Physics Cheat Sheet Master

High School Physics - Core Concept Master Cheat Sheet O1: Basic Skills in Physics

03: Solving Physics Problems

• Physics: Study of the physical world. Science of energy • Metric System: System of measurement based on multiples of 10. • SI System: Systeme International d’Unites (International system of units). • Uncertainty: The last digit in a measurement is uncertain—each person may see it slightly differently when reading the measurement. • Significant Figures: Digits that were actually measured and have physical significance. (Also called “significant digits”)

General Problem Solving Strategy: Step 1: Identify what’s being given Step 2: Clarify what’s being asked. If necessary, rephrase the question Step 3: Select a strategy Trial & error, search, deductive reasoning, knowledge-based, working backwards Step 4: Solve using the strategy Step 5: Review the answer

The metric system uses prefixes to indicate multiples of 10

K = Known U = Unknown D = Definition O = Output S = Substantiation

Metric Prefixes commonly used in physics Prefix Symbol Multiple Kilo k 1000 Deci d 0.1 Centi c 0.01 Milli m 0.001 Micro μ 0.000001 Nano n 0.000000001 The “base unit” is when there’s no prefix.

Multiple-choice tips: Scan all the choices Avoid word confusion Beware of absolutes Essay tips: Understand the question Answer the whole question and only the question Watch your time Free-Response tips: Show partial work Don’t forget units Don’t be fooled by blank space

To determine the equivalent in “base units”: 1. Use prefix to determine multiple 2. Multiply number by the multiple 3. Write the result with the base unit Examples: 1.25 mL Æ “milli” means 0.001 Æ 0.00125 L 87.5 kg Æ “kilo” means 1000 Æ 87500 g

04: Motion in One Dimension

02: A Mathematical Toolkit If a # is … to a variable, Added

then … the # to solve for the variable Subtract

Subtracted

Add

Multiplied

Divide

Divided

Multiply

Use the KUDOS method for solving word problems.

• Vector: A quantity that represents magnitude (size) and direction. It is usually represented with an arrow to indicate the appropriate direction. They may or may not be drawn to scale. • Scalar: A quantity that can be completely described its magnitude, or size. It has no direction associated with its size. • Velocity: Speed of an object which includes its direction of motion. Velocity is a vector quantity. • Acceleration: Rate at which an object’s velocity changes with time; this change may in speed, direction, or both.

Example

5=x+2 -2 -2 5-2 = x 3=x–6 +6 +6 3-6 = x 2 = 4x 1. 4 2/4 = x 2·6=x·2 2 2·6=x

• • • • •

On Your Calculator: • Always use the ÷ key to designate a number is on the bottom of an expression. • Always use the EE (or EXP) key to enter scientific notation. • Always use parenthesis around addition or subtraction when combining it with other operations • To make something negative (when taking the number to a power), keep the negative outside of the parenthesis.

v=d/t a = Δv/Δt=(vf-vi)/t d=vit+at2/2 vf2=vi2+2ad acceleration due to gravity = -9.8 m/s2

• For sign conventions, assign a direction as positive, keep this convention throughout the problem, any quantities in the opposite direction must be negative. • Often, up and right are positive, while down and left are negative. The motion of an object moving with a constant acceleration is pictured below. The distance moved in each unit of time increases. In fact, it is proportional to the square of the time.

Important Formulas:

sinθ = cosθ =

opposite hypotenuse adjacent hypotenuse

tanθ =

x=

opposite adjacent

− b ± b − 4ac 2a 2

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• An object moving with a constant velocity would cover equal amounts of distance in equal time intervals. • An object moving with a constant acceleration would cover varying amounts of distance in equal time intervals.

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05: Vectors and Motion in Two Dimensions

07: Work and Energy

• Resultant: the result of adding two or more vectors; vector sum. • Vector Component: the parts into which a vector can be separated and that act in different directions from the vector. • Vector Addition: The process of combining vectors; added tip to tail.

• Work: Product of force on an object and the distance through which the object is moved. • Power: Work done per unit of time. • Energy: The ability to do work. • Base level: An arbitrary reference point from which distances are measured. • Kinetic Energy: The energy an object has due to its motion. • Gravitational Potential Energy: The energy an object has due to its position above some base level. • Work Energy Theorem: The work done is equal to the change in energy. • Conservation of Energy: energy is not created or destroyed, just transformed from one type to another.

