Rotation between Angular and linear velocity and acceleration

8.4 Rotation between Angular and linear velocity and acceleration
Consider a point p, p moves in a circle, the linear velocity vector is thus tangent to this circle. Magnitude is ???????? , where s is distance travelled along the circular path
??=???? [?? ???? ????????????]
??=????????=??????????
??=????
We can find the radiation between the linear acceleration and the angular acceleration, by taking the time derivative of ??
????=????????=??????????=???? [???? the tangential acceleration]
????=??2??=??2??2??=????2 [???? the radial acceleration]
Total linear acceleration of the particle is
???=?????+?????=????+????2 (??/??2)
8.5 Rotational Kinetic Energy
The kinetic energy K of a rigid body rotating about a fixed axis is given by:
??=12????2
??=?????????2?? [moment of Inertia] [??]=????.??2
??,I? Resistance to rotational motion
??,m? Resistance to linear motion
8.6 Angular momentum of a Particle
Consider a particle of mass m, located at the position vector ??? and moving the velocity ??? . The instantaneous angular momentum ???? of the particle relative to the origin “O” is defined by the cross product of its instantaneous position vector and it’s instantaneous ??? :