DuckieDai Centripetal Force Python Program

physics · MIT License

Overview

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

Tested on a TI calculator
Downloaded 44 times
Version 1.0.0
4928 bytes
Uses math

Download CENFORCE.py Read the source How to install

Before you run it

TI-84 Plus CE Python · tested on OS 5.8.3, Python App 5.8.3.0048
TI Connect CE .py conversion to a Python AppVar in RAM; physically verified one program at a time
Motion is circular and the supplied values describe the same instant.
Mass, speed, radius, and force inputs must be positive and below 1e100.
Zero or negative inputs are rejected.

Try the DuckieDai calculator screen

Follow the reviewed program's real menu, prompts, validation, calculation, and result flow before downloading.

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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.

Learn the math

How centripetal force works

The idea

An object moving in a circle is always turning, so it is always accelerating toward the center. The force that causes this is the centripetal force.

It is not a new kind of force. Tension, friction, or gravity supplies it, depending on the situation.

The formula

Fc = m*v^2/r

Fc: centripetal force (N)
m: mass (kg)
v: speed along the circle (m/s)
r: radius of the circle (m)

Using the program

Choose what to solve for: 1 force, 2 mass, 3 speed, or 4 radius.
Enter the three values you know, then press Enter for the answer.

Worked example

A 2 kg ball moves at 3 m/s around a circle of radius 4 m. Choose 1 and enter 2, 3, and 4.

Fc = 2.0 x 3.0^2 / 4.0

The program shows Fc = 4.5 newtons.

Tips and common mistakes

Speed is squared, so doubling the speed needs four times the force.
Use the radius, not the diameter.
The force points toward the center of the circle, not outward.

Where this comes up

It belongs to the circular motion unit: cars rounding curves, objects on strings, loops, and satellites. In college physics it is combined with gravity to derive orbital speed.

Exact reviewed bytes

Source code

Download .py

View source below, copy it when JavaScript is available, or download the exact .py bytes.

"""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

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.

Transfer and launch

Download the .py file, send it to your calculator with TI Connect CE as CENFORCE or another name, then open the Python App and try the worked example on this page first.

Full installation and troubleshooting guide. Check your teacher's or exam's rules before using any program.

Version history

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

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