BvU said:
Welcome, Goodwill!Goodwill said:
Lnewqban said:
Your diagram above appears to show a vertical axis. As I understand the question, the cube is swinging backwards and forwards under gravity.Goodwill said:
,Goodwill said:
A rigid body in physics is an idealized solid object in which the distances between points are fixed and do not change, regardless of external forces or torques applied to it. This means that the body does not deform, and its shape and size remain constant.
The equations of motion for a rigid body consist of Newton's second law for translational motion and Euler's equations for rotational motion. For translational motion, the equation is F = ma, where F is the total force, m is the mass, and a is the acceleration. For rotational motion, Euler's equations are τ = Iα, where τ is the torque, I is the moment of inertia, and α is the angular acceleration.
The moment of inertia is a measure of an object's resistance to changes in its rotational motion about a specific axis. It depends on the mass distribution relative to the axis of rotation. For a discrete system, it is calculated as I = Σmᵢrᵢ², where mᵢ is the mass of the i-th particle and rᵢ is its distance from the axis of rotation. For continuous bodies, it is calculated using integral calculus.
A rigid body is an idealization where the distances between points within the body remain constant, meaning it does not deform under external forces. A deformable body, on the other hand, can change its shape and size when forces or torques are applied. In real-world applications, most objects exhibit some degree of deformability, but rigid body assumptions simplify analysis and calculations.
To solve a rigid body dynamics problem, follow these steps: (1) Identify and isolate the rigid body, (2) Draw a free-body diagram showing all external forces and torques, (3) Apply Newton's second law for translational motion (F = ma) and Euler's equations for rotational motion (τ = Iα), (4) Solve the resulting equations for the unknown quantities, such as accelerations, forces, or torques, and (5) Use kinematic equations to find velocities and displacements if needed.
