Oars beat engines (sometimes)
Viking longships had rowers placed far from the rudder hinge so a modest force delivered huge torque—equivalent to tens of horsepower—just by stretching the lever arm.
Ancient leverage
Torque & Moment of Inertia Calculator
Inputs
Lever arm = perpendicular distance to the axis (i.e., r·sinθ).
Assumes the applied force is the net torque contributor and the axis is fixed. For non-perpendicular forces, use r⊥ = r·sinθ as the lever arm.
Results
Moment of inertia I (from shape):
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Torque τ (about axis):
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τ = F · r⊥
Angular acceleration α:
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α = τ / I
Rotational kinetic energy (if ω > 0):
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K = ½ I ω²; Power P = τ ω
How Torque, Moment of Inertia, and Rotation Fit Together
This calculator is a practical guide to rotational motion. It helps you connect torque, moment of inertia, and angular acceleration in the same way that force, mass, and linear acceleration work for straight-line motion. If you have ever pushed a door near the hinge and wondered why it barely moves, you have already met torque and lever arms. This tool turns that intuition into numbers you can use for learning, homework, or quick engineering estimates.
The key idea is that torque measures how strongly a force twists around an axis. It is computed as τ = r⊥F, where r⊥ is the perpendicular distance from the axis to the line of action of the force. That distance is called the lever arm, and it is why a long wrench makes it easier to loosen a bolt. How much an object resists angular acceleration depends on its moment of inertia I, which increases when more mass is spread farther from the axis. A heavy ring is harder to spin than a same-mass disk because more of its mass is at the rim.
To use the calculator, choose a shape and enter its dimensions and mass so the tool can compute the moment of inertia. Then enter the applied force, the lever arm (or perpendicular distance), and optionally the angular speed. Click Calculate to see the torque, angular acceleration, rotational kinetic energy, and power. The results show how changing the force or the geometry affects the rotational response. If your force is applied at an angle, first compute r⊥ = r · sin(θ) and enter that value.
This calculator is useful in many real situations: sizing a motor for a flywheel, estimating how quickly a wheel speeds up, analyzing a door closer, or exploring sports mechanics like swinging a bat or spinning a figure skater. It is also a staple concept in physics and mechanical engineering courses because it links geometry and motion in a clear, measurable way. Keep in mind that real systems can include friction, drag, or shifting mass, which add extra torques not captured by the ideal rigid-body formulas.
Notes: This calculator assumes a rigid body and a fixed rotation axis with the applied force creating the net torque. Real systems may have opposing torques (friction, drag, gravity on offset masses). SI units are used throughout: N, m, kg, rad/s, J.
5 Fun Facts about Torque & Inertia
A yo-yo “falls” slower when it spins fast
Drop a yo-yo with the string wound and it descends gently because some gravitational energy diverts into rotational KE. Same m and g, but a hefty I stretches the fall time.
Energy split
Olympic hammer throw is an inertia masterclass
Spinning athletes shorten the cable mid-throw. Pulling the mass inward lowers I, which spikes ω (angular speed) without adding torque—just like a figure skater’s arms-in twirl.
Angular gain
Torque wrenches talk in Newton-meters
When a mechanic clicks a lug nut to 120 N·m, that’s ~90 lb·ft—basically hanging a 90 lb person one foot out on a bar. Lever length translates directly into twist.
Garage physics
Satellites use reaction wheels to pirouette
Spin up a flywheel and conserve angular momentum: the satellite rotates in the opposite direction even in vacuum. Torque without thrusters, powered purely by shifting I·ω internally.
Space ballet