 # The Ultimate Cram Sheet for Physics (+ Extra study guides, formula sheets, and practice exams!)

Below you will find A LOT of resources for Physics, including AP Physics 1 and C. More practice AP tests and general practice problems are coming! It took me over 4 years to compile these resources. So if this does help you out, all I ask is for you to share the page with your fellow scholars. Cheers!

### General Reminders

1. ALL equations are listed at the end. Remember: concepts come before the equations, not the other way around.
2. “Normal” means perpendicular to the surface
3. Always choose a coordinate system for each problem and use it consistently. If you set up to be positive then, all vectors pointing down, like gravity, will be negative.
4. Net force is simply the sum of the vectors in x or y direction. In other words, ΣFx = max, ΣFy = may.
5. On FRQ problems that require a solution in terms of given variables, use the variables given, not your own.
6. AP Physics questions test two concepts at once which makes ordinary problems much more difficult. Make sure to practice plenty of AP style question to get the hang of it.
7. Momentum (linear and angular) is almost ALWAYS conserved. Energy is only conserved if there is no external forces (such as friction).
8. The best way to study for AP Physics 1 exam, midterms, and finals, it to do as many practice problems as you can. Make sure to fully understand the ones you got wrong.
9. Important AP Physics 1/C concepts are indicated by (AP)

### (1) Kinematics

1. 3 steps to solve ALL kinematic problems: (a) read the problem and write down 3 known variable and 1 unknown; (b) Pick and equation that uses given variables; (c) plug numbers in and solve
2. A ball rolled off a horizontal table will take the same amount of time to hit the ground as another dropped from the same height. In other words time in air is based on height.
3. To solve 2d motion problems (Projectile motion) list variables based on horizontal and vertical direction separately and then apply kinematic equations normally.
4. Distance v. time –> slope is velocity
5. Velocity v. time –> slope is acceleration; area under curve is displacement
6. Acceleration v. time –> area under curve is velocity
7. If acceleration and velocity and parallel, the object speeds up; if in opposite directions, the object slows down.
8. As a falling object approaches terminal velocity means the an object is moving at constant velocity.
9. (AP) Make sure you can read word problems and make graphs out of them. This is a commonly missed free response question.

### (2) Mechanics

1. 1st Law –> Inertia = mass = resistance to objects motion.
2. 2nd Law –> Net Force = ma
3. 3rd Law –> Every action force has an equal and opposite reaction force
4. Three steps to solving all force problems: (a) Draw an FBD, (b) Find the net force in the required direction, (c) set net force equal to ma and solve
5. 10 main types of forces: Weight, gravity, tension, friction, centripetal, torque, spring, electric, and magnetics, forces.
6. Object in equilibrium = no net force = no acceleration = moving at 0 or constant velocity.
7. The tension in a rope holding an object in equilibrium is equal to the weight of the object. If the object is accelerating upwards, T > mg. If the object is accelerating downwards, T < mg.
8. The only force on any projectile (neglecting air friction) is the projectile’s weight (directed downwards).
9. The angle of an inclined plane is the same as the angle between the line of the weight of the object on the incline and the normal line.
10. The normal force exerted on an object (even on a horizontal surface) is not always equal to the object’s weight.
11. For Atwood’s machines (a pulley system), treat the whole thing as one system not individual components.
12. Static friction is a range of values such that 0 ≤ fs ≤ µN . Kinetic (sliding) friction is just fk = µN.
13. Tires rotate because of static friction. Tires/objects slide because of kinetic friction.
14. A planet’s gravitational field is greatest at its surface. For earth this is 9.81 m/s2. The further you move away from the surface, the weaker gravity becomes.
15. To find force of gravity between two objects: Fg = Gm1m2/r2

