DuckieDai Centripetal Force Python Program

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physics · MIT License

Overview

Solve centripetal force, mass, speed, or radius from Fc = m*v^2/r with guided inputs and paginated results.

Usage

Inputs

Requested unknown: force, mass, speed, or radius
Three known positive values in consistent SI units

Outputs

Requested centripetal quantity with formula and labelled unit

Units: Use kilograms, metres per second, metres, and newtons consistently.

Assumptions and limitations

Assumptions

Motion is circular and the supplied values describe the same instant.

Constraints

Mass, speed, radius, and force inputs must be positive and below 1e100.

Known failures

Zero or negative inputs are rejected.
Inconsistent units produce an incorrect numerical result.

Compatibility and review

Review status: Tested on a TI calculator
Tested on: TI-84 Plus CE Python; OS 5.8.3; Python App 5.8.3.0048; exact paginated .py transferred through TI Connect CE into RAM and tested individually
What happened: Passed: branded intro, paginated menu, force/mass/speed/radius workflow, formula display, and answer screen ran on the physical calculator
Dependencies: math
Suggested calculator name: CENFORCE — you can give it another valid, unique name when you transfer it
Desktop test cases: Not available for this interactive-only source

This exact source auto-launches an interactive calculator session, so compatibility evidence comes from the recorded physical-device review rather than an importable desktop fixture.

Browser preview

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Simulation boundary: This preview uses a reviewed browser adapter. It does not execute the downloaded Python and does not prove TI-Python or calculator compatibility.

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Exact reviewed bytes

Source code

Download .py

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"""DuckieDai Centripetal Force for TI-84 Plus CE Python."""

from math import sqrt


def duckiedai_intro(program_name, wait=True):
    """Show the reusable DuckieDai program opening."""
    title = program_name[:16]
    empty = 16 - len(title)
    left = empty // 2
    right = empty - left

    print("+----------------------+")
    print("|   " + " " * left + title + " " * right + "   |")
    print("|                      |")
    print("|       __             |")
    print("|   ___(o )>  quack!   |")
    print("|   \\ <_. )           |")
    print("|    `---'             |")
    print("|     by DuckieDai     |")
    print("+----------------------+")
    print("Loading...")

    if wait:
        input("Press enter to start ")
        print("\n" * 6)


def positive_number(prompt):
    """Require a value greater than zero."""
    while True:
        try:
            value = float(input(prompt))

            if value > 0 and value < 1e100:
                return value

        except ValueError:
            pass

        print("Enter a number above 0.")


def nonnegative_number(prompt):
    """Allow zero or positive values."""
    while True:
        try:
            value = float(input(prompt))

            if value >= 0 and value < 1e100:
                return value

        except ValueError:
            pass

        print("Enter 0 or greater.")


def show_answer(name, value, unit):
    input("Press enter for answer ")
    print("\n" * 6)
    print("ANSWER")
    print(name + " = " + str(value))
    print(unit)


def main():
    duckiedai_intro("CENTRIPETAL")

    print("CENTRIPETAL FORCE")
    print()
    print("Formula:")
    print("Fc = m*v^2/r")
    input("Press enter for menu ")
    print("\n" * 6)
    print()
    print("What do you need?")
    print()
    print("1. Centripetal force")
    print("2. Mass")
    print("3. Speed")
    print("4. Radius")
    print()

    choice = input("Choose 1-4: ")

    print()

    # ==========================================
    # 1. SOLVE CENTRIPETAL FORCE
    #
    # Fc = m*v^2/r
    # ==========================================

    if choice == "1":

        mass = positive_number("Mass (kg): ")
        speed = nonnegative_number("Speed (m/s): ")
        radius = positive_number("Radius (m): ")

        force = (
            mass * speed ** 2 /
            radius
        )

        print()
        print("Using:")
        print("Fc = m*v^2/r")
        print()
        print("Fc = " + str(mass))
        print("x " + str(speed) + "^2")
        print("/ " + str(radius))

        show_answer(
            "Fc",
            force,
            "newtons"
        )

    # ==========================================
    # 2. SOLVE MASS
    #
    # m = Fc*r/v^2
    # ==========================================

    elif choice == "2":

        force = positive_number("Force (N): ")
        radius = positive_number("Radius (m): ")
        speed = positive_number("Speed (m/s): ")

        mass = (
            force * radius /
            (speed ** 2)
        )

        print()
        print("Using:")
        print("Fc = m*v^2/r")
        print()
        print("Rearranged:")
        print("m = Fc*r/v^2")

        show_answer(
            "m",
            mass,
            "kg"
        )

    # ==========================================
    # 3. SOLVE SPEED
    #
    # v = sqrt(Fc*r/m)
    # ==========================================

    elif choice == "3":

        force = nonnegative_number("Force (N): ")
        radius = positive_number("Radius (m): ")
        mass = positive_number("Mass (kg): ")

        speed = sqrt(
            force * radius /
            mass
        )

        print()
        print("Using:")
        print("Fc = m*v^2/r")
        print()
        print("Rearranged:")
        print("v = sqrt(Fc*r/m)")

        show_answer(
            "v",
            speed,
            "m/s"
        )

    # ==========================================
    # 4. SOLVE RADIUS
    #
    # r = m*v^2/Fc
    # ==========================================

    elif choice == "4":

        mass = positive_number("Mass (kg): ")
        speed = positive_number("Speed (m/s): ")
        force = positive_number("Force (N): ")

        radius = (
            mass * speed ** 2 /
            force
        )

        print()
        print("Using:")
        print("Fc = m*v^2/r")
        print()
        print("Rearranged:")
        print("r = m*v^2/Fc")

        show_answer(
            "r",
            radius,
            "meters"
        )

    else:
        print("Invalid choice.")

    print()
    print("DuckieDai says: done!")


