Mechanics Formula Sheet

τ = r x F = r F sin θ

∆p ∆t

∆x x f − xi Average velocity v = = ∆t t f − t i

F=

Average acceleration =

I = F ∆t = ∆p

v f − vi ∆v a = = ∆t t f − ti

τ = Iα (Analogous to F = ma)

Rotational KE = ½ I ω 2

v = u + at (for constant acceleration, a)

L=Iω

v2 = u2 + 2as (for constant acceleration, a) s = ut + ½ at2 (for constant acceleration, a)

I1 ω1 = I2 ω2 s=rθ θ in deg. =

180 (θ in rad) π

vt = rω

Fnet = ma Fk = μk R Fs ≤ μs R

ω=

dθ dt

α=

d 2θ dt 2

at = r α ω = ωo + αt ω2 = ωo2 + 2αθ θ = ω ot +

1 2 αt 2

mvt 2 r v 2 a(c.p) = t r F(c.p) =

W = F cos θ * s K = ½ m v2 W = Kf - Ki Gravitational Potential Energy = mgh Potential energy stored in spring = ½ kx2 P=

W t

p=mv

I = ∑ mr 2

g(r) = G

Fg = G

M r2

m1m2 r2

T2 = Constant r3

(Analogous to p = mv) for τnet = 0

a = acceleration [ms-2] a(c.p) = centripetal acceleration [ms-2] a = Average acceleration [ms-2] at = tangential acceleration [ms-2] F = force [N] F(c.p) = centripetal force [N] Fg = gravitational force [N] Fk = kinetic friction [N] Fs = static friction [N] g = acceleration of gravity = 9.8 ms-2 G = gravitational constant = [Nm2kg--2] h = height [m] I = impulse [kg ms-1] k = spring constant [Nm-1] K = kinetic energy [J] L = angular momentum [m2kgs-1] m = mass [kg] M = mass [kg] p = linear momentum [kgms-1] P = Power PE = potential energy = [J] r = radius [m] R = Normal force (or Reaction force) [N] s = distance or arc length [m] t = time [s] T = period [s] u = initial velocity [ms-1] v = velocity [ms-1] vt = tangential velocity [ms-1] v = Average velocity [ms-1] x = spring extension [m] W = work [J] α = angular acceleration [s-2] μk = coefficient of kinetic friction μs = coefficient of static friction ω = angular velocity [s-1] ωo = initial angular velocity [s-1] ∆ = represents change θ = angular displacement [rad] τ = torque [mN]