# Kinetics of Particles

Part of the Dynamics course offered by the Division of Applied Mechanics, School of Engineering and the Engineering and Technology Portal

## Lecture

The application of particle kinematics to systems of forces is wholly dependent upon Newton's Second Law. Solutions to kinetics problems may be obtained by using Newton's Law directly, Work/Energy methods or through Impulse/Momentum calculations.

### Newton's Equation of Motion

${\displaystyle \sum {\vec {F}}_{(x,y,z)}=m{\vec {a}}_{(x,y,z)}}$
${\displaystyle \sum {\vec {F}}_{(r,\theta ,z)}=m{\vec {a}}_{(r,\theta ,z)}}$
${\displaystyle \sum {\vec {F}}_{(R,\theta ,\phi )}=m{\vec {a}}_{(R,\theta ,\phi )}}$


### Kinetic Energy Analysis (Energy of Motion)

${\displaystyle E=\int {\vec {F}}*d{\vec {r}}=\int ({\vec {F}}_{x}*dx+{\vec {F}}_{y}*dy+{\vec {F}}_{z}*dz)=\int m{\vec {a}}*d{\vec {r}}={\frac {1}{2}}m(v_{2}^{2}-v_{1}^{2})}$


Activities: