CIRMOT: Circular & Rotational Motion TI-84 Plus CE Solver

CIRMOT is a dedicated circular and rotational motion solver for the TI-84 Plus CE. It covers every formula students need for circular motion and rotation in one organized, menu-driven program — from centripetal force and banked road problems to torque, moment of inertia, and rolling kinetic energy.

Built for AP Physics 1 and algebra-based college physics. Works on the TI-84 Plus CE and TI-84 Plus CE Python only.

Circular Motion

The circular motion section handles every variable combination for the core circular motion formulas. Choose your formula, choose your unknown, enter what you know, and get the answer instantly.

Centripetal Force — F_c = mv²/r

• Solve for F_c, m, v, or r

Period T

• T = 2πr/v
• T = 1/f
• T = 2π/ω

Frequency f

• f = 1/T
• f = v/(2πr)
• f = ω/(2π)
• f and r from centripetal acceleration a_c

Angular Velocity ω

• ω = 2π/T
• ω = 2πf
• ω = v/r

More — Advanced Circular Motion

Vertical Circles

• Tension at the top: T_top = mv²/r − mg (with slack warning if T < 0)
• Tension at the bottom: T_bot = mv²/r + mg
• Minimum speed at the top: v_min = √(gr)

Loop-the-Loop

• Minimum speed at the top: v_top = √(gr)
• Minimum speed at the bottom: v_bot = √(5gr)
• Energy method: given v_bottom, find v_top (with loop-completion warning)

Banked Road

• Ideal speed (no friction): v = √(rg·tanθ)
• Maximum speed with friction
• Minimum speed with friction

Rotation

The rotation section covers every standard rotational mechanics topic, organized into six submenus. All three rotational kinematics equations are fully solved for any variable, just like linear kinematics.

Torque

• τ = rF sinθ
• τ = rF_n (perpendicular component)
• τ_net = Iα — solve for τ_net, I, or α

Rotational Kinematics

• ω = ω₀ + αt — solve for any variable
• θ = θ₀ + ω₀t + ½αt² — solve for any variable
• ω² = ω₀² + 2α(θ − θ₀) — solve for any variable

Moment of Inertia

• Solid disk/cylinder: I = ½MR²
• Solid sphere: I = ⅖MR²
• Hollow sphere (thin shell): I = ⅔MR²
• Rod about center: I = 1/12 ML²
• Rod about end: I = ⅓ML²
• Point mass: I = mr²

Angular Momentum

• L = Iω — solve for L, I, or ω
• Conservation: I₁ω₁ = I₂ω₂, find final ω
• Rotational collision: I₁ω₁ + I₂ω₂ = I_fω_f

Rolling Motion

• v = rω — solve for v, r, or ω
• a = rα — solve for a, r, or α
• Rolling KE = ½mv² + ½Iω² (enter I from the Moment of Inertia solver)

Rotational Energy

• KE_rot = ½Iω² — solve for KE_rot, I, or ω

Concept Help

Built-in concept help screens cover the key ideas behind each section — useful for a quick review before diving into calculations.

• Circular Motion help: centripetal force direction, period, frequency, angular velocity, v = rω
• Rotation help: torque, τ = Iα, rotational kinematics, angular momentum, rolling motion, rotational KE
• Rotation concepts: full linear ↔ rotational analogies (x→θ, v→ω, a→α, m→I, F→τ), moment of inertia explained, ice skater angular momentum example

What's Included

• CIRMOT program file (.8xp) — instant digital download
• PDF User Guide with screenshots and formula reference
• Free lifetime updates

Also included in the AP Physics 1 Mechanics Solver Bundle. If you already own the bundle, you do not need to purchase CIRMOT separately.

Compatible Calculators

TI-84 Plus CE, TI-84 Plus CE Python and TI-84 Plus CE-T only. Not compatible with TI-84 Plus, TI-84 Plus Silver Edition, or TI-83 series.

How to Install

Download the .8xp file, transfer it to your calculator using TI Connect CE, and run it from the PRGM menu. Full setup instructions are included in your PDF User Guide and available at our Setup Guide.