HP 32SII Applications: Moments of Inertia, Conductor Temperature Change, Slit Patterns
Moment of Inertia - Uniform Disk
The moment of inertia on a uniform disk of radius r is:
I = 2 * π * L * ρ * ∫(r^3 dr, 0, R)
where ρ = M ÷ ( π * R^2 * L)
The formula of inertia for the uniform disk can be simplified to:
I = M * R^2 * 1/2
where
M = mass of the disk
R = radius of the disk
I = inertia of the center of the mass
HP 32SII Program:
I01 LBL I
I02 INPUT M
I03 INPUT R
I04 x^2
I05 ×
I06 2
I07 ÷
I08 RTN
(12.0 bytes, CK = B55F)
Example:
Inputs:
M = 8 kg
R = 0.2 m
Result:
I = 0.16 kg * m^2
Source:
Texas Instruments Incorporated. Texas Instruments TI-55III Scientific Calculator Sourcebook Second Edition. 1984
Conductor Temperature Change
The temperature change due to the change of the resistance can be calculated as:
∆t = 1 ÷ α * ( R_2 ÷ R_1 - 1)
where:
∆t = change of temperature in °C
R_2 = new resistance in Ω (R)
R_1 = new resistance in Ω (F)
α = temperature coefficient of resistance (A) (see table below and source)
Selected Temperature Coefficients of Resistance at 20°C (α):
Material: α
Nickel: 0.005866
Iron: 0.005671
Aluminum: 0.004308
Copper: 0.004041
Silver: 0.003819
Gold: 0.003715
Alloy Steel (99.% iron): 0.003
HP 32SII Program:
T01 LBL T
T02 INPUT A
T03 INPUT R
T04 INPUT F
T05 ÷
T06 1
T07 -
T08 x<>y
T09 1/x
T10 ×
T11 RTN
(16.5 bytes, CK = DDA9)
Example:
Inputs:
A = 0.004041 (α, Copper)
R = 58 Ω (new resistance)
F = 50 Ω (old resistance)
Result:
39.594160 °C
Sources:
"Temperature Coefficient of Resistance" All About Circuits. Last Retrieved May 17, 2022. https://www.allaboutcircuits.com/textbook/direct-current/chpt-12/temperature-coefficient-resistance/#:~:text=The%20resistance%2Dchange%20factor%20per,with%20an%20increase%20in%20temperature.
National Radio Institute Alumni Association Mathematics For Radiotricians Washington, D.C. 1942
Slit Patterns
The intensity of diffraction pattern of the single slit can be calculated by the formula:
I = Im * (sin α ÷ α)^2
where:
Im = potential maximum intensity
α = (π * s * sin θ ÷ λ) in radians
s = slit width
λ = wavelength in Hz
θ = angle of diffraction in degrees
For a double slit:
I = Im * (cos B)^2 * (sin α ÷ α)^2
where:
B is in radians and
B = (π * d * sin θ ÷ λ)
d = distance between slits
θ = angle of diffraction in degrees
α = see the single slit formula above
HP 32SII:
A: θ
S: slit wdith
W: wavelength, λ
I: maximum intensity
LBL S: single slit
LBL D: double slit, uses LBL S
HP 32SII Programs:
Single Slit:
S01 LBL S
S02 DEG
S03 INPUT A
S04 SIN
S05 INPUT S
S06 ×
S07 π
S08 ×
S09 INPUT W
S10 ÷
S11 RAD
S12 ENTER
S13 SIN
S14 x<>y
S15 ÷
S16 x^2
S17 INPUT I
S18 ×
S19 RTN
(28.5 bytes, CK = 40E0)
Double Slit:
D01 LBL D
D02 XEQ S
D03 DEG
D04 RCL A
D05 SIN
D06 INPUT D
D07 ×
D08 π
D09 ×
D10 RCL÷ W
D11 RAD
D12 COS
D13 x^2
D14 ×
D15 RTN
(22.5 bytes, CK = 8BC7)
Example:
Inputs:
A = 8°
S = 1.96E-6 m
W = 500E-9Hz
I = 1
Single Slit Calculation:
XEQ S: 0.333496
Double Slit Calculation:
XEQ D
D = 3E-5 m
Result: 0.068409
Source:
Saul, Ken. The Physics Collection: Ten HP-41C Programs for First-Year Physics Class Corvallis, OR. 1986
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Eddie
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