Eukaryotes: CAC occurs in mitochondrial matrix
Prokaryotes: CAC occurs in cytoplasm

Oxidative Phosphorylation

Eukaryotes: ETC occurs in mitochondria
Prokaryotes: ETC occurs in the cell membrane

 DescriptionATP Produced
Glycolysis:2 NADH and 2 ATP2 NADH + 2 ATP = 7 ATP
Pyruvate Dehydrogenase Complex:1 pyruvate makes 1 NADH. Glucose forms 2 pyruvates, so PDC generates a total of 2 NADH per molecule of glucose.2 NADH = 5 ATP
Citric Acid Cycle:One Acetyl-CoA leads to 3 NADH, 1 FADH2, and 1 GTP. Glycolysis forms two pyruvates, so two Acetyl-CoA molecules exit the PDH complex. A total of 6 NADH, 2 FADH2, and 2 GTP per molecule of glucose.6 NADH + 2 FADH2 + 2 GTP = 20 ATP
1 Glucose =32 ATP

Each NADH ⇒ 2.5 ATP: 10 NADH form 25 ATP
Each FADH2 ⇒ 1.5 ATP: 2 FADH2 form 3 ATP

More Metabolic Pathways

Fatty Acid Synthesis

Occurs in the cell’s cytoplasm

Initiation of Fatty Acid Synthesis

  1. Fatty acid synthesis begins with the transfer of Acetyl-CoA from the mitochondria to the cytosol.
  2. Activation of Acetyl-CoA through the synthesis of Malonyl-CoA. Enzyme is Acetyl-CoA Carboxylase (regulatory enzyme for fatty acid synthesis).
  3. Malonyl-CoA elongation using ACR DR.

β-Oxidation

Occurs in the mitochondrial matrix

β-Oxidation Energy Products

Example: C16 Fatty Acid

Urea Cycle

Occurs in the cytosol and mitochondrial matrix of liver.

Pentose Phosphate Pathway

and its link to glycolysis. Occurs in cytosol.

Essential Equations
Kinematics

vf = v0 + a Δt
vf2 = v02 + 2 a Δx
Δx = v0 Δt + ½ a (Δt)2
ac = v2 / r
Fc = m v2 / r
vx = V0 cos(θ)
vy = V0 sin(θ)

Mechanics

F = m a
FA on B = – FB on A
Ffriction = μ Fnormal
FG = G m1 m2 / r2
Fg = m g
τ = r F sin(θ)
W = F d cos(θ)
P = W / t = F v cos(θ)
KE = ½ m v2
F = –k x
U = ½ k x2
U = m g h
U = – G m1 m2 / r

Inclined Plane

Fincline = m g sin(θ)
FN = m g cos(θ)
Ffric = μ m g cos(θ)

Thermochemistry

ΔU = Q – W
U = 3/2 n R T
W = –P ΔV
Q = m c ΔT
Q = m HL
ΔG = ΔH – T ΔS
ΔHrxn = ΔHprod – ΔHreact

Gases

P V = n R T
Boyle: P V = k
Gay-Lussac: P / T = k
Charles: V / T = k
Avogadro: V / n = k
R1 / R2 = √(m2 / m1)

Solutions

pH = pKa + log ([A] / [HA])
M = mol / L
m = mol / kg
N = M × (# of H+)
pH = –log [H+]
M1 V1 = M2 V2
π = i M R T
ΔTf = i kf m
ΔTb = i kb m
XA = molA / moltotal

Waves

v = λ f
T = 1 / f

Light

n1 sin(θ1) = n2 sin(θ2)
n = c / v
E = h f
h × c ≈ 2.0 × 10–25 J·m
M = di / do
M = – i / o
P = 1 / f
1 / f = 1 / di + 1 / do
h f = R (1 / n2final – 1 / n2initial)

Sound

dB = 10 log (I / I0)
λ = 2L / n (n = 1, 2, …)
λ = 4L / n (n = 1, 3, …)
fbeat = |f1 – f2|
f′ = f [(v ± vo) / (v ± vs)]

Fluids

ρ = m / V
P = F / A
P = Patm + ρ g h
Fb = ρ V g = m g
Q = A v
P + ρ g h + ½ ρ v2 = constant

Electricity & Magnetism

F = k (|q1| |q2|) / r2 = q E
E = k Q / r2
V = k Q / r
Uelect = k q1 q2 / r = q V
F = q v B sin(θ)
F = I L B sin(θ)
V = I R
Ecap = Q2 / (2 C) = ½ C ΔV2
Q = C ΔV
C = ε0 A / d
Ucap = ½ C ΔV2
Ecell = Ecath – Ean
R = ρ L / A
Vrms = Vmax / √2
Irms = Imax / √2

Resistors in Series

Rtot = R1 + R2 + …

Resistors in Parallel

1 / Rtot = 1 / R1 + 1 / R2 + …

Capacitors in Series

1 / Ctot = 1 / C1 + 1 / C2 + …

Capacitors in Parallel

Ctot = C1 + C2 + …

Constants & Units