Fundamental Dynamics

Fundamental Dynamics Calculator

Rectilinear & Fixed Axis Rotational Motion

Initial Velocity ($v_0$) [m/s] / ($\omega_0$) [rad/s]

Constant Acceleration ($a_c$) [m/s²] / ($\alpha_c$) [rad/s²]

Time Duration ($t$) [seconds]

Radius of Rotation ($r$) [meters] (For Point P conversion)

Final Linear Velocity ($v$): 0.00 m/s

Linear Displacement ($\Delta s$): 0.00 m

Final Angular Velocity ($\omega$): 0.00 rad/s

Angular Displacement ($\theta$): 0.00 rad

Tangential Acceleration ($a_t$): 0.00 m/s²

Normal Acceleration ($a_n$): 0.00 m/s²

Curvilinear Profiles ($n, t, b$ Geometry)

Evaluates profile radius $\rho = \frac{[1 + (dy/dx)^2]^{3/2}}{|d^2y/dx^2|}$

Instantaneous Velocity ($v$) [m/s]

First Derivative ($dy/dx$) [Slope]

Second Derivative ($d^2y/dx^2$) [Curvature rate]

Radius of Curvature ($\rho$): 0.00 m

Normal Acceleration ($a_n = v^2/\rho$): 0.00 m/s²

Mass Properties & Work Parameters

Mass ($m$) [kg]

Radius of Gyration ($k$) [meters]

Constant Force ($F_c$) [Newtons]

Force Angle ($\theta$) [Degrees]

Displacement ($\Delta s$) [meters]

Mass Moment of Inertia ($I_G$): 0.00 kg·m²

Required Unopposed Force ($\Sigma F$): 0.00 N

Work Done by Force ($U_F$): 0.00 J

Energy, Power & Restitution

Spring Constant ($k_s$) [N/m]

Spring Compression/Extension ($s$) [m]

Efficiency ($\varepsilon$) [Decimal, e.g., 0.85]

Coefficient of Restitution ($e$)

Elastic Potential Energy ($V_e$): 0.00 J

Kinetic Energy (Translational, $T$): 0.00 J

Useful Power Output ($P_{\text{out}}$ @ $v_o$): 0.00 W

Required Power Input ($P_{\text{in}}$): 0.00 W

Relative Separation Velocity: 0.00 m/s