Dynamics Of Rigid Bodies Simulations

A collection of interactive 3D visualizations and simulations to help you master concepts in dynamics of rigid bodies.

Kinematics of Particles - Theory & Concepts

Study of the geometry of motion of particles without considering the forces causing the motion, including rectilinear and curvilinear motion.

Radial and Transverse Velocity Components

Radius (r)150 m

Angle (θ)45°

Radial Velocity (v_r)40 m/s

Transverse Velocity (v_θ)60 m/s

Total Velocity:

|\mathbf{v}| = \sqrt{v_r^2 + v_\theta^2} = 72.1 \text{ m/s}

Kinetics of Particles: Force and Acceleration - Theory & Concepts

Application of Newton's Second Law to determine the motion of a particle subjected to unbalanced forces.

Orbital Mechanics: Conic Sections

Eccentricity (e)0.50

Orbit Type: Elliptical

Scale Parameter (a)100

Polar Equation of Orbit:

r = \frac{a(1 - e^2)}{1 + e \cos \theta}

Kinetics of Particles: Work and Energy - Theory & Concepts

Application of the Principle of Work and Energy to solve kinetics problems involving displacement and speed, including conservative and non-conservative forces.

System Parameters

Mass (kg)2.0

Spring Stiffness (N/m)500

Initial Compression (m)0.20

Kinetic Friction (

\mu_k

)0.00

2kg

-0.5m0m0.5m1.0m1.5m2.0m

Energy Conservation (J)

PE0

KE0

Heat0

Total0

Velocity: 0.00 m/s

Kinetics of Particles: Impulse and Momentum - Theory & Concepts

Application of the principle of linear impulse and momentum to solve problems involving force, mass, velocity, and time, including systems of particles.

Collision Simulator (Impulse & Momentum)

APPROACHING

Object A

Mass (kg)

Vel (m/s)

Object B

Mass (kg)

Vel (m/s)

Restitution (

e

)0.8

Plastic (0)Elastic (1)

Initial Momentum:2.00

Final Momentum:2.00

Initial KE:22.00 J

Final KE:14.22 J

Energy Loss:7.78 J

Kinematics of Rigid Bodies - Theory & Concepts

Analysis of the motion of solid bodies where distances between any two points remain constant, including translation, rotation, and general plane motion.

Rigid Body Translation Simulation

Notice how the line connecting points A and B remains parallel to its original orientation throughout the motion.

Kinetics of Rigid Bodies: Force and Acceleration - Theory & Concepts

Application of Newton's Second Law and Euler's Equations to determine the general plane motion of rigid bodies.

Mass Moment of Inertia Calculator

Shape

Mass (

m

)10 kg

Radius (r)0.50 m

I_G = 1/2 m r^2

Moment of Inertia (

I_G

)1.250kg·m²

Kinetics of Rigid Bodies: Work and Energy - Theory & Concepts

Energy methods applied to rigid bodies, including rotational kinetic energy, potential energy of rigid bodies, and conservation of energy.

Rolling Sphere Simulator

Height (

h

)2.0 m

Incline Angle (

\theta

)30°

Current Time (

t

)0.00 s

Current Velocity (

v

)0.00 m/s

Max Velocity (v_max)5.29 m/s

Kinetics of Rigid Bodies: Impulse and Momentum - Theory & Concepts

Analysis of impulsive forces and moments acting on rigid bodies, introducing angular momentum and the principle of impulse and momentum.

Angular Momentum Conservation: Bullet & Rod

Bullet Mass (

m

)0.010 kg

Bullet Velocity (

v

)400 m/s

Rod Mass (

M

)4 kg

Initial Ang. Mom. (

H_O

)2.00 kg·m²/s

Total Inertia (I_total)1.336 kg·m²

Final Ang. Vel. (

\omega

)1.50 rad/s

Mechanical Vibrations - Theory & Concepts

Introduction to free and forced vibrations of single-degree-of-freedom systems, including torsional vibrations and damping.

Mechanical Vibrations Simulator

Underdamped (

\zeta = 0.06

)

Mass (

m

)5 kg

Stiffness (

k

)50 N/m

Damping (

c

)2 Ns/m

Initial Disp (

x_0

)1 m

Natural Freq (

\omega_n

):3.16 rad/s

Critical Damping (

c_c

):31.62 Ns/m

Damped Freq (

\omega_d

):3.16 rad/s