The Planar Kinematics of A Rigid Body Engineering Research Paper

Topics

Chapters of the book

Rigid body kinematics

16.1-16.3

General motion, absolute and relative motion: velocity

16.4-16.5

Instantaneous centers of rotation

16.6

Relative motion analysis: acceleration

16.7

Relative motion in a rotating coordinate system

16.8

Rigid body kinetics: translation

17.2-17.3

Rigid body kinetics: Rotation about a fixed axis

17.4

General plane motion

17.5

Work and energy in rigid bodies

18.1–18.4

Conservation of energy in rigid bodies, Angular Momentum of Particles

18.5
15.5 – 15.7

Impulse and momentum in rigid bodies

19.1-19.2

The moment of a force is the tendency for the force to cause rotation of a particle/rigid body about a given point in space. One of the key features here is that the moment of the force is dependent upon where we measure it from; the point in space that we calculate the moment. Mathematically, we calculate the moment of the force about a point A as MA=rA×F$M_A=r_A\times F$ , where MA is the moment of the force as a vector, F is the force vector, and rA is the position vector from A to any location along the line of action of the force. The above mathematical representation is in vector form and works in all situations. However, sometimes the scalar form of the equation is easier to work with: MA=rA∗F∗sin(θ)$M_A=r_A\ast F\ast \sin \left(\theta \right)$

where the moment, position vector are in scalar form and θ$\theta$ is the angle between the position vector and force vector. (A visual drawing of this would really make this definition amazing)

Mathematically, we calculate the moment of the force about a point A as MA=rA×F$M_A=r_A\times F$ , where MA is the moment of the force as a vector, F is the force vector, and rA is the position vector from A to any location along the line of action of the force. The above mathematical representation is in vector form and works in all situations. However, sometimes the scalar form of the equation is easier to work with: MA=rA∗F∗sin(θ)$M_A=r_A\ast F\ast \sin \left(\theta \right)$

where the moment, position vector are in scalar form and θ$\theta$ is the angle between the position vector and force vector.

Mathematically, we calculate the moment of the force about a point A as MA=rA×F$M_A=r_A\times F$ , where MA is the moment of the force as a vector, F is the force vector, and rA is the position vector from A to any location along the line of action of the force.