## Saturday, July 23, 2022

### HP 32SII Applications: Moments of Inertia, Conductor Temperature Change, Slit Patterns

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  ÷

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

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

Coming up:  Python Week:  August 1 to August 5, 2022

Eddie

All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

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