Rigid body mechanics

uniform rotational motion and torque and whatever else belongs to that

angular displacement (θ)

the change in angle through which a rigid body has rotated relative to a fixed point; s = rθ; measured in radians

angular velocity

the rate of change of angular displacement; ⍵ = θ/t; measured in radians/second

linear velocity

v=r⍵

angular acceleration

the rate of change of angular velocity; 𝛼=⍵/t or 𝛼=v/rt

linear (tangential) acceleration

a=r𝛼

centripetal acceleration

a=r⍵² or a=v²/r

moment of inertia

the resistance to a change of rotational motion, depending on the distribution of mass around the axis of rotation; I=mr² or I = L/⍵; measured in kgm²

torque

depends on the object’s moment of inertia; 𝜏=I𝛼 or 𝜏=L/t

angular momentum

L=I⍵ or L = mvr

Angular impulse

ΔL=𝜏 ⋅ t or change in angular momentum

rotational kinetic energy

KE = ½ I⍵² or KE = L²/2I

centripetal force

∑maC or mv²/r or mr⍵²