Hey everyone! Physics can seem daunting, especially when you're staring down a mountain of formulas. But don't worry, I’ve got your back. This cheat sheet is designed to help you navigate the essential physics formulas you'll encounter in high school. Let’s break it down and make it super easy to understand. Think of this as your trusty sidekick as you tackle those tough problems!

Mechanics

Kinematics

Kinematics is all about motion – describing how things move without worrying about why they move. It's the foundation for understanding more complex physics concepts. The key here is mastering these formulas and knowing when to apply them. Let's dive in!

Displacement:

• Δx = x_f - x_i

Displacement (Δx) measures the change in position of an object. It's simply the final position (x_f) minus the initial position (x_i). Understanding displacement is crucial because it sets the stage for understanding velocity and acceleration. Always remember, displacement is a vector quantity, meaning it has both magnitude and direction.

Average Velocity:

• v_avg = Δx / Δt

Average velocity (v_avg) is the displacement divided by the change in time (Δt). It tells you how fast an object is moving on average over a certain period. This is super useful for calculating how long it will take to travel a certain distance at a consistent speed. Keep in mind that average velocity doesn't tell you about the instantaneous velocity at any specific moment, just the overall average.

Average Acceleration:

• a_avg = Δv / Δt

Average acceleration (a_avg) is the change in velocity (Δv) divided by the change in time (Δt). Acceleration tells you how quickly the velocity of an object is changing. A positive acceleration means the object is speeding up, while a negative acceleration means it's slowing down. Understanding acceleration is key to understanding how forces affect motion.

Equations of Motion (Constant Acceleration):

These equations are your bread and butter for solving kinematics problems when the acceleration is constant. Mastering these will make those tricky problems much more manageable.

• v = v_0 + at
• x = x_0 + v_0t + (1/2)at^2
• v^2 = v_0^2 + 2a(x - x_0)
• x = x_0 + (1/2)(v + v_0)t

Where:

• v = final velocity
• v_0 = initial velocity
• a = acceleration
• t = time
• x = final position
• x_0 = initial position

Dynamics

Dynamics explores the reasons behind motion, focusing on forces and their effects. This section is all about understanding how forces cause objects to move and interact. Grasping these concepts is essential for understanding everything from why a ball falls to the ground to how rockets launch into space.

Newton's Second Law:

• F = ma

Newton's Second Law is the cornerstone of dynamics. It states that the net force (F) acting on an object is equal to the mass (m) of the object multiplied by its acceleration (a). This equation tells you that the greater the force, the greater the acceleration, and the greater the mass, the smaller the acceleration. This is fundamental for solving any problem involving forces and motion.

Weight:

• W = mg

Weight (W) is the force of gravity acting on an object. It's equal to the mass (m) of the object multiplied by the acceleration due to gravity (g), which is approximately 9.8 m/s² on Earth. Understanding weight is important for distinguishing it from mass – mass is a measure of how much matter an object contains, while weight is the force of gravity acting on that mass.

Friction:

• F_f = μF_N

Friction (F_f) is the force that opposes motion between two surfaces in contact. It's equal to the coefficient of friction (μ) multiplied by the normal force (F_N). The coefficient of friction depends on the nature of the surfaces in contact. There are two types of friction: static friction (which prevents an object from starting to move) and kinetic friction (which acts on an object already in motion). Friction is a crucial concept for understanding why objects slow down and stop.

Work and Energy

Work and energy are fundamental concepts in physics that describe how forces can change the state of motion of an object. Understanding these concepts allows you to analyze everything from the efficiency of machines to the motion of planets. Let's dive into the key formulas.

Work:

• W = Fdcosθ

Work (W) is done when a force (F) causes a displacement (d). It's calculated as the product of the force, the displacement, and the cosine of the angle (θ) between the force and the displacement. If the force is in the same direction as the displacement (θ = 0°), then cosθ = 1, and the work is simply Fd. Work is a scalar quantity and is measured in joules (J).

Kinetic Energy:

• KE = (1/2)mv^2

Kinetic energy (KE) is the energy an object possesses due to its motion. It's equal to one-half times the mass (m) of the object multiplied by the square of its velocity (v). The faster an object moves, the more kinetic energy it has. Kinetic energy is also measured in joules (J).

Potential Energy:

• Gravitational PE: PE_g = mgh
• Elastic PE: PE_e = (1/2)kx^2

Potential energy (PE) is stored energy that an object has due to its position or condition. There are two main types:

• Gravitational Potential Energy (PE_g): This is the energy an object has due to its height (h) above a reference point. It's calculated as the product of the mass (m), the acceleration due to gravity (g), and the height (h). The higher the object, the more gravitational potential energy it has.
• Elastic Potential Energy (PE_e): This is the energy stored in a spring or other elastic material when it is stretched or compressed. It's calculated as one-half times the spring constant (k) multiplied by the square of the displacement (x) from its equilibrium position. The stiffer the spring and the greater the displacement, the more elastic potential energy it has.

Conservation of Energy:

• E_initial = E_final

The law of conservation of energy states that energy cannot be created or destroyed, but it can be transferred from one form to another. This means that the total energy in a closed system remains constant. In problems, this often translates to the initial energy (E_initial) being equal to the final energy (E_final). This principle is incredibly useful for solving problems where energy is transformed between kinetic and potential forms.

