Symbols and Formulas

Symbols and Formulas

Symbols:

These are the symbols that are used in the lessons:

```
s    Displacement (meters: m)
```
```
t    Time (seconds: s)
```

u   Initial velocity (meters per second: m/s)

v_av   Average Velocity (meters per second: m/s)

v    Final Velocity (meters per second: m/s)

a    Acceleration (meters per second per second: m/s/s)

g    Acceleration of Gravity on Earth (meters per second per second: 9.80 m/s/s)

```
m    Mass (kilograms: kg)
```
```
F    Force (Newtons: N = kg m/s/s)
```

F_N   Normal Force (Newtons: N = kg m/s/s)

```
m   Coefficient of Friction 
```
```
W    Work (Joules: J = kg m²/s/s)
```

E_P   Potential Energy (Joules: J = kg m²/s/s)

E_K   Kinetic Energy (Joules: J = kg m²/s/s)

```
P    Power (Watts: W = kg m²/s/s/s)
```
```
p    Momentum (Bergevins: B = kg m/s)
```

G    Universal Gravitation Constant (6.67 x 10^-11 Nm²/kg²)

```
r    Radius of a circle (m)
```

q   Angular Displacement (Radians: rad)

w_o  Angular Initial velocity (radian per second: rad/s)

w_ave  Angular Average Velocity (radian per second: rad/s)

w   Angular Final Velocity (radian per second: rad/s)

```
a   Angular Acceleration (radians/s/s)
```
```
t   Torque (Nm)
```
```
I    Moment of Inertia (kg m²)
```
```
L    Angular Momentum (kg m²/s)
```
```
r    Density (kg/m³)
```
```
V    Volume (m³)
```

Formulas:

Topic 2 - Mechanics

```
v_av=Ds/Dt
```
```
a_av=Dv/Dt
```
```
v = u + at
```
```
s = t(u + v)/₂
```
```
v² = u^{2 +}2as
```
```
s = ut + ¹/₂at²
```
```
F = ma
```
```
P = F/A
```
```
Stress = ^F/_A
```
```
p  = mv
```
```
F  = Dp/Dt
```
```
Impulse = Dp = FDt
```
```
F_fr £ µ_sF_N
```
```
F_fr = µ_kF_N
```

W = Fs(cos(q)) = Fs (if F and X are parallel)

```
E_k = ¹/₂mv²
```
```
DE_P = mgDh 
```
```
E_elas = ¹/₂ks²
```
```
P  = DW/Dt
```
```
s = rq
```
```
w = Dq/Dt
```
```
v = rw
```
```
a = v²/r = rw²
```
```
F = mv²/_r= mrw² = (m4p²r)/T²
```
```
x = x_osinwt
```
```
v = v_ocoswt
```
```
a = a_osinwt
```
```
a = ^-k/_mx = -w²x
```
```
F = -kx
```
```
T = 2p Ö^m/_k
```
```
T = 2p Ö^l/_g
```
```
F = G(m₁m₂)/(r²)
```
```
V = -G^m/_r
```
```
w = w_o+ at
```
```
q = w_ot + ¹/₂at²
```
```
w² = w_o² + 2aq
```
```
t = r x F = rFsinq
```
```
I = Sm_ir_i²
```
```
L = Iw
```
```
t = Ia
```
```
E_{k rot}= ¹/₂Iw²   
```

Chapter 2 Two Dimensional Motion

```
opp = hyp(sin(angle))
```
```
adj = hyp(cos(angle))
```
```
tan(angle) = opp/adj
```
```
speed² = V_x² + V_y²
```

Topic 3: Thermal Physics and Properties of Matter

```
r = m/v
```

C = DQ/DT     C = Heat Capacity

```
DQ = mcDT
```
```
DQ = mL
```
```
DL = aL_oDT
```
```
DV = gV_oDT
```
```
PV = nRT
```
```
DQ/Dt = -kA(DT/Dx) 
```
```
DQ = DU + DW
```
```
Efficiency = (Q₁ - Q₂)/Q₁
```

Efficiency = (T₁ - T₂)/T₁      (Carnot Ideal)

```
DS = DQ/T
```

Topic 4 Waves

```
¦ = 1/T
```
```
v = ¦l
```

y = Asin(wt ± kx)   where k = 2p/l and w = 2p¦

```
y = 2Acos(kx)sin(wt)
```
```
¦_beat = |¦₁ - ¦₂|
```
```
n = c/v
```
```
₁n₂ = sinq₁/sinq₂=c₁/c₂
```

¦^'= ¦/(1 ± v_s/v)   moving source

```
¦^'= (1 ± v₀/v)¦   moving observer
```
```
v = ÖT/µ
```

Topic 5: Electricity and Magnetism

F =  k(q₁q₂)/r²   =         1        x   (q₁q₂)/r² 
                                   4pe₀

```
E = F/q
```
```
E = -DV/Dx 
```

E = kq/r²=      1     x      q            where q is point charge
                     4pe₀          r²

```
DV = DW/q
```
```
½mv² = eV
```

V = kq/r   =      1     x      q            where q is point charge
                     4pe₀          r

```
I = Dq/Dt
```
```
R = V/I
```
```
P = VI = I²R = V²/R
```
```
F = qVxB = qVBsinq
```
```
F = IlxB = IlBsinq
```
```
B = m₀I/2πr
```
```
B = m₀(NI/l) 
```
```
F =  (m₀I₁I₂l)/2πr
```
```
F = B  A = BAcosq
```
```
e = -DF/Dt
```
```
e = -N(DF/Dt)
```
```
e = Blv
```
```
(V_p/V_s) = (n_p/n_s) = (I_s/I_p)
```
```
P_av = I_rms V_rms
```
```
I_rms = (I₀/Ö2), where I = I₀ sinwt
```

Topic 6: Atomic and Nuclear Physics

```
E = DV/Dd
```
```
½mv² = eV
```
```
E = hf
```
```
½mv²_max= hf - W₀
```
```
hf = hf₀ + eV_s
```
```
(1/l) = R_H((1/n²) - (1/m²))
```
```
mrv_n = (nh/2p)
```
```
l_min = (hc/eV)
```
```
nl = 2dsinq  (X-ray diffraction)
```
```
l = (h/p)
```
```
N = N₀(e^-^l^t)
```
```
T₁ = (ln2/l)
 ²
```
```
DE = Dmc²
```