=-1.8cm Some Formulas

Selected Math Formulas
Circumference of a circle: $C=2\pi R$
Area of a cricle: $A=\pi R^2$
Volume of a sphere: $V=\frac{4}{3}\pi R^3$
Surface area of sphere: $A=4\pi R^2$

International System of Units

Unit of	is the
length	meter (1 m)
time	second (1 s)
mass	kilogram (1 kg)

If prefix	multiply by	if prefix	divide by
giga- (G)	1 billion	centi- (c)	100
mega- (M)	1 million	milli- (m)	1000
kilo- (k)	1000	micro- ($\mu$)	1million
		nano- (n)	1 billion

Motion
Speed: $v=\frac{d}{t}$; $[v]$=m/s
Velocity: $\vec v$ = speed and direction
Acceleration: $\vec a=\frac{\Delta\vec v}{t}$; $[a]$=m/s$^2$
Uniform acceleration: $a =$ constant:
$v=v_0 + at$
$d=v_0 t + \frac{1}{2} at^2$
Free fall:
vertical acceleration $a=g=9.8$ m/s$^2$
horizontal acceleration $a=0$

Forces
Newton's second law: $\vec F=m\vec a$; $[F]$=kg m/s$^2$=N (newton)
Newton's third law: action = reaction
Weight: force of gravity $w=mg$
Centripetal acceleration: $a_c=v^2/r$
Centripetal force: $F_c=ma_c$

$$\mbox{\it Newton's law of universal gravitation: } F=G\frac{m_1m_2}{r^2}$$

Gravitational constant: $G=6.67\times 10^{-11}$ Nm$^2$/kg$^2$

Work and Energy
Work: $W=Fd$; $[W]$=Nm=J (joule)
Power: $P=W/t$; $[P]$=J/s=W (watt)
Kinetic energy: $KE=\frac{1}{2}mv^2$; $[KE]$=J
Gravitational potential energy: $PE=mgh$; $[PE]$=J
Conservation of energy: $E = KE + PE =$constant.

Linear Momentum
Impuls and Momentum: $F\Delta t=\Delta p$, $p=mv$
Conservation of momentum: If $F_{external}=0$ then $p_{total}=$constant; $m_1\vec v_{1i}+m_2\vec v_{2i} = m_1\vec v_{1f}+m_2\vec v_{2f}$

width3.55in height0.6pt Instructor: Joerg Reinhold, Department of Physics, FIU CAPA©msu