#### (2.1) Circular Motion

1. If an object is moving in a circle, there must be a component of the net force towards the center equal to F = m(v2/r).
2. The centripetal force is usually friction or gravity. For example, a car can go around a curve because friction causes the centripetal acceleration.
3. On a banked curved, an object weight points into the curve thus contributing to centripetal acceleration. Thus you don’t need friction (for centripetal acceleration) on a banked curve.
4. For satellites, the centripetal force is gravity: F = GMm/r2 = mv2/r (assuming the orbit is circular and >>> m). Notice: the mass of a satellite doesn’t matter.
5. The closer a satellite is to what it orbits, the faster its orbital spee
6. Geosynchronous orbit (rotating with the earth) is approximately 22,300 mi. above the earth’s surface.
7. For satellites and planets, angular momentum (L = mvr) is always conserved (in the absence of any outside forces/torques). In other words, the closer a planet is to the sun, the faster it goes.
8. Planets have elliptical NOT circular obits. Thus use Kepler’s Law.
9. Pendulums under go circular motion. Tension causes the centripetal acceleration: Tx = mv2/r. Ty = mg.
10. Period of a pendulum: T = 2pi √(L/g). Frequency = f = 1/T. Do not confuse Tension with Period (T)
11. This equation goes a long way: ω =2πf= 2π/T = √(k/m) = √(g/L); the first part is applicable to waves. K and m refer to springs. While g and L refer to pendulums.

#### (2.2) Torque

1. Circular motion is to Kinematics, as Torque is to Forces
2. Torque is a rotational force. In other words it accelerates an object rotationally.
3. Every linear variable has a rotational (angular) counterpart. ∆x is ∆ø (theta). ∆v is ∆ω (omega). a is 𝜶 (alpha).
4. (AP) Any object rotating has rotational mass I also known as moment of inertia. The general formula is I = mr2, however, I depends on the point of rotation and the shape of the object.
• AP Physics C students need to know how to derive moment of inertia of any object.
5. The first step in any torque problem is to determine the point about which torques are calculated.
6. Torque is a vector cross product. τ = r × F = rFsinø. This basically means that only the force that is perpendicular to the radius affects the torque.

#### (2.3) Spring Force

1. Hooke’s Law (Fs = kx) tells us that the force on a spring increases as you stretch or compress it from its equilibrium position
2. There are horizontal and vertical spring questions.
3. Acceleration of a mass on a spring is greatest at the amplitude (or the ends of motion) and 0 m/s2 at the center (equilibrium position).
4. Velocity of a mass on a spring is the greatest at the center and greatest at the amplitude.
5. (AP) It is important to understand what affects the amplitude of a spring in different situations. For example what’s happens to the amplitude of a mass on a spring moving horizontally, when you drop another mass on it?

### (3) Momentum and Impulse

1. Momentum (p = mv)is conversed if there is no external force (∆p= 0). Do not mix up signs for velocity.
2. Impulse measures the change of momentum of an object (∆p ≠ 0). It has the same units as momentum (kg m/s). I = Δp = mΔv = mv – mvi = FΔt.
3. If an object strikes a surface and bounds back the sign on velocity becomes negative.
4. Momentum is generally always conserved in collisions.
5. 3 types of collisions
• Elastic collision: Kinetic energy is also conserved. The energy transfer is perfect and lossless. Think of two rubber balls bouncing off each other.
• Inelastic collision: There is some loss of energy from deformation/heat loss. Think of a car hitting a bike and denting both (work done to dent is energy lost).
• Perfectly inelastic: loss of energy and objects are stuck together afterward and move together. Think of a truck crushing a car and they keep driving.
6. Conservation of momentum: m1v1i + m2v2i = m1v1f + m2v2f | Note that for perfectly inelastic, the right half is (m1+ m2)v

