OAT PHYSICS

Round 2

Average Velocity

Vavg= ∆d/∆t

• Vavg= average velocity (m/s)

• ∆d= displacement (m)

• ∆t= time (s)

Average Acceleration

aavg-= ∆v/∆t

• aavg= average acceleration (m/s²)

• ∆v= change in velocity (m/s)

• ∆t= timr (s)

Displacement

∆X= Vit + ½at²

Velocity (including time)

vf=vi + at

Velocity (including displacement)

vf²= vi²+2a∆x

Net Force (Newtons 2nd Law)

Fnet=ma

• Fnet= Net force (N)

• m=mass (kg)

• a=acceleration (m/s²)

Weight

W=mg

• W= weight (N)

• m=mass(kg)

• g=gravity (10 m/s²)

Normal Force (horizontal surface)

FN=mg

• FN= Norman Force(N)

• m=mass (kg)

• g=gravity (10 m/s²)

Normal force (inclined surface)

FN=mgcos(θ)

• FN= Norman Force(N)

• m=mass (kg)

• g=gravity (10 m/s²)

• θ=inclined angle (rad)

Force of Friction

Ff= μFn

• Ff=Force of friction (N)

• μ= coefficient of friction

• Fn=norman force (N)

Gravatational Force (two bodies)

F= Gm₁m₂ / d²

• F=gravitational force (N)

• G=gravity constant (6.67×10^-11Nm²/kg²)

• m1= mass of object 1 (kg)

• m2=mass of object 2 (kg)

• d=distance between centers (m)

Gravatational Force (one body)

g= Gm / r²

• g=gravitational acceleration (10m/s²)

• G=gravity constant (6.67×10^-11Nm²/kg²)

• m= mass of body (kg)

• r=distance from body’s center (m)

Linear Displacement (Arc Length)

d=rθ

• d=linear displacement (m)

• r=radius (m)

• θ=angular displacement (rad)

Linear Velocity (Tangential)

v=rw

• v=linear velocity (m/s)

• r=radius (m)

• w=angular velocity (rad/s)

Linear Acceleration (Tangential)

a=rα

• a=linear acceleration (m/s²)

• r=radius (m)

• α=angular acceleration (rad/sec²)

Uniform Circular Speed (Tangential)

Vc= 2πr/ T

• Vc=circular speed (m/s)

• r=radius (m)

• T=period (s)

Centripetal Acceleration

ac= v²/ r

• ac=centripetal acceleration (m/s²)

• v=velocity (m/s)

• r= radius (m)

Centripetal Force

Fc= mac = mv²/r

• Fc=centripetal force (N)

• m=mass (kg)

• ac= centripetal acceleration (m/s²)

• v=velocity (m/s)

• r=radius (m)

Torque

Vector Form: T= r x F

Magnitude: |T| = rF sinθ

• T= Torque (Nm)

• r= lever arm distance (m)

• F= Force (N)

• θ= angle between r and F (rad)

Constant Velocity implies….

0 acceleration

Kinetic Energy

KE= ½ mv²

• Ke= kinetic energy (J)

• m=mass (kg)

• v= speed (m/s)

Gravitational Potential Energy

PE=mgh

• PE= potential energy (J)

• mass=(kg)

• gravitational acceleration (10 m/s²)

• height change (m)

Total Mechanical Energy

ME= KE + PE

• ME= total mechanical energy (J)

• KE=kinetic energy (J)

• PE= potential energy (J)

Work (with a constant Force)

W= Fd sinθ

• W=work (J)

• F=force (N)

• d=displacement (m)

• θ= angle between F and d (rad)

Work Energy Theorem

W=ΔKE

• W= net work (J)

• ΔKE= change in kinetic energy (J)

Power

P=W/t

• P=power (W)

• W=work (J)

• t=time (s)

Momentum

p=mv

• p=momentum (kg.m/s)

• m=mass(kg)

• v=velocity (m/s)

Impulse

i= FΔt= Δp

• i=impulse (N.s)

• F=force (N)

• Δt=time (s)

• Δp = change in momentum

Inelastic Collision Equation (perfectly inelastic)

m1v1 + m2v2 = m3v3

Elastic Collision Equation (Momentum Conservation)

m1v1i + m2v2i = m1v1f + m2v2f

In elastic collision the objects…

bounce off each other

Photon Energy

E= hc / λ

• E=photon energy (J)

• h= planck’s constant (6.626 × 10^-34 J.s)

• c=speed of light (3×10⁸ m/s)

