AP Physics C Formula Derivations Flashcards

AP Physics C Equations

Constant Speed

s = d/t where s is speed, d is distance, and t is time. Units are meters/second (m/s), meters (m), and seconds (s) respectively.

Constant Velocity

v = Δx/t where v is velocity, Δx is displacement, and t is time.

Acceleration

a = Δv/t where a is acceleration, Δv is the change in velocity, and t is time. Units are meters/second2 (m/s2), meters/second (m/s), and seconds (s) respectively.

ΣF = ma

Sum of forces in one dimension equals mass times acceleration. Units are Newton (N), kilogram (kg), and meters/second2 (m/s2).

Weight

w = mg where w is weight, m is mass, and g is gravity.

Friction Force

Ff = µFN where Ff is friction force, µ is the coefficient of friction, and FN is the normal force. Units are Newton (N), no unit, and Newton (N) respectively.

Torque

τ = r x F or τ = Fdsinθ where τ is torque, F is force, r is the lever arm, and θ is the angle between the force and the lever arm. Units are Newton meter (Nm).

Work

W = Fdcosθ where W is work, F is force, and d is distance (parallel to force). Units are Joule (J), N, and m respectively.

Kinetic Energy

KE = ½ mv2 where KE is kinetic energy, m is mass, and v is velocity. Units are Joule (J), kilogram (kg), and meters/second (m/s) respectively.

Gravitational Potential Energy

Ug = mgh where Ug is potential energy, m is mass, g is gravity, and h is height. Units are J, kg, m/s2, and m respectively.

Spring Potential Energy

Us = ½ kx2 where Us is potential energy, k is the spring constant, and x is the position from equilibrium. Units are J, Newton/meter (N/m), and meter (m) respectively.

Spring Force

F = -kΔx where F is spring force, k is the spring constant, and Δx is the position from equilibrium. Units are Newton (N), Newton/meter (N/m), and meter (m) respectively.

Power

P = W / t = ΔET / t where P is power, W is work, ΔET is the total change in energy, and t is time. Units are Watts (W) or Joule/second (J/s), Joule (J), and second (s) respectively.

Momentum

p = mv where p is momentum, m is mass, and v is velocity. Units are kilogram meter/second (kg m/s), kilogram (kg), and meters/second (m/s) respectively.

Impulse

J = ʃ Fnet(t) dt = Δp where J is impulse, Fnet is force, t is time, and Δp is the change in momentum. Units are Ns, N, sec, kg*m/s.

Tangential Velocity

vT = 2πr / T where vT is tangential velocity, r is radius, and T is the period of orbit. Units are meters/second (m/s), meter (m), and seconds (s) respectively.

Centripetal Acceleration

ac = vT2 / r = rω2 where ac is centripetal acceleration, vT is tangential velocity, r is radius, and ω is angular velocity. Units are meters/second2 (m/s2), meters/second (m/s), meter (m), and radians /second (rad/s) respectively.

Gravitational Force

F = Gm1m2 / r2 where F is gravitational force, G is the gravitational constant, m1 and m2 are masses, and r is radius. Units are Newton (N), Nm2 / kg2, kilogram (kg), and meter (m) respectively.

Angular Velocity

ω = dθ / dt where ω is angular velocity, dθ is angular displacement, and dt is time. Units are radians/second (rad/s), radians (rad), and second (s) respectively.

Angular Acceleration

α = dω / dt where α is angular acceleration, dω is the change in angular velocity, and dt is time. Units are radians/second2 (rad/s2), radians/second (rad/s), and second (s) respectively.

Rotational Kinetic Energy

KER = ½ Iω2 where KER is rotational KE, I is rotational inertia, and ω is angular velocity. Units are Joule (J), kilogram meter2 (kg m2), and radians/second (rad/s) respectively.

External Torque

α = Στ / I where angular acceleration equals the net external torque divided by the rotational inertia. Nm, kg*m2, rad/s2

Angular Momentum

L = r x p = Iω where L is angular momentum, r is the lever arm, p is linear momentum, I is rotational inertia, and ω is angular velocity. Units are kg m2/s, m, kgm/s, kgm2, rad/s.

Gravitational Potential Energy (General)

UG = -GMm / R where UG is potential energy, G is the gravitational constant, M is the mass of the planet, m is the mass of the satellite, and R is the radius. Units are Joule (J), Nm2 / kg2, kilogram (kg), kilogram (kg), and meter (m) respectively.

Period and Frequency Relationship

T = 1/f where T is period and f is frequency. Units are seconds (s) and Hertz (Hz) or cycles/second respectively.

Pendulum Period

T = 2π √(L/g) where T is period, L is the length of the pendulum, and g is gravity. Units are second (s), meter (m), and m/s2 respectively.

Mass-Spring Period

T = 2π √(m/k) where T is period, m is mass, and k is the spring constant. Units are second (s), kg, and Newton/meter (N/m) respectively.