Translational Mechanics

Translational Motion

Newton’s 2nd Law
$F=ma$
equivalently
$m\frac{dv}{dt}=f$
If the mass only moves in the x-direction we have the following and its derivatives
$v\left(t\right)=\frac{dx\left(t\right)}{dt}$ Assuming:

• The object is rigid
• Force distributions are neglected Then we can treat the object as a concentrated mass (point mass); the dimensions are ignored
  This is a |Lumped Element

Moment about Point P for a rigid Body

$M_p=I_p\alpha +m{r}_x{a}_y-m{r}_y{a}_x$

Note on problems

A lot of the PS3 problems seems to include making an equation of motion by taking a moment about a pivot point, or just straight up combining inertias of a rigid body

ex. $I_A=I_C=I_B$
Where $I_C$ and $I_B$ are the inertias of two ends of a bent rod where they are both $M{L}^2$ where L varies based on length