Torque & Rotational Motion Simulator
Wrench • Seesaw • Spinning Disc • Rolling Race — Simulate • Explore • Practice • Quiz
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 TVET 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.
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