Plane Kinetics of Rigid Bodies

Flashcards for reviewing plane kinetics of rigid bodies, focusing on key concepts and definitions.

Plane Motion

Motion of a body approximated as a thin slab, confined to the plane of the slab, with the plane containing the mass center.

Mass Moment of Inertia

A property of a body that accounts for the radial distribution of its mass with respect to a particular axis of rotation.

General Equations of Motion

ΣF = ma and ΣMG = I𝛼, where ΣF is the resultant external force, a is the acceleration of the mass center G, ΣMG is the resultant moment about G, I is the mass moment of inertia, and 𝛼 is the angular acceleration.

Rotational Inertia

Resistance to change in rotational velocity due to the radial distribution of mass around the z-axis through G.

Unconstrained Motion

Motion where there are no physical confinements (e.g., a rocket moving in a vertical plane).

Constrained Motion

Motion where physical constraints impose a kinematic relationship between acceleration components (e.g., a bar with ends in vertical and horizontal guides).

Translation

Rigid-body motion where every line in the body remains parallel to its original position; includes rectilinear and curvilinear types.

Fixed-Axis Rotation

Motion where all points in the body describe circles about the rotation axis, with all lines in the plane of motion having the same angular velocity 𝜔 and angular acceleration 𝛼.

Center of Percussion

Point Q on line OG where the resultant of all forces applied to the body must pass through, and the sum of moments about this point is always zero.

General Plane Motion

Combination of translation and rotation; analyzed using ΣF = ma and ΣMG = I𝛼.