V_x=vcosθ

V_y=vsinθ

V=√V_x²+V_y²

θ=tan^-1(V_y/V_x)

Distance

Time

Displacement

Time

Δx

Δt

m/s

Average Velocity

Time

Δv

Δt

m²/s

1. v₀ (initial velocity)
2. v_i (final velocity)
3. Δx (displacement)
4. a (acceleration)
5. t (time interval)

x=x₀+v₀t+.5at²

m

v²=v₀²+2a(x-x₀)

m/s

v=v₀+at

m/s

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F_net,x=T₁(cosθ₁)-T₂(cosθ₂)

F_net,y=T₁(sinθ₁)+T₂(sinθ₂)-mg

F_f=μF_N

N=Newtons

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F_net,x=F_Nμ-F_p(cosθ)

F_net,y=F_N+F_p(sinθ)-mg

[image]

F_net,x=F_N-mg(cosθ)

F_net,y=F_Nμ-mg(sinθ)

T=Fd

T_net=counterclockwise-clockwise

N=Newtons

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[image]

a=-mg                                       a=g(M-m)        

   m+M                                             M+m

p=mv

kg•m/s or N•s

J=FΔt=Δp

kg•m/s or N•s

W=F•d_ll

N•m=J=Joule

Energy of motion

K=½mv²

J=Joules

W_net=ΔKE=K_f-K_i

J=Joules

Energy of position

U=mgh

J=Joules

K_i+U_i+W=K_f+U_f

J=Joules

(W is only included for friction problems)

Force=F_spring=kx

Potential Energy=U_spring=½kx²

J=Joules

P=W/t=work/time

Joules/second=W=Watts

The acceleration keeping an object in motion in uniform circular motion

a_c=v²/r

m/s²

Gravatational Force=F_G=GM₁M₂

                                   r²

Gravational Potential Energy=U_G=GM₁M₂

                                               r

N=Newtons

T=1/ƒ

Period of Oscillation for a Spring=T=2π√(m/k)

Period of Oscillation for a Pendulum=T=2π√(L/g)

The sum of all the of the molecules in a substance

J=Joules

THe average kinetic energy per molecule

ΔL=[image]L₀ΔT

H=kAΔT

   L

• Metals carry heat better than non-metals
• More are makes it easier for heat to flow
• The longer the distance, the slower the heat transfer

Moles of Gas=PV=nRT

Molecules of Gas=PV=Nk_bT

1. Molecules move in continuous randomn motion
2. Large amounts of molecule in any gas container
3. Large separation between molecules
4. Molecules do not affect other molecules
5. All collisions are elastic

   ---

Molecular Kinetic Energy (U or K) =K_avg=³/₂nRT

v_rms=Γ3k_bT

   √  m

ΔU=Q+W

Internal Energy=heat added+work done on the gas

Q: negative if heat removed; positive if heat added

W: negative if gas expanded; positive if gas compressed

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1. Isothermal: the gas is held at constant temperature
2. Adiabatic: no heat flows into or out of the gas
3. Isobaric: the gas is held at constant pressure
4. Isochoric: the gas is held at constant volume

-PΔV=W

J

[image]

Efficiency=e=W/Q_H (e<1)

e_ideal=T_H-T_C

        T_H

P=Force

    Area

Pressure in a Static Column=P=P₀+ρgh

N/m²=Pa=Pascals

ρ=Mass

       Volume

kg/m³

The bouyant force of an object is equal to the weight of the fluid displaced by the object

F_B=(ρ_fluid)(V_submerged)g

V_submerged=ρ_object

V_{object     =} ρ_fluid