### (4) Energy

1. If conservative forces are the only forces doing work, mechanical energy is conserved.
2. Mechanical energy = total energy in a system. The sum of KE and PE.
3. Solve any energy problem in 3 steps: (a) Use conservation of energy (Ei = Ef) also known as the work-energy theorem; (b) Determine the initial and final energy (is it KE, PE or Work); (c) solve for the unknown.
4. If there is a difference in between the initial energy and final energy, then there is energy being lost as Work (like work due to friction).
5. Work = W = Fdcosϴ
• Work is measured as the force applied in the direction of displacement.
• The work done by any centripetal force is always zero.
• Normal force does no work.
• Measured in Joules or kg*m2/s2
• Work done is the area under a force-position graph.
6. The work done in stopping an object is equal to its initial kinetic energy (likewise, the work done in getting an object up to speed is equal to its final kinetic energy).
7. Kinetic Energy: KE = ½mv2
8. Potential Energy (gravity): PE = mgh
• Space/orbiting: U = -GMm/R
9. Power – measured in watts where 1 Watt = 1 J/s (rate of change of energy)
• P = ΔW / Δt = Fv = change in work per change in time
10. If you’re being asked for the kinetic energy of an object, don’t be too quick to use KE = 1/2(mv2) unless the mass and speed are obvious and available. Think about using work-energy considerations and if energy is conserved.
11. Relationship between kinetic energy and momentum: K = p2/2m
12. An object can be in translational or rotational equilibrium or both or neither.
13. Work done by kinetic friction is negative.

#### (4.1) Rotational Energy

1. Any object that is rotating has rotational energy.
2. Remember that if its rolling then it has rotational energy + linear kinetic energy (i.e a ball rolling down a ramp)
3. Rotational Energy = 1/2Iω2, where I is the rotational inertia and ω is the angular velocity.

#### (4.2) Spring Energy

1. The energy from a spring (PEs = 1/2kx2) is a type of potential energy. It causes a mass (attached or detached to the spring) to accelerate.
2. PE is at a maximum at the amplitudes, while KE is at a maximum at the equilibrium position.

### (5) Waves

1. Mechanical waves can be longitudinal (displacement is parallel to motion) or transverse (displacement is perpendicular to motion).
2. EM waves are treated as transverse waves, while sound is a longitudinal wave.
3. v = fλ (for both sound and light waves)
• Speed of wave is determined by medium, not frequency. This is why when you change f, you change λ, but not v. Think about sound – the speed of sound isn’t faster for 20Hz than it is for 20,000Hz.
• Frequency only changes when the type of light changes. For example XRAYs have a higher frequency than radio waves.
• velocity on a string: vstring = √(T/µ). Where T is tension and µ is linear density.
4. Speed of sound is 343 m/s @ 20°C. Otherwise use vsound = 331 +.6T. Where T is the temperature in °C.
• Sound travels faster in water than air.
5. Wave energy is generally directly associated with amplitude
6. Properties of waves include refraction, superposition & interference, and diffraction. Waves also reflect, but so do particles.
7. Doppler affected explained the perceived effect a change in frequency of sound, for a stationary person and moving sound source.
• Just because the sound is perceived to change in frequency does not actually mean it does. A person sitting in an ambulance will not hear a change in frequency as the vehicle moves.

#### 5.1) Harmonics

1. (AP) There will 3 types of harmonics you will need memorized: string, tube open on both ends, tube closed on one end. It is super helpful to understand and memorize the graphs of the first 3 harmonics of each type.
• On a string (or in a pipe) where a standing wave occurs, the number of loops (antinodes) is the number of the harmonic.
• Fundamental frequency comes before the 1st harmonic.
2. Frequency determines pitch. Amplitude determines loudness.

