Dynamics Equation Sheet: Symbol Definitions (SI Units)

Dynamics Equation Sheet – Complete Symbol Definitions (SI
Units)
Rectilinear & Curvilinear Kinematics
Symbol
Meaning
SI Units
t
Time
s
s, s■
Path position, initial position
m
x, y, z
Cartesian coordinates
m
r, θ, z
Cylindrical coordinates
m, rad, m
v, v■
Velocity, initial velocity
m/s
v■, v■, v_z
Velocity components
m/s
a, a_c
Acceleration, constant acceleration
m/s²
a■, a■, a_z
Acceleration components
m/s²
a_t
Tangential acceleration
m/s²
a_n
Normal acceleration
m/s²
ρ
Radius of curvature
m
Relative Motion
Symbol
Meaning
SI Units
v_A, v_B
Velocity of points A and B
m/s
a_A, a_B
Acceleration of points A and B
m/s²
v_B/A
Velocity of B relative to A
m/s
a_B/A
Acceleration of B relative to A
m/s²
r_B/A
Position vector from A to B
m
Ω
Angular velocity of rotating frame
rad/s
Rigid Body Rotation
Symbol
Meaning
SI Units
θ, θ■
Angular position, initial angular position
rad
ω, ω■
Angular velocity, initial angular velocity
rad/s
α, α_c
Angular acceleration, constant angular acceleration
rad/s²
r
Distance from rotation axis
m
v
Tangential velocity (ωr)
m/s
a_t
Tangential acceleration (αr)
m/s²
a_n
Normal acceleration (ω²r)
m/s²
Mass Properties
Symbol
Meaning
SI Units
m
Mass
kg
I
Mass moment of inertia
kg·m²
I_G
MOI about center of mass
kg·m²
k
Radius of gyration
m
d
Distance between parallel axes
m
Forces & Moments
Symbol
Meaning
SI Units
F
Force
N
ΣF
Resultant force
N
M, M_G, M_O Moment / torque
N·m
W
Weight
N
k_s
Spring constant
N/m
∆s
Displacement
m
Energy, Work, Power
Symbol
Meaning
SI Units
T
Kinetic energy
J
V, V_g, V_e
Potential energies (total, gravity, elastic)
J
U
Work
J
P
Power
W
ε
Efficiency
—
Impulse & Momentum
Symbol
Meaning
SI Units
p
Linear momentum
kg·m/s
H_O
Angular momentum about point O
kg·m²/s
H_G
Angular momentum about center of mass
kg·m²/s
∫F dt
Linear impulse
N·s
∫M dt
Angular impulse
N·m·s
Impact & Collisions
Symbol
Meaning
SI Units
e
Coefficient of restitution
—
v■, v■
Velocities before and after impact
m/s