Momentum and Impulse

Momentum and impulse are key concepts for understanding collisions and other interactions where forces act over a short period. These concepts are particularly useful for analyzing situations where energy conservation alone isn't enough to solve the problem.

Momentum:

• p = mv

Momentum (p) is a measure of an object's mass in motion. It's equal to the mass (m) of the object multiplied by its velocity (v). Momentum is a vector quantity, meaning it has both magnitude and direction. An object with a large mass or a high velocity has a large momentum.

Impulse:

• J = Δp = FΔt

Impulse (J) is the change in momentum of an object. It's equal to the force (F) applied to the object multiplied by the time interval (Δt) over which the force acts. Impulse is also a vector quantity. The impulse-momentum theorem states that the impulse acting on an object is equal to the change in its momentum.

Conservation of Momentum:

• p_initial = p_final

The law of conservation of momentum states that the total momentum of a closed system remains constant if no external forces act on the system. This means that in a collision, the total momentum of the objects before the collision is equal to the total momentum of the objects after the collision. This principle is crucial for analyzing collisions and explosions.

Waves and Optics

Wave Properties

Understanding wave properties is essential for grasping how light and sound behave. These formulas help you describe and analyze wave motion.

Wave Speed:

• v = fλ

The speed of a wave (v) is equal to the frequency (f) of the wave multiplied by its wavelength (λ). This equation relates the fundamental properties of a wave: how fast it travels, how often it oscillates, and the distance between successive crests or troughs.

Period and Frequency:

• T = 1/f
• f = 1/T

The period (T) of a wave is the time it takes for one complete cycle to pass a given point. The frequency (f) is the number of cycles that pass a given point per unit time. Period and frequency are inversely related.

Optics

Optics deals with the behavior of light. These formulas are essential for understanding how lenses and mirrors form images.

Index of Refraction:

• n = c/v

The index of refraction (n) of a material is the ratio of the speed of light in a vacuum (c) to the speed of light in the material (v). It tells you how much slower light travels in a particular medium compared to a vacuum. This is crucial for understanding refraction.

Snell's Law:

• n_1sinθ_1 = n_2sinθ_2

Snell's Law describes how light bends when it passes from one medium to another. It relates the angles of incidence (θ_1) and refraction (θ_2) to the indices of refraction of the two media (n_1 and n_2). This law is fundamental for understanding lenses and prisms.

Thin Lens Equation:

• 1/f = 1/do + 1/di

The thin lens equation relates the focal length (f) of a lens to the object distance (do) and the image distance (di). This equation is used to determine where an image will be formed by a lens.

Magnification:

• M = -di/do

Magnification (M) is the ratio of the image height to the object height. It also can be calculated as the negative ratio of the image distance (di) to the object distance (do). A magnification greater than 1 indicates an enlarged image, while a magnification less than 1 indicates a reduced image. The negative sign indicates an inverted image.

Electricity and Magnetism

Electrostatics

Electrostatics deals with charges at rest. These formulas help you understand the forces and fields created by static charges.

Coulomb's Law:

• F = k(q_1q_2)/r^2

Coulomb's Law states that the electric force (F) between two point charges is directly proportional to the product of the magnitudes of the charges (q_1 and q_2) and inversely proportional to the square of the distance (r) between them. The constant k is Coulomb's constant. This law is fundamental for understanding electric forces.

Electric Field:

• E = F/q

The electric field (E) is the force per unit charge at a given point in space. It's defined as the force (F) that a positive test charge (q) would experience at that point divided by the magnitude of the test charge. Electric fields are vector quantities.

Circuits

Circuits involve the flow of electric charge. These formulas are essential for analyzing circuits and understanding how components behave.

Ohm's Law:

• V = IR

Ohm's Law states that the voltage (V) across a resistor is equal to the current (I) flowing through it multiplied by the resistance (R). This law is fundamental for analyzing simple circuits.

Power:

• P = IV = I^2R = V^2/R

Electrical power (P) is the rate at which electrical energy is converted into other forms of energy, such as heat or light. It can be calculated using several different formulas involving voltage (V), current (I), and resistance (R).

Series and Parallel Resistors:

• Series: R_eq = R_1 + R_2 + ...
• Parallel: 1/R_eq = 1/R_1 + 1/R_2 + ...

Resistors in series have the same current flowing through them, and their equivalent resistance (R_eq) is the sum of their individual resistances. Resistors in parallel have the same voltage across them, and the reciprocal of their equivalent resistance is the sum of the reciprocals of their individual resistances.

Thermal Physics

Heat and Temperature

Thermal physics deals with heat, temperature, and energy transfer. These formulas are essential for understanding thermodynamics.

Heat Transfer:

• Q = mcΔT

Heat (Q) is the energy transferred between objects due to a temperature difference. It's equal to the mass (m) of the object multiplied by its specific heat capacity (c) and the change in temperature (ΔT).

Phase Change:

• Q = mL

During a phase change (e.g., melting or boiling), the temperature remains constant, and the heat (Q) required is equal to the mass (m) of the substance multiplied by the latent heat (L) of the phase change.

Conclusion

So there you have it! A comprehensive cheat sheet of essential high school physics formulas. Keep this handy as you work through problems, and remember that understanding the concepts behind the formulas is just as important as memorizing them. Good luck, and happy studying!