### (6) Circuits

1. Note: Circuits are no longer covered on the AP Physics 1 or C exam.
2. Current = I = ∆Q/∆t or amount of charge flowing through a cross section of a conductor
• The direction of conventional current is the way positive charges go in a circuit, even though the actual charges that move are electrons.
3. Voltage/ emf is the force that “pushes” electrons.
• Positive charges flow from high potential (higher voltage) to lower potential (lower voltage)
• Batteries are a source of emf. They have a positive cathode and negative anode (by convention – this is because positive charge flows from positive to negative while negative charge flows from the anode to cathode. Because oxidation occurs at the anode (loss of electrons) it actually gets positively charged and will attract anions – think of a gel)
• Batteries have internal resistance such that the true potential difference in a battery is emf minus the voltage drop due to internal resistance. Together this is called terminal potential (potential between the terminals)
4. Resistance V=IR and also R = ρL/A
• ρ is the resistivity of a material, which is a constant based on the material. A bigger cross-sectional area will let me charge through, so it reduces resistance. A longer wire will be more material to traverse so it increases resistivity
• Resistivity is a general characteristic of a material (e.g. copper) while resistance is a specific characteristic of a sample of a material (e.g. 2 ft of 14 gauge copper wire).
5. Superconductors have zero resistance when cooled below a critical temperature (different for different materials). Currently, high temperature superconductors – ceramics mostly – have critical temperatures of around 100 K).
6. Power is dissipated by a resistor and given off as heat. Stuff that requires a lot of heat uses the most electricity.
7. The equivalent resistance of any two identical resistors in parallel is half of either resistor. (e.g. two 8Ω resistors in parallel give an eqiv. R = 4Ω).
• The equivalent resistance of any number of resistors in parallel is always less than that of the smallest resistor.
8. Kirchhoff’s Loop Rule (∑ V = 0) is an expression of conservation of energy (per unit charge).
9. Kirchhoff’s Point Rule (∑ I = 0) is an expression of the conservation of electric charge (per unit time).
10. If you must use the Loop Rule or the Point Rule, remember your sign conventions for emf’s and IR’s in a loop. The convention for the Point Rule is too obvious to print.
11. Voltmeters have a high resistance (to keep from drawing current) and are wired in parallel (because voltage is the same in parallel).
12. Ammeters have a low resistance (to keep from reducing the current) and are wired in series (because current is the same in series).
13. A light bulb lights up because of current. The more current, the brighter it is. Generally, we’ll treat the resistance of the light bulb as ohmic (i.e. constant – it follows Ohm’s Law), although actually, most metallic conductors increase in resistance when heated.

### (7) Electrostatics – Guass’ Law

1. Note: This is no longer covered on by AP Physics 1 and C. Only force between charges (Coulombs Law) is covered.
2. Excess charge resides on the outer surface of a conductor.
3. The field anywhere inside a conductor in electrostatic equilibrium is zero.
4. The surface of any charged conductor in electrostatic equilibrium is a surface of equipotential.
5. The electric potential on the surface of conducting sphere is inversely proportional to the radius of the sphere. (i.e., given the same quantity of charge, surfaces of smaller spheres are at a higher quantity of potential).
6. On irregularly shaped conductors, the surface charge density (and therefore the field and potential) is higher at locations where the radius of curvature is smallest (like ends of lightning rods and golf clubs).
7. If two charged objects are connected by a conductor, the difference in potential will cause the charges to move until the potentials are the same. And don’t forget, positive charges move from high to low potential – negative charges (e.g., electrons) go from low to high potential.
8. For a conducting sphere of radius R: the electric field at the surface is kQ/R2. The field anywhere inside the sphere is 0. The field at a distance r away from the center of the sphere (where r > R)is E = kQ/r2.
9. For the same conducting sphere: The potential at the surface is kQ/R. The potential anywhere inside the sphere is the same as at the surface, otherwise, there would be a difference in potential and therefore an electric field that is ≠ 0. The potential at a distance away from the center of the sphere (where ) is kQ/r
10. For an insulating sphere of uniform charge density, the field inside the sphere varies directly with the distance from the center (just like gravitational fields inside the earth). Outside it’s like the case above.

### (12) FREE resources for more practice

1. For practice on concepts such as forces, kinematics, momentum, etc., use the Mind on Physics Modules made by Physics Classroom.
2. For amazing demonstrations on solving ALL types of Physics problems, watch Michel van Biezen’s Physics videos on Youtube.

## More help!

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