Rotational Dynamics Equation Derivation

I=∑miri2= ∫r2dm

Ip= ∫r2dm
= ∫(h+r)2dm

= ∫(h2+2hr=r2)dm

= ∫h2dm + ∫r2dm + ∫2hr dm

= h2 ∫dM + r2 ∫dm

Ip = Mh2 + Icm

τ = r x F
= rFsinθ


F=ma

τ=rF=rma
= rm(rα)
=mr2α
=(∑miri2)α
= Iα

p=mv

l=m(r x v)

dl/dt = m[dr/dt x v + r x dv/dt]

= m [0 + r x a]

=mαr2

dl/dt=Iα