1) objects in motion stay in motion, a body at rest stays at rest, until a force is applied ("law of inertia")
2) change in momentum of a body is equal in magnitude and direction to the force applied to it (force = mass * acceleration)
3) when two bodies interact, they apply forces that are equal to each other, and opposite in direction ("law of action and reaction")
Basic definitions:
Fnet = Δp / Δt (since p = mv and Δv/Δtime = acceleration)
Change in potential energy is given by U=mgh
dimensional homogeneity - units must be correct for parts added together, left side matches right side, etc.
Displacement is change in position.
s(t) = s0 + t*(v0+vt)/2 s = displacement from origin at time t vt = v0 + a*t if v0 = 0 then s(t) = s0 + t²*(a)/2 so in free-fall, from position 0, you have: s(t) = g * t²/2
coefficient of restitution = ratio of energy conserved after collision
e = (vel. after collision) / (vel. before collision) (for collision with immovable object) e = (Vfa * Vfb) / (Via * Vib) (for collision between objects a and b. f = final, i = initial velocity) e = 1 for perfectly elastic, 0 for perfectly inelastic
conservation of momentum: p1i + p2i = p1f + p2f
for m1 having velocity u1 to the right, m2 initially at rest, ends with velocity v2. x dimension: m1u1 = m1u2cosθ1 + m2v2cosθ2 y dimension: 0 = m1u2sinθ1 - m2v2sinθ2
Glancing blow: If and only if both masses are equal (like billiards), then the angle between the resulting vectors is always 90 degrees.
normal force = force perpendicular to the plane normal force on a block resting on a slope, θ = degrees from horizontal: f = m*g*cos(θ) parallel force = force parallel to the inclined plane f = m*g*sin(θ) When parallel force > friction, it is unbalanced and objects will move down the plane Applied force - friction = net force
Coefficient of friction
static friction -
μS (mu static) = fS/N
(fS = force where static friction is overcome
N = normal force) must be overcome before the mass moves
μS = fs/N = m*g*sin(θ) / m*g*cos(θ) = sin(θ)/cos(θ) = tan(θ)
kinetic friction - moving friction
only one type of friction applies at a time
Vx = Vo*cos(θ) Vy = Vo*sin(θ) - gt x = Vx*t y = Vy*t - g*t²/2
projectile follows the shape of a parabola
y = Ax² + Bx y = -gx²/(2(VoCos(θ))²) + xtan(θ) time of flight: t = 2Vosin(θ)/g max height: H = (Vosin(θ))²/2g distance: x = sin(2*θ)*Vo² / g
Vo = initial velocity Can use 2sin(θ)cos(θ) = sin(2θ) if filling in t with time of flight in the x = Vx*t formula
Vf² = Vi² + 2ad ?
pressure P = F/A (force/area)
hydrostatic gauge pressure: P = pgh, p = density of fluid, g=gravity, h=height (depth)
buoyant force Fb = Fup - Fdown
Fb = pgVf, where Vf = volume of displaced fluid, and density * volume = mass, so Fb = mf*g, where mf = mass of displaced fluid => buoyant force depends on mass of displaced fluid, not the mass of the object
gravitational constant between two bodies
F = G * m1 * m2 / r² and g = G * m1 / r² gE (gravity Earth) = 9.8 m/s²
no use of forces in the equations
typical equations: d = vo*t + 1/2*a*t² d = (vo + vf)/2 * t vf²= vo² + 2ad vf = v0 + at
Refraction on going into a different medium
Snell's law sin(θ₁) / sin(θ₂) = v₁/v₂ = n₂/n₁ (note that the n values are reversed)
v = velocity of light in that medium, n = index of refraction v = c/n (c = speed of light in a vacuum) it bends towards the normal direction when entering denser material (and slows down). bend is because photons are waves. Critical angle : smallest angle that results in total reflection, no refraction θc = arcsin(n₂/n₁)