CU-ATS PHYSICS FORMULAE

Combining vectors - สามเหลี่ยม

$$c=\sqrt{a^2+b^2-2ab\cos C}$$

Combing vectors - สามหัว

$$c=\sqrt{a^2+b^2+2ab\cos C}$$

SUVAT - no v

$$s=ut+\frac12at^2$$

SUVAT - no u

$$s=vt-\frac12at^2$$

SUVAT - no t$v^2=u^2+2as$ $v^2=u^2+2as$

SUVAT - no a$s=\frac{\left(v-u\right)}{2}\cdot t$

Weight

W = mg

Spring Force

F = kx

Resultant force

F = ma

Max Static Friction

$$F=\mu\times N$$

Kinetic Friction

$$F=\mu\times N$$

Inclined plane - normal force

mgcos$\theta$

Inclined plane - force along surface

mgsin$\theta$

Gravitational Force

$$F=\frac{GMm}{r^2}$$

Gravitational fielD

$$g=\frac{GM}{r^2}$$

a in circular motion - with v

$$a=\frac{v^2}{r}$$

a in circular motion - with $\omega$

$$a=\omega^2r$$

distance in circular motion

s = θr

total a in circular motion

$$a=\sqrt{ac^2+at^2}$$

max v in SHM

$$v=\omega A$$

max a in SHM

$$a=\omega^2A$$

v in SHM at any point

$$v=\omega\sqrt{A^2-x^2}$$

a in SHM at any point

$$a=\omega^2x$$

Wave function in SHM

$$y=\max\sin\left(\omega t+\phi\right)$$

$\omega$ in SHM Mass-Spring system

$$\omega=\sqrt{\frac{k}{m}}$$

$\omega$ in SHM Pendulum system

$$\omega=\sqrt{\frac{g}{l}}$$

Moment

M = Fd

Angular moment (turning force)$Ia$

M = $Ia$

Center of mass (CM)

center of mass = (location x mass) + (location x mass)… / total mass

Kinetic energy

KE = $\frac12mv^2$

Gravitational potential energy on earth

GPE = mgh

Gravitational potential energy in space

GPE = $\frac{GMm}{r}$

Work done (all ways to find)

W = Fd, E2 - E1, Area under graph of F-d, dot product.

Power

P = Fv or P =$\frac{E}{t}$

Momentum

p = mv

Impulse

mv - mu or Force = $\frac{impulse}{t}$

Angular momentum

L = $I$ x $\omega$

Density

mass/volume

Specific gravity

S.G. = density / water density

Pressure

Force / area

Pressure difference in liquid

density x g x h

Buoyant force

F = density x V x g

Stress in solid $\sigma$

Force / Area

Young’s modulus

Stress over strain or ดัน over deformed

Strain in solid $\varepsilon$

$$\frac{\Delta L}{L}$$

Charge or one electron/proton

1.6 x $10^{-19}$

Electrical force - 1 charge

F = qE

Electrical force - 2 charges

F =$\frac{kQq}{r^2}$

Electrical field - relation to force

E = $\frac{kQ}{r^2}$

Electrical field in parallel plates

E = $\frac{V}{d}$

Electrical potential

V =$\frac{kQ}{r}$

Electrical potential energy at a point

U = qV or U = IVt

Electrical potential energy - 2 charges

U =$\frac{kQq}{r}$

Electrical energy and field inside a charged conductor

Energy = 0, field is constant and equal to the surface V =$\frac{kQ}{r}$

Current

I = Q/t or Q=It

Resistance - no voltage and current

R =$res\times\frac{l}{A}$

Voltage

Potential บวก - potential ลบ or V = IR

Current for components in series

เส้นเดียวกัน เท่ากันไม่แบ่ง

Voltage for components in series

แบ่งจาก total

Resistance in series

R total = sum of all R

Current for components in parallel

คนละเส้น แบ่งกัน

Voltage for components in parallel

ได้เท่ากัน ไม่แบ่ง

Resistance in parallel

Inverse sum

Capacitors

Q = cV

Energy in capacitors

U = $\frac12$ QV

Capacitance in series

Inverse sum - ตรงข้ามกัน resistance

Capacitance in parallel

sum or all capacitance - ตรงข้ามกับ resistance

Energy in an inductor

U =$\frac12$ inductance x $I^2$

Magnetic field

B = $\frac{\mu}{2\pi}$$\times\frac{I}{r}$

Magnetic force

F = qvB or F =$I\times l\times B$

Radius in circular motion with magnetic field

R =$\frac{mv}{qB}$

Magnetic force on parallel current-carrying wires/rods

F = $\frac{\mu}{2\pi}\times\frac{I\times I\times l}{d}$

Magnetic flux

Magnetic field x perpendicular Area

Faraday’s law - induced voltage when changing magnetic flux

emf = coils \times\frac{d\phi}{\differentialD t}

Induced voltage in rod passing through a magnetic field

emf = $v\times l\times B$

Voltage and number of coils in transformers

Directly proportional - more coils more voltage

Rate of conduction

=$\frac{kA\Delta T}{l}$

Rate of emission of black body is proportional to…

A and $T^4$

Peak wavelength that a black body can radiate is proportional to…

$$\frac{1}{T^{}}$$

Energy when a material is changing temperature

Q = $mc\Delta T$

Energy when material is changing state

Q = mL

Thermal expansion

$$\Delta L=\alpha\times L\times\Delta T$$

Speed of a string wave

v =$\sqrt{\frac{Tension\times L}{M}}$

Wave equations of wave

$$y=A\sin\left(kx\pm\omega t+\phi\right)$$

Right (-)

Left (+)

Wave number

k =$\frac{2\pi}{\lambda}$

Wave speed - from a wave function

v =$\frac{\omega}{k}$

Refraction

$$\frac{\lambda i}{\lambda r}=\frac{vi}{vr}=\frac{\sin i}{\sin r}$$

Interference pattern - values of n in 2 or more slits

A - n is integers, N - n is .5

Interference pattern - values of n for single slit

A0 n=0, N - n is integer, A - n is .5

Interface pattern with path difference

Path difference =$n\lambda$

Interference pattern with given angle

$$d\sin\theta=n\lambda$$

Interference pattern with given length from screen or slit separation

$$d\times\frac{y}{L}=n\lambda$$

Beat frequency

Frequency1 - frequency2

Average frequency for beats

$$\frac{f+f}{2}$$

Wavelength in front of a moving source of sound

$$\lambda=\frac{vsound-vsource}{f}$$

Wavelength behind a moving source of sound

$$\lambda=\frac{vsound+vsource}{f}$$

Wavelength behind a moving source of sound

$$\lambda=\frac{vsound+vsource}{f}$$

Intensity

Power/surface area of sphere, $\frac{P}{4\pi r^2}$

dB from intensity

dB = $10\log_{10}\left(\frac{I}{Io}\right)$ or dB =$10\log_{10}\left(\frac{L}{10^{-12}}\right)$

Difference in dB

$$10\log_{10}\left(\frac{L2}{L1}\right)$$