• λ= wavelength (m)

Center of Mass

xcm= ∑mx / ∑m

(or replace x with y for the y cordinate center of mass)

• xcm= x coordinate of COM (m)

• m= mass of object (kg)

• x= x postion of object from origin (m)

Hookes Law (Spring Force)

Fs = -kx

• Fs= spring force (N)

• k=spring constant (N/m)

• x= displacement from equilibrium (m)

Work Done on Spring

Ws= ½ kx²

• Ws= work done on a spring (J)

• k=spring constant (N/m)

• x=displacement from equilibrium (m)

Elastic Potential Energy (Spring)

PEs= ½ kx²

• PEs= elastic potential energy (J)

• k=spring constant (N/m)

• x=displacement from equilibrium (m)

Period (Mass-Spring)

Ts= 2π (√m/k)

• Ts= Period of a spring (s)

• m=mass (kg)

• k=spring constant (N/m)

Period (pendulum)

Tp= 2π (√L/g)

• Tp= period of pendulum (s)

• L= pendulum length (m)

• g= gravitational acceleration (10 m/s²)

Angular Frequency (general)

w= 2π / T = 2πf

• w=angular frequency (rad/s)

• T=period (s)

• f= frequency (Hz)

Angular Frequency (mass-spring)

w= √k/m

• w= angular frequency (rad/s)

• k= spring constant (N/m)

• m= mass (kg)

Angular Frequency (pendulum)

w= √g/L

• w= angular frequency (rad/s)

• g= gravitational acceleration (m/s²)

• L= pendulum length (m)

General Period Equation

T= total time / # of cycles

Wave Velocity (Speed)

v=λf

• v=velocity (m/s)

• λ= wavelength (m)

• f= frequency (Hz)

Period Frequency Relation

T= 1/f

• T=period (s)

• f=frequency (Hz)

Intensity

I= P / A

• I=Intensity (W/m²)

• P=power (W)

• A= area (m²)

Point Source Intensity

I= P / 4πr²

• I=Intensity (W/m²)

• P=power (W)

• r=distance from point source (m)

Sound Intensity Level

β = 10log₁₀ (I/threshold)

• β=sound intensity level (dB)

• I=Intensity (W/m²)

• threshold of hearing (10^-12 W/m²)

Frequency of string/pipe one end attached/open

f= nv/4L

Frequency of string/pipe on both ends

f= nv/2L

Which type of wave has the longest wave length?

Radio Waves

Which type of wave has the shortest wave length?

Gamma Waves

Which type of wave has the highest frequency?

Gamma

Which type of wave has the lowest frequency?

Radio

Density

ρ= m/V

• ρ=density (kg/m³)

• m=mass (kg)

• V=volume (m³)

Buoyant Force (Archimedes Principle)

Fb= ρVg

• Fb=buoyant force (N)

• ρ=density (kg/m³)

• V=displaced fluid volume (m³)

• g=gravitational acceleration (10 m/s²)

• m=mass (kg)

Floating (equilibrium)

Fb=mg

Pressure

P= F/A

• P= pressure (Pa=N/m²)

• F= force (N)

• A= area (m²)

Hydrostatic Pressure

P= P_o+ ρgh

• P=Hydrostatic Pressure (Pa)

• P_o= surface pressure (Pa)

• ρ= density (kg/m³)

• g=gravitational acceleration (10 m/s²)

• h= depth below the surface (m)

Pascals Principle

F1 / A1 = F2 /A2

Area of a circle

A= πr²

Floating Objects (a fraction is submerged)

Vsub / Vobj = ρobj / ρfluid

Volume Flow Rate

Q=vA

• Q=volume flow rate(m³ / s)

• v=velocity (m/s)

• A= cross sectional area (m²)

1 atm is equal to…

101,325 Pa

Index of Refraction

n= c/v

• n= medium index of refraction

• c=speed of light constant (3×10⁸ m/s)

• v=speed of light in medium (m/s)

Snells Law

n₁sinθ₁ = n₁sinθ₂

Apparent Depth

Dapp= Dact (n2 /n1)

• Dapp= apparent depth (m)

• Dact= actual depth (m)

• n2= index observers medium

• n1= index of objects medium

Critical Angle

Sinθ_c= n2/n1

• θc= critical angle from normal (rad)

• n2=index of refraction (refracting medium)

• n1= index of refraction (incident medium)

Total internal reflection condition

n1 > n2

• n1= index of refraction (incident medium)

• n2=index of refraction (refracting medium)