# TI-Python imports the selected AppVar rather than
# setting __name__ to main.
main()

"""DuckieDai Centripetal Force for TI-84 Plus CE Python."""
from math import sqrt
def duckiedai_intro(program_name, wait=True):
"""Show the reusable DuckieDai program opening."""
title = program_name[:16]
empty = 16 - len(title)
left = empty // 2
right = empty - left
print("+----------------------+")
print("| " + " " * left + title + " " * right + " |")
print("| |")
print("| __ |")
print("| ___(o )> quack! |")
print("| \\ <_. ) |")
print("| `---' |")
print("| by DuckieDai |")
print("+----------------------+")
print("Loading...")
if wait:
input("Press enter to start ")
print("\n" * 6)
def positive_number(prompt):
"""Require a value greater than zero."""
while True:
try:
value = float(input(prompt))
if value > 0 and value < 1e100:
return value
except ValueError:
pass
print("Enter a number above 0.")
def nonnegative_number(prompt):
"""Allow zero or positive values."""
while True:
try:
value = float(input(prompt))
if value >= 0 and value < 1e100:
return value
except ValueError:
pass
print("Enter 0 or greater.")
def show_answer(name, value, unit):
input("Press enter for answer ")
print("\n" * 6)
print("ANSWER")
print(name + " = " + str(value))
print(unit)
def main():
duckiedai_intro("CENTRIPETAL")
print("CENTRIPETAL FORCE")
print()
print("Formula:")
print("Fc = m*v^2/r")
input("Press enter for menu ")
print("\n" * 6)
print()
print("What do you need?")
print()
print("1. Centripetal force")
print("2. Mass")
print("3. Speed")
print("4. Radius")
print()
choice = input("Choose 1-4: ")
print()
# ==========================================
# 1. SOLVE CENTRIPETAL FORCE
#
# Fc = m*v^2/r
# ==========================================
if choice == "1":
mass = positive_number("Mass (kg): ")
speed = nonnegative_number("Speed (m/s): ")
radius = positive_number("Radius (m): ")
force = (
mass * speed ** 2 /
radius
)
print()
print("Using:")
print("Fc = m*v^2/r")
print()
print("Fc = " + str(mass))
print("x " + str(speed) + "^2")
print("/ " + str(radius))
show_answer(
"Fc",
force,
"newtons"
)
# ==========================================
# 2. SOLVE MASS
#
# m = Fc*r/v^2
# ==========================================
elif choice == "2":
force = positive_number("Force (N): ")
radius = positive_number("Radius (m): ")
speed = positive_number("Speed (m/s): ")
mass = (
force * radius /
(speed ** 2)
)
print()
print("Using:")
print("Fc = m*v^2/r")
print()
print("Rearranged:")
print("m = Fc*r/v^2")
show_answer(
"m",
mass,
"kg"
)
# ==========================================
# 3. SOLVE SPEED
#
# v = sqrt(Fc*r/m)
# ==========================================
elif choice == "3":
force = nonnegative_number("Force (N): ")
radius = positive_number("Radius (m): ")
mass = positive_number("Mass (kg): ")
speed = sqrt(
force * radius /
mass
)
print()
print("Using:")
print("Fc = m*v^2/r")
print()
print("Rearranged:")
print("v = sqrt(Fc*r/m)")
show_answer(
"v",
speed,
"m/s"
)
# ==========================================
# 4. SOLVE RADIUS
#
# r = m*v^2/Fc
# ==========================================
elif choice == "4":
mass = positive_number("Mass (kg): ")
speed = positive_number("Speed (m/s): ")
force = positive_number("Force (N): ")
radius = (
mass * speed ** 2 /
force
)
print()
print("Using:")
print("Fc = m*v^2/r")
print()
print("Rearranged:")
print("r = m*v^2/Fc")
show_answer(
"r",
radius,
"meters"
)
else:
print("Invalid choice.")
print()
print("DuckieDai says: done!")
# TI-Python imports the selected AppVar rather than
# setting __name__ to main.
main()

Filename: CENFORCE.py
Size: 4928 bytes
SHA-256: f4aa188d0e10e5cb6b6afa22fbb6354da2a86a61a467ec0fa1db78eee7e43e67

Transfer and launch

Confirm that your calculator is the Python-capable model named above. Check that its OS and Python App versions match the reviewed record.
Download the .py source above and verify its SHA-256 digest if your computer provides that option.
Use TI Connect CE to send the Python file to a compatible calculator. CENFORCE is a suggested name; you may choose another valid, unique calculator name.
Open the Python App, select the program, and check sample inputs before relying on other results.

Read the complete installation, launch, troubleshooting, and removal guide.

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Version history

1.0.0 — current version, published 2026-09-23. Download this reviewed version

Any source change requires a new immutable version and digest. Historical downloads remain available only while their review records remain valid.

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