Torque & Rotational Motion Simulator
Wrench • Seesaw • Spinning Disc • Rolling Race — Simulate • Explore • Practice • Quiz
1 Overview
This free torque simulator lets you explore moment of force, lever arm mechanics, angular acceleration, and rotational equilibrium through four interactive scenarios. The tool calculates torque using τ = F × r × sinθ, demonstrates Newton’s second law for rotation (τ = Iα), and shows how shapes with different moments of inertia behave during rolling motion on inclined planes.
Designed for engineering students, mechanical engineering undergraduates, and technicians, this simulator covers wrench torque for bolt tightening, seesaw balance, spinning disc dynamics, and rolling race comparisons — all with real-time animated free body diagrams and precise numerical readouts.
2 Getting Started
The simulator opens in Simulate mode with the Wrench & Bolt scenario. The canvas shows a wrench applying force to a bolt with the torque vector visualised. Five readout cards display Applied Torque, Required Torque, Moment Arm, Angle Factor, and Status.
Use the Scenario pills to switch between Wrench & Bolt, Seesaw Balance, Spinning Disc, and Rolling Race. Each scenario has its own sliders and controls. The four mode pills (Simulate, Explore, Practice, Quiz) are at the top of the page.
3 Simulate Mode
Wrench & Bolt: Adjust the applied force (10–500 N), lever arm length (0.05–0.60 m), and angle (0–90°). Select a bolt size (M8, M12, M16, M20) to set the required torque. The animation shows whether the applied torque is sufficient to tighten the bolt, with the status changing to “Tightened” when τapplied ≥ τrequired.
Seesaw Balance: Set masses and distances on both sides. The animation shows the seesaw tilt direction, and the readouts display the clockwise and counterclockwise moments. Balance is achieved when M1·d1 = M2·d2.
Spinning Disc: Apply torque to a disc of specified mass and radius. Choose the shape (Solid Disc, Ring, Solid Sphere) to set the moment of inertia formula. The animation shows the disc accelerating angularly, and readouts display τ, I, and α = τ/I.
Rolling Race: Set the incline angle and watch three shapes (solid cylinder, hollow cylinder, solid sphere) race down the ramp. The solid sphere wins because it has the lowest I/mr² ratio, leaving more energy for translational speed.
4 Explore Mode
Explore mode offers concept cards across three categories: Torque Basics (definition, lever arm, angle effect, units), Rotational Dynamics (moment of inertia, Newton’s 2nd law for rotation, angular momentum, rolling motion), and Applications (bolt tightening, seesaw design, flywheel energy storage). Each card includes a formula, canvas diagram, and worked example.
Key equations covered: τ = Fr·sinθ, τ = Iα, I formulas for standard shapes, rolling acceleration a = g·sinθ/(1 + I/mr²), and rotational kinetic energy Erot = ½Iω².
5 Practice & Quiz
Practice mode generates unlimited random problems: calculate the torque needed to tighten a bolt, find the balancing distance for a seesaw, determine angular acceleration for a spinning disc, or compare rolling speeds of different shapes. Full step-by-step solutions are shown for incorrect answers.
Quiz mode presents 5 randomised questions per session covering all four scenarios. Questions mix conceptual items with numerical calculations about torque, moment of inertia, and rotational equilibrium. A detailed score breakdown is shown at the end.
6 Tips & Best Practices
- Wrench scenario: Reduce the angle from 90° to see how torque drops — at 0° the force passes through the pivot and produces zero torque.
- Seesaw tip: Keep one side fixed and adjust the other to find the exact balance point — a practical demonstration of rotational equilibrium.
- Spinning Disc: Compare Solid Disc (I = ½mr²) with Ring (I = mr²) — the ring has twice the moment of inertia, so it accelerates half as fast for the same torque.
- Rolling Race: Note that mass and radius cancel out — only the shape factor I/mr² determines rolling speed.
- Use the bolt presets (M8 through M20) to see how required torque scales with bolt size in real mechanical assemblies.
- The simulator works on tablets and mobile devices in landscape mode.
Understanding Torque & Rotational Motion — Free Interactive Simulator
Torque, also called moment of force, is the rotational analogue of linear force. It measures how effectively a force causes an object to rotate about a pivot point. This interactive simulator lets you explore torque in four real-world scenarios: tightening bolts with wrenches, balancing seesaws, spinning discs with applied torque, and racing shapes down inclines to understand moment of inertia.
Torque: The Rotational Force
Torque is calculated as τ = F × r × sinθ, where F is the applied force, r is the lever arm (distance from pivot to force application), and θ is the angle between the force vector and the lever arm. Maximum torque occurs when force is applied perpendicular to the lever arm (θ = 90°). This principle is fundamental to wrench design — longer wrenches provide greater torque for the same applied force, which is why mechanics use breaker bars for stubborn bolts. The SI unit of torque is the Newton-metre (N·m).
Moment of Inertia & Angular Acceleration
Moment of inertia (I) describes an object’s resistance to angular acceleration, just as mass resists linear acceleration. Newton’s second law for rotation states τ = Iα, where α is angular acceleration in rad/s². The moment of inertia depends on both mass and how that mass is distributed from the rotation axis: a solid disc has I = ½mr², a ring has I = mr², and a solid sphere has I = ⅖mr². This is why figure skaters spin faster when they pull their arms in — reducing I while conserving angular momentum L = Iω.
Rolling Motion & Energy Conservation
When objects roll down an incline without slipping, gravitational potential energy converts to both translational kinetic energy (½mv²) and rotational kinetic energy (½Iω²). Objects with higher rotational inertia ratios (I/mr²) convert more energy into spinning and less into forward motion, making them roll slower. The acceleration down an incline is a = g·sinθ / (1 + I/mr²). A solid sphere (I/mr² = 0.4) always beats a solid cylinder (0.5), which beats a hollow cylinder (1.0). Mass and radius cancel out — only the shape matters!
Who Uses This Simulator?
This torque and rotational motion simulator is designed for engineering students, mechanical engineering undergraduates, physics learners, and technicians studying dynamics of machines. It covers concepts tested in engineering mechanics courses including torque calculations, moment of inertia for standard shapes, rotational equilibrium, and rolling motion dynamics. Use the Explore mode to study 12 torque concepts with worked examples, Practice mode for unlimited random problems, and Quiz mode to test your mastery.
Explore Related Simulators
If you found this torque simulator helpful, explore our Friction & Contact Forces simulator, Simple Machines simulator, Newton’s Laws of Motion simulator, and Flywheel Energy Storage calculator for more hands-on practice.