### General Reminders

- AP Physics is really a test on reasoning and logical derivation of equation, not memorization
- Concepts come before the equations, not the other way around
- This is a comprehensive list of key concepts, but here are the top 10 must know equations and concepts for your Physics test.
- This cheat sheet is for all levels of Physics (but with AP Physics 1 in mind)
- “Normal” force means perpendicular to a surface
- Always choose a coordinate system for each problem and use it consistently. If you set up to be positive then all downward vectors, like gravity, should negative.
- Net force is the sum of the forces in x or y direction. In other words, \Sigma F_x = ma_x and \Sigma F_y = ma_y.
- Acceleration can be linear or centripetal.
- For FRQs that require a solution in terms of given variables, use the variables given, not your own.
- AP Physics questions test two concepts (like forces and energy) together which makes problems much more difficult. Make sure to practice plenty of AP style question to get the hang of it.
- Momentum (linear and angular) is ALWAYS conserved in collisions. Energy is only conserved if there is no external forces (such as friction).
- The best way to study for AP Physics 1 is it to do as many practice problems as you can. Completely understand the ones you got wrong and discuss them with a teacher or tutor to quickly clear up misconceptions.
- You can find speed reviews of the each unit here.
- If you’re taking the AP Physics 1 Exam, check out 5 hacks to score a 5 guide.
- For individualized and professional help, check out nerd-note’s AP Physics Prep program to help you score a 5.

### Kinematics

- 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
- Time in air is based on height. 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. For FRQs be able to prove this using equations
- To solve 2d motion problems (Projectile motion) list variables based on horizontal and vertical direction separately and then apply kinematic equations normally
- Distance v. time –> slope is velocity
- Velocity v. time –> slope is acceleration; area under curve is displacement
- Acceleration v. time –> area under curve is velocity
- For any graph, look at the units to figure out what the slope or area under the curve represents.
- If acceleration and velocity are in the same direction, the object speeds up; if in opposite directions, the object slows down.
- Object at terminal velocity means the object is moving at constant velocity. This happens when the downwards weight force equals the upwards air drag (thus no change in velocity)
- Make sure you can read word problems and make graphs out of them. Ex: draw the velocity vs time graph of a ball thrown up and off a cliff.

Here’s a more in depth speed review of linear kinematics.

### Mechanics (Forces)

- 1st Law –> Inertia = mass = resistance to objects motion.
- 2nd Law –> \text{Net Force} = ma
- 3rd Law –> Every action force has an equal and opposite reaction force. Ex: Big car will hit a small car at an equal but opposite force.
- Three steps to solving all force problems: (a) Draw an FBD, (b) Find the net force in the x and y direction separately (c) set
equal to*net force*and solve**ma** - 8 common types of forces: Weight, normal, gravitational, tension, friction, centripetal, torque, and spring
- Object in equilibrium = no net force = no acceleration = moving at 0 or constant velocity. Ex: an object moving at terminal velocity.
- Net force should always point in the direction of acceleration and vice vera. See the tension example below.
- 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. - The only force on any
**projectile**(neglecting air friction) is the projectile’s weight (mg, directed downwards). - A planet’s
**gravitational**field is greatest at its core (or surface for simplicity). For earth this is 9.81 m/s^{2}. The further you move away from the surface, the weaker gravity becomes. - The gravitational force (force of attraction) between two masses: F_g = G\frac{m_1m_2}{r^2}

#### Friction

- Static
**friction**is a range of values such that 0 \leq f_s \leq \mu N. Kinetic (sliding) friction is just f_k = \mu N. - Tires
*rotate*because of static friction. Tires/objects*slide*because of kinetic friction.

#### Inclined Planes

- 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 line perpendicular to the incline. - The
**normal force**exerted on an object (even on a horizontal surface) is not always equal to the object’s weight.

#### Simple Pulleys

- For Atwood’s machines (a
**pulley**system): solve the problem as a system. In other words, treat the whole thing as one system not individual components.

Here’s a more in depth speed review of linear forces.