Vertical component

Velocity of a projectile

Horizontal component • • • • • • • • • •

v=d/t a = Δv/Δt=(vf-vi)/t d=vit+at2/2 vf2=vi2+2ad Pythagorean Theorem: c2=a2+b2 Sin θ = opp/hyp Cos θ = adj/hyp Tan θ = opp/adj acceleration due to gravity = -9.8 m/s2 Important formula note: All of these formulas could apply to any direction. Common subscripts are shown that indicate the direction of a particular quantity • v or y = vertical direction • h or x = horizontal direction

• Projectiles move with a constant acceleration due to gravity only in the vertical direction. • Projectiles move with a constant velocity only in the horizontal direction.

• • • • • • •

W= F d = mad W = F d cos θ P = W/t a = Δv/Δt cos θ = adjacent / hypotenuse KE = ½ mv2 PE = mgh

• Work is done only when a force acts in the direction of motion of an object • If the force is perpendicular to the direction of motion, then no work is done. • Power is the ratio of work done per time • Energy may appear in different forms, but it is always conserved. • The total amount of energy before and after some interaction is constant. • Work and energy are interchangeable.

06: Forces and the Laws of Motion • Static Equilibrium: A motionless state where all the forces acting on an object yield a net force of zero. • Dynamic Equilibrium: A condition of constant motion/zero acceleration where all the forces acting on an object yield a net force of zero. • Friction Force: A force that acts to resist motion of objects that are in contact. • Normal Force: Support force that acts perpendicular to a surface. If the surface is horizontal, this force balances the weight of the object. • Force: A vector quantity that tends to accelerate an object; a push or a pull. • Net Force, Fnet: : A combination of all the forces that act on an object • Fnet=ma • μ=Ff/FN • Fnet=ΣF = the sum of all forces • Newton’s 1st law: An object at rest wants to stay at rest, an object in motion tends to stay in motion; inertia. • Newton’s 2nd law: Fnet=ma. • Newton’s 3rd law: For every force that is an equal and opposite force; action and reaction. An inclined plane showing all the forces acting on the object:

FN

F┴

W

θ

• Explosion: one object breaking into more objects. 0=mv+mv+… • Hit and stick: one object striking and joining to the other. m1v1+m2v2=(m1+m2)v3 • Hit and rebound: one object striking and bouncing off of the other. m1v1+m2v2=m1v3+m2v4

A

m Ff

08: Momentum and Collisions • Momentum: A vector quantity that is the product of mass and velocity of an item. It may be considered as inertia in motion. • Impulse: A change in momentum. The product of force and the time through which the force acts. • Conservation of Momentum: The momentum of a system will remain constant. Momentum isn’t created or destroyed unless an outside force is acting on the system. • Elastic Collision: A collision where there is no kinetic lost, momentum is still conserved, the object have no deformation. • Inelastic Collision: A collision where kinetic energy is lost due to heat, deformation, or other methods. However, momentum is still conserved for the system. • P=mv • Ft=mΔv • J=Ft

A

B B

F║

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Ball A strikes motionless ball B. After the collision they move off as shown.

Note how momentum is conserved. In the X direction, the moments add up to the original momentum before the collision. In the Y direction, the moments cancel out since there was no momentum in that direction initially.

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09: The Law of Gravity and Circular Motion

11: Solids and Fluid Dynamics

• Centripetal Force: a center seeking force for an object moving in a circular path. • Centrifugal Force: An apparent, but nonexistent, outward pointing force for an object moving in a circular path. A rotating object may seem to be pushed outward, but actually must be pulled inward in order to maintain any circular path. • Inverse Square Law: A relationship relating the strength of an effect to the inverse square of the distance away from the source. • Gravitational Field: The map of influence that a massive body extends into space around itself. • Linear Speed: Straight path distance moved per unit of time, also referred to as tangential speed. • Rotational Speed: Number of rotations or revolutions per unit of time, often measured in rpm, revolutions per minute. • Universal Gravitational Constant: A proportionality constant that relates the strength of gravitational attraction in Newton’s law of universal gravitation.

