Master Rigid Body Dynamics through interactive simulations. Learn about moments of inertia, angular momentum, torque, and rotational motion with hands-on examples and visualizations.
Rigid body dynamics studies the motion of solid objects where deformation is negligible. Unlike point masses, rigid bodies have size and shape, leading to complex rotational behaviors governed by moments of inertia and torque.
Resistance to rotational acceleration
Rotational analog of linear momentum
Rotational force causing angular acceleration
Fundamental equations describing rigid body rotation
Explore rigid body dynamics through interactive visualizations with adjustable parameters
Adjust mass distribution to see how it affects rotational resistance
Observe how angular momentum is conserved when moment of inertia changes
Explore the relationship between applied force, lever arm, and rotational acceleration
Visualize the complex motion of asymmetric rigid bodies
Step-by-step breakdown of key concepts and mathematical foundations
The moment of inertia measures an object's resistance to changes in its rotational motion. It depends on both the mass of the object and how that mass is distributed relative to the axis of rotation.
I = Σ mᵢrᵢ²
Where I is the moment of inertia, mᵢ is the mass of each particle, and rᵢ is the distance from the axis of rotation.
Angular momentum is the rotational equivalent of linear momentum. For a rigid body rotating about a fixed axis, it equals the product of the moment of inertia and angular velocity.
L = Iω
Where L is angular momentum, I is moment of inertia, and ω is angular velocity.
Torque is the rotational equivalent of force. Newton's second law for rotation states that the net torque equals the moment of inertia times angular acceleration.
τ = Iα
Where τ is torque, I is moment of inertia, and α is angular acceleration.
For the general motion of a rigid body, Euler's equations describe the relationship between angular velocities, moments of inertia, and external torques in a body-fixed coordinate system.
I₁(dω₁/dt) + (I₃ - I₂)ω₂ω₃ = τ₁
I₂(dω₂/dt) + (I₁ - I₃)ω₃ω₁ = τ₂
I₃(dω₃/dt) + (I₂ - I₁)ω₁ω₂ = τ₃
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