Determine system (machinery/ application).

• Determine size, material and mass.
• Determine coefficient of friction.
• Calculate forces.
• Calculate torque.
• Calculate inertia.

Force

Normal Force		$$F_N=m \cdot g$$
Acceleration Force		$$F_a=m \cdot a$$
Gravitational Force		$$F_G=m \cdot g$$
Frictional Force		$$F_f=μ \cdot m \cdot g$$ $$=μ \cdot F_N$$
Compression Force		$$F_p=p \cdot A$$
Spring Force		$$F_s=k \cdot l$$

Torque

Torque = force ∙ arm		$$M=F \cdot r \cdot sin⁡θ$$
Torque = moment of inertia ∙ angular acceleration		$$M=J \cdot α$$

Inertia

Point		$$J=m \cdot R^2$$
Solid Sphere		$$J=\frac{2}{5} \cdot m \cdot R^2$$
Hollow Sphere		$$J=\frac{2}{5} \cdot m \cdot \left(\frac{{R_1}^5-{R_2}^5}{{R_1}^3-{R_2}^3}\right)$$ Hollow thin-walled sphere: $$J=\frac{2}{3} \cdot m \cdot {R_1}^2$$
Solid Cylinder		(1)$$J=m \cdot R^2$$ (2)$$J=\frac{1}{4} \cdot m \cdot R^2+\frac{1}{12} \cdot m \cdot L^2$$
Eccentric Solid Cylinder		$$J=J_c+m \cdot {R_e}^2$$
Hollow Cylinder		(1)$$J=\frac{1}{2} \cdot m \cdot ({R_1}^2+{R_2}^2)$$ Hollow thin-walled cylinder: $$J=m \cdot {R_1}^2$$ (2)$$J=\frac{1}{4} \cdot m \cdot ({R_1}^2+{R_2}^2+\frac{L^2}{3})$$ Hollow thin-walled cylinder: $$J=\frac{1}{2} \cdot m \cdot {R_1}^2+\frac{1}{12} \cdot m \cdot L^2$$
Circular Cone		(1)$$J=\frac{3}{10} \cdot m \cdot R^2$$ Hollow thin-walled cone: $$J=\frac{1}{2} \cdot m \cdot R^2$$ (2)$$J=\frac{3}{20} \cdot m \cdot (R^2+4L^2)$$ Hollow thin-walled cone: $$J=\frac{1}{4} \cdot m \cdot (R^2+2L^2 )$$
Cuboid		(1)$$J=\frac{1}{12} \cdot m \cdot (a^2+b^2 )$$ (2)$$J=\frac{1}{12} \cdot m \cdot (a^2+c^2 )$$ (2)$$J=\frac{1}{12} \cdot m \cdot (a^2+4c^2 )$$
Rod		(1)$$J=\frac{1}{3} \cdot m \cdot L^2$$ (2)$$J=\frac{1}{12} \cdot m \cdot L^2$$