• Solids: Matte with definite shape and volume • Fluids: Matter with indefinite shape and definite volume • Thermal expansion: Volume of matter increase with temperature • Stress: Force causing deformation • Strain: Degree of deformation • Buoyancy: The force caused by pressure variation with depth to lift immersed objects • Surface tension: The force to attract surfaced molecular to make the surface area of fluid as small as possible • Capillary action: The phenomena of fluids automatically raising in open-ended tubes • Viscosity: The inter-friction mechanism in fluid to dissipate energy • Laminar flow: Every particle passing a particular point moves exactly along the smooth path followed by particles passing that point early • Turbulent flow: The irregular flow when the velocity of the flow is high

• • • •

2

Fg=Gm1m2/d G=6.67x10-11Nm2/kg2 ac=v2/r Fc=mv2/r

• Thermal expansion:

(L − L0 ) = α (T − T0 )

= ρgh Buoyancy (Archimedes’ principle): B = ρgV

• Pressure variation with depth: P •

• Bernoulli’s equation (along any streamline):

• Weightlessness: Astronauts “floating” in space may appear to be weightless. However, the pull from gravity definitely still acts on them. If it didn’t, their inertia would carry them off in a straight line never to return to the earth. Instead, the pull from gravity acts as a centripetal force to maintain their orbit about the earth.

1 2 ρv + ρgh = const 2 Applied force = Loaded area P+

• Stress

12: Temperature and Heat

10: Rotational Equilibrium • Torque: The rotational quantity that causes rotation; the product of force times lever arm. • Lever Arm: The distance from the axis of rotation to the location where the force is applied. • Moment of Inertia: The rotational equivalent of linear inertia; a measure of the ease of rotating some object. • Angular Momentum: The rotational equivalent of linear momentum that describes the tendency of an object to continue rotating. • Rotational Equilibrium: The situation when the net torque on an object equals zero. • Radian: A unit of rotational displacement; one revolution equals 2 ∏ radians.

Kelvin: The Kelvin scale measures absolute temperature. At 0 Kelvin, particles in an object are still. Other temperature scales related to the Kelvin scale. Celsius: A temperature increase of 1°C is equal to an increase in temperature of 1K. However, 0°C ≠ 0K. The Celsius scale is based on the boiling and freezing points of water. Thus, water freezes at 0°C and boils at 100°C D

C + 273 = K

Fahrenheit: The Fahrenheit scale is set such that water freezes at 0°F and boils at 212°F. D

9 F = DC + 32 5

For changes in temperature:

• I=Σmr2 • L=Iω

Qheat = m × C p × ΔT

• Ƭ=F l Linear motion formula v=

d t

∆θ ∆t

∆ω α= ∆t

∆v a= ∆t

d = v i t + at /2

θ = ωi t + αt /2

v = v + 2ad

ω2f = ωi2 + 2αθ

2

2 f

For increases in temperature that cross several phases simply sum the Qfus, Qvap, and Qheat as needed. For changes in state: Temperature doesn’t change as the added energy is used to break intermolecular forces.

Rotational motion formula ω=

2 i

Melting:

ΔQ fus = m × L fus

Qfus = heat of fusion

Boiling:

ΔQvap = m × Lvap

Qvap = heat of vaporization

Heat, Work, and Internal Energy: The internal energy U of a system is defined as the sum of the heat energy Q in the system and the work W done on or by the system.

2

U = Q +W

• θ= angular displacement • ω=angular speed • α=angular acceleration • Ƭ=torque • I=rotational inertia • Draw a diagram if needed. Identify all given information. Be sure to make diagrams or calculations with direction in mind. Draw all forces and components.

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m = mass; ΔT = T2 – T1

Calorimetry: Calorimetry is used to measure the heat given off from or taken up by a reaction. Calorimetry assumes that heat released by the system to the surroundings is used to heat or cool the surroundings.

ΔQsystem = −ΔQsurroundings

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13: Thermodynamics

15: Sound

• Zeroth Law of Thermodynamics: Objects in thermal equilibrium are at the same temperature. Objects in contact will eventually come to thermal equilibrium. • 1st Law of Thermodynamics (Law of Conservation of Energy): Energy cannot be created nor destroyed in a chemical or physical process.

ΔU = ΔQ + W

U = internal energy (in J) Q = heat (in J); W = work done on (W>0) or by (W