AP Physics 1 Formula Sheet Quiz

Kinematic Equations

• The 1st kinematic equation expresses final velocity as a function of initial velocity, acceleration, and time: v = v₀ + at.
• The 2nd kinematic equation describes displacement in terms of initial velocity, time, acceleration, and provides a means to calculate distance traveled: x = x₀ + v₀t + ½at².
• The 3rd kinematic equation relates final velocity, initial velocity, acceleration, and displacement, useful for calculating velocity changes: v² = v₀² + 2a(∆x).

Newton’s Laws and Forces

• Newton's 2nd Law, solving for acceleration, is represented by: a = ∑F/m = Fnet/m, illustrating the relationship between net force, mass, and acceleration.
• The force of friction is defined by the equation: |Ff| = µ|Fn|, where the frictional force is proportional to the normal force and the coefficient of friction.

Circular Motion

• Centripetal acceleration, necessary for objects moving in a circle, is given by: a = v²/r, linking the speed of the object, radius, and acceleration.

Momentum

• Linear momentum is determined by the product of mass and velocity: p = mv.
• The Impulse Momentum Theorem states that the change in momentum is equal to the force applied multiplied by the time duration: ∆p = F∆t.

Energy Definitions

• Kinetic energy (translational) is calculated with the formula: K = ½mv², indicating the energy an object possesses due to its motion.
• The Work Energy Theorem relates work done to energy change: ∆E = W = Fd = Fdcos(θ), linking force, distance, and angle of application.
• Power is defined as the rate of energy change over time: P = ∆E/∆t.

Spring and Gravitational Energy

• Hooke's Law describes the force exerted by a spring: |Fs| = k|x|, where k is the spring constant and x is the displacement from equilibrium.
• The potential energy stored in a spring is given by: Us = ½kx².
• Gravitational potential energy near the surface of a planet is calculated as: ∆Ug = mg∆y, where m is mass, g is gravitational acceleration, and ∆y is the change in height.

Gravitational Forces

• The gravitational force between two masses is quantified by: |Fg| = Gm₁m₂/r², where G is the gravitational constant, m₁ and m₂ are masses, and r is the distance between centers.

Rotational Motion

• The 1st angular kinematic equation relates angular position, initial angular position, angular velocity, and angular acceleration: θ = θ₀ + ω₀t + ½αt².
• The 2nd angular kinematic equation relates final angular velocity to initial velocity and angular acceleration: ω = ω₀ + αt.
• Newton's second law for rotation, solved for angular acceleration, is: α = ∑τ/I = τnet/I, where τ is torque and I is moment of inertia.
• Torque is defined as: τ = rF = rFsinθ, illustrating its dependence on radius, force, and the angle between the force and radius vector.

Angular Momentum and Energy

• Angular momentum is defined as the product of moment of inertia and angular velocity: L = Iω.
• The Angular Impulse Momentum Theorem states the change in angular momentum equals torque multiplied by time: ∆L = τ∆t.
• Rotational kinetic energy is calculated using: K = ½Iω².

Oscillations and Frequency

• The period of a wave is expressed in terms of angular frequency: T = (2π)/ω = 1/f, connecting the concepts of frequency and time.
• The period of a spring is given by: Ts = 2π√(m/k).
• The period of a pendulum is defined as: Tp = 2π√(l/g), where l is the length of the pendulum and g is gravitational acceleration.

Simple Harmonic Motion

• The position of an object in Simple Harmonic Motion (SHM) is described by: x = Acos(2πft), where A is the amplitude and f is frequency.

Gravitational Potential Energy Between Masses

• Gravitational potential energy between two masses is calculated with the formula: Ug = (-Gm₁m₂)/r, highlighting the negative potential associated with gravitational interactions.

Density and Gravitational Field

• Density is defined as mass divided by volume: ρ = m/V.
• The gravitational field strength (acceleration due to gravity) is given by: g = Fg/m, where Fg is the gravitational force acting on a mass m.