Physics 121

Trig

sin q = o/h

cos q = a/h

tan q = o/a

area = pr² (circle)

Kinematics

v = Dx/Dt

a = Dv/Dt

Dx = v_ot + ½ at²

v_f² = v_o² + 2aDx

g = 9.8 m/s²

Dynamics

F_net = ma

F_g = Gm₁m₂/r²

F_g = mg (near surface of earth)

f_k = m_k F_N

f_s < m_s F_N

a_c = v²/r

Work and Energy

W = Fd cos q

KE = ½ m v²

W_net = DKE

W_nc = DKE + DPE

PE = mgh

Impulse and Momentum

Impulse = F t = Dp

p = mv

m₁v₁ + m₂v₂ = (m₁+m₂)v_f (Inelastic)

V_cm = Sm_iv_i/Sm_i

Elastic Collisions

1) Find V_cm

2) Subtract V_cm from each velocity

3) Change sign of each velocity

4) Add V_cm to each velocity

Springs

F = -kDx

PE = ½ k Dx²

Rotations

Rolling without slipping

x = qr

v = wr

a = ar

Rotations (cont.)

Dq = w_ot + ½ at²

w_f² = w_o² + 2aDq

w = Dq/Dt

a = Dw/Dt

KE = 1/2Iw²

t_net = I a

t = f r sinq

I = mr²

l = Iw (Angular momentum)

Simple Harmonic Motion

x(t) = A cos(wt)

x(t) = A sin(wt)

w = Ök/m (mass and spring)

w = Ög/L (pendulum)

T = 2p/w

Waves & Sound

w = 2pf

v = f λ

l₂ – l₂ = m λ (Constructive)

l₂ – l₂ = (m+ ½) λ (Destructive)

λ_n = 2L/n (string)

λ_n = 4L/n (Pipe open 1 end)

λ_n = 2L/n (Pipe open both ends)

v = Ö(T/(m/L))

f_o = f_s [(1 +/- v_o/v)/(1 +/- v_s/v)] (Doppler)

B = 10 log₁₀ (I/I_o)

Fluids

r = m/V

P = F/A

F_B = r_fV_{dis f} g

P₂-P₁ = rgh

Q=v₁A₁=v₂A₂

P₁+1/2rv₁²+rgy₁= P₂+1/2rv₂²+rgy₂

Expansion

DL = aL_oDT

DV= bVDT

Heat

^oC = (^oF – 32)5/9

Q=mcDT

Q=mL

Heat Transfer

Q= (k A DT)t/L

Q= esT⁴At

Thermodynamics

DU = Q – W

W = P DV (Isobaric)

e = W/Q_H = 1- Q_C/Q_H

e _carnot= 1- T_C/T_H