quantity

symbol

relation to other variables

SI units

type

NI units

type

Kinematics

Circumference

C

C = 2πr

m

m

base unit

Circular arc length

Arc

Arc: = rθ

m

m

Radius of rotation

r

R = C/(2π)

m

base unit

m/rad

Angle

θ

θ = angle = Arc/r

1

base unit

rad

base unit

Angular velocity

ω

ω: = dθ/dt = 2πf

1/s

rad/s

Angular acceleration

Α

α: = dω/dt

1/s²

rad/s²

2π

Convert cycle to radian

1

rad/cycle

Frequency

f

f: = ω/2π

1/s

cycle/s

Period

T

T = 1/f

S

s/cycle

Mechanics

Mass density (2-D)

ρ

ρ:= dmass/dArea

kg/m²

base unit

kg/m²

base unit

Moment of inertia

I

${\rm I}:={\displaystyle \int \rho r^2\text{dArea}}$

Kg/m²

kg m²/rad²

Angular momentum

L

Iω

J s = kg m²/s

J s/rad = kg m²/s/rad

Torque (rotational force)

τ

τ: = dL/dt, or τ: = −dKE/dθ

N m N m/rad

J/rad = N m/rad J/rad= N m/rad

Kinetic energy

KE

$KE:={\displaystyle \int \tau \text{d}\theta }=\frac{1}{2}I{\omega }^2$

J

J = N m

Potential energy (k = elastic constant)

PE

$PE:={\displaystyle \int \tau \text{d}\theta }=\frac{1}{2}k{\theta }^2$

J

J = N m