Kinematics:
Motion constant acceleration
$v=u+ft$
$s=ut+\frac{1}{2}ft^2=\frac{1}{2}(u+v)t$
$v^2=u^2+2f.s$
General solution of $\frac{d^2x}{dt^2}=-w^2x$ is
x=a.coswt + b.sinwt = R.sin(wt+φ)
where $R=\sqrt{a^2+b^2}$ and cosφ = a / R, sinφ = b / R.
In polar coordinates the celocity is 
and the acceleration is
and the acceleration is
Centres of mass:
The following results are for uniform bodies:
- hemispherical shell, radius r ⇾ $\frac{1}{2}r$ ⇾ from centre
- hemisphere, radius r ⇾ $\frac{3}{8}r$ ⇾ from centre
- right circular cone, height h ⇾ $\frac{3}{4}h$ ⇾ from vertex
- arc, radius r and angle 2θ ⇾ (r sinθ) / θ ⇾ from centre
- sector, radius r and angle 2θ ⇾ ($\frac{2}{3}r$ sinθ) / θ ⇾ from centre
