## Calculus Based Physics Formulas: Mechanics

This is just a basic equation list, explanations can be found elsewhere. For the most part derivations are done for you, but it is beneficial to understand how an equation goes from one form to another.

**One dimensional Equations of motion (along a single vector direction)**

Velocity as a function of time :

Position as a function of time:

Velocity as a function of position:

**Projectile Motion**

*Horizontal motion*

Velocity along x:

Position from position as a function of time:

Max Horizontal dist:

*Vertical Motion*

Velocity along y:

Position: from position as a function of time

Maximum Height:

**Circular Motion**

Radial Acc:

Tan. Acc:

Total Acc (magnitude) from Pythagoras:

**The Laws of Motion**

Newtons Second Law:

Equilibrium Conditions:

Force of Static Friction

Force from Kinetic Friction

**Force/Work**

Constant Force:

Variable Force:

Hooke’s Law:

Spring Work:

Kinetic energy:

Work – kinetic energy theorem:

Power: , ,

gravitational potential energy:

conservation of mechanical energy:

elastic collision conserved moment and KE:

2d elastic (comp): ,

KE conservation for elastic:

Momentum:

**Mass**

Center of mass (comp):

Position vector for CM:

Continuous mas dist:

Mass of Uniform:

Linear Mass Dist:

Area Mass Dist:

**Rotational Motion**

angular speed:

angular acceleration: ,,

Moment of Inertia: ,,,

Rotational KE:

Work:

Net torque : ,

Work :

Power :

Angular Momentum :

Torque: :

**Moments of Inertia**

Hoop :

Cylinder (hollow) :

Cylinder :

Rectangular Plate :

Rod (center rotate):

Rod (end Rotate):

Solid Sphere :

Spherical Shell :