#### Circular Motion

- Centripetal force is just another type of force. So apply the same problem solving strategy as above
- If an object is moving in a circle, there must be a component of the net force towards the center equal to F_{\perp} = m\frac{v^2}{r}.
- In a circle, speed is constant but velocity is not (you are changing directions), hene a [centripetal] acceleration.
- The centripetal force is
*usually*friction, weight, or tension. For example, a car can go around a curve because friction points into the curve causing a centripetal acceleration. - On a banked curved
*(removed from AP 1)*, it is the object’s normal force pointing into the curve that causes the centripetal acceleration. Thus you don’t need friction (for centripetal acceleration) on a banked curve.

#### Orbits

- Orbits are a part of circular motion.
- For satellites in orbit, the centripetal force is gravity: F = \frac{GMm}{r^2} = \frac{mv^2}{r}
- The closer a satellite is to what it orbits, the faster its linear speed (shown in equation above)
- Geosynchronous orbit is when a satellite maches the rotational speed of the earth. This happens at approximately 36,888 kilometers above the earth’s surface.
- 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.
- Planets have elliptical NOT circular obits. Thus use Kepler’s Law, unless you are told to assume a circular orbit.

#### Pendulums

- Pendulums technically under go circular motion. Tension causes the centripetal acceleration: T_x = \frac{mv^2}{r},\ T_y = mg
- Period of a pendulum: T = 2\pi \sqrt{\frac{L}{g}}. Do not confuse Tension with Period
- Frequency = f = \frac{1}{T}.
- This equation goes a long way:\omega = 2\pi f = \frac{2\pi}{T} = \sqrt{\frac{k}{m}} = \sqrt{\frac{g}{L}}; the first part is applicable to waves. K and m refer to springs. While g and L refer to pendulums.

Here’s a more in depth speed review of circular motion.

#### Torque

- Torque is like any other force. But its rotational, so you must use rotational variables. See this chart to see how you can easily convert linear equations into rotational ones.
- Torque accelerates an object rotationally, shown by the equation \tau = I\alpha
- As stated above, every linear variable has a rotational (angular) counterpart.
- \Delta x \text{ is } \Delta \theta
- \Delta v \text{ is } \Delta \omega
- a \text{ is } \alpha

- Any object rotating has rotational mass
*I*also known as moment of inertia. The general formula is I = mr^2, however,*I*depends on the point of rotation and the shape of the object.- To find the total moment of inertia of any object: find the moment of inertia of each piece then add it up.
- AP Physics C students need to know how to derive moment of inertia of any object.

- The first step in any torque problem is to determine the point about which torques are calculated.
- Torque is a vector cross product.

Here’s a more in depth speed review of Torque (rotational forces).

#### Spring Force

- Hooke’s Law, F_s = -kx, tells us that the force on a spring increases as you stretch or compress it from its equilibrium position. The negative sign tells us that it is a restoring force (it can be ignored in most cases)
- There are horizontal and vertical spring questions.
- Acceleration of a mass on a spring is greatest at the amplitude (or the ends of motion) and 0 m/s
^{2}at the center (equilibrium position). - Velocity of a mass on a spring is the greatest at the center and greatest at the amplitude.
- 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? (This was on an real AP Exam FRQ)

### Linear Momentum and Impulse

- Momentum, p = mv, is
*always*conversed in ALL collisions. Also conserved when there is no external force (\Delta p = 0). - 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.
- *In an explosion, momentum is also conserved

- Conservation of momentum: P_i = P_f. Note that for perfectly inelastic, the masses combine and move with the same final velocity. Don’t memorize the equation for each collision. Understand how to start from scratch and derive it. This will be tested for on the exam.
- Velocity is a vector, so use the +/- signs! This is the most common mistake. For example, if an object strikes a surface and bounces back the change in velocity is = v - (-v)
- Impulse measures the
**change of momentum**of an object (\Delta p \neq 0)). It has the same units as momentum (kg m/s). - I = \Delta p = m\Delta v = mv_f - mv_i = F\Delta t

Here’s a speed review of linear momentum and impulse.

