**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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