#### Angular Momentum

- One of the most commonly missed questions on AP physics 1.
- Extremely similar to linear momentum P = mv \rightarrow L = I\omega
- Conservation of linear and angular momentum should be done separately.
- You can do conservation of angular momentum L_i = L_f, then replace rotational variables with linear ones. However, this does NOT make it linear momentum.
- Ex: momentum of clay about to hit rod = I\omega = (mr^2)\left(\frac{v}{r}\right) = mvr

- When angular momentum is NOT conserved there is impulse.
- \text{Impulse} = I = \Delta L = m\Delta \omega = m\omega_f - m\omega_i = F\Delta t

Here’s a speed review of angular momentum (this is a part of the Rotational Motion Speed Review)

### Energy

- If conservative forces are the only forces doing work, mechanical energy is conserved.
- Mechanical energy = total energy in a system. The sum of KE and PE.
- Solve any energy problem in 3 steps:
- (a) Use conservation of energy – E_i = E_f
- (b) Determine the initial and final energy (is it KE, PE or Work)
- (c) solve for the unknown.

- 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).
- Work \text{Work} = W = Fd\cos\theta
- 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 \text{kg} \cdot \text{m}^2/\text{s}^2
- Work done is the area under a force-position graph.

- 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).
- Power – measured in watts where 1 Watt = 1 J/s (rate of change of energy)
- P = \frac{\Delta W}{\Delta t} = Fv = change in work per change in time

#### Kinetic and Potential

- \text{KE} = \frac{1}{2}mv^2(Kinetic energy)
- Potential Energy (gravity): \text{PE} = mgh
- In orbit or far from planet: U = -\frac{GMm}{R}

- If you’re being asked for the kinetic energy of an object, don’t be too quick to use \text{KE} = \frac{1}{2}mv^2 unless the mass and speed are obvious and available. Think about using work-energy considerations and if energy is conserved.
- Relationship between kinetic energy and momentum: K = \frac{p^2}{2m}
- An object can be in translational or rotational equilibrium or both or neither.
- Work done by kinetic friction is negative.

Here’s an in depth speed review of work, energy, and power.

#### Spring Energy

- The energy from a spring, \text{PE}_s = \frac{1}{2}kx^2, is a type of potential energy. It causes a mass (attached or detached to the spring) to accelerate.
- PE is at a maximum at the amplitudes, while KE is at a maximum at the equilibrium position.

#### Rotational Energy

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

This speed review goes over rotational energy.

END OF AP PHYSICS 1 TOPICS. As of 2021, AP Physics 1 no longer covers general waves, circuits, electricity, and electrostatics.

### General Waves

**No longer on the AP Physics 1 Exam**- Mechanical waves can be longitudinal (displacement is parallel to motion) or transverse (displacement is perpendicular to motion).
- EM waves are treated as transverse waves, while sound is a longitudinal wave.
**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:
**v**. Where T is tension and µ is linear density._{string}= √(T/µ)

- Speed of wave is determined by
- Speed of sound is 343 m/s @ 20°C. Otherwise use
**v**. Where T is the temperature in °C._{sound}= 331 +.6T- Sound travels faster in water than air.

- Wave energy is generally directly associated with amplitude
- Properties of waves include refraction, superposition & interference, and diffraction. Waves also reflect, but so do particles.
- 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.

#### Harmonics

**No longer on the AP Physics 1 Exam**- 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.

- Frequency determines pitch. Amplitude determines loudness.

### Circuits and Electricity

**No longer covered on the AP Physics 1 or C exam.**- 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.

- 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)

- 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).

- 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).
- Power is dissipated by a resistor and given off as heat. Stuff that requires a lot of heat uses the most electricity.

#### Circuit Analysis

- Kirchhoff’s Loop Rule (∑ V = 0) is an expression of conservation of energy (per unit charge).
- Kirchhoff’s Point Rule (∑ I = 0) is an expression of the conservation of electric charge (per unit time).
- 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.
- Voltmeters have a high resistance (to keep from drawing current) and are wired in parallel (because voltage is the same in parallel).
- Ammeters have a low resistance (to keep from reducing the current) and are wired in series (because current is the same in series).
- 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.
- 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.

### FREE Cram Sheets

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### FREE resources

- For a quick review on all core concepts, be sure to check out Nerd-Note’s free Physics speed reviews here.
- For practice on concepts such as forces, kinematics, momentum, etc., use the Mind on Physics Modules made by Physics Classroom.
- For amazing demonstrations on solving ALL types of Physics problems, watch Michel van Biezen’s Physics videos on Youtube.
- His playlists are extensive. His playlist for Work, Energy, and Power has 37 videos in which he shows how to solve challenging problems.

- For professional 1-to-1 help, get started here on nerd-notes. We help students easily excel in the shortest time possible.

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