Torque is a measure of the force that can cause an object to rotate about an axis. Just as force causes an object to accelerate linearly, torque is what causes an object to acquire angular acceleration.

Audio Explanation

Prefer to listen? Here's a quick audio summary of the "twist" behind torque.

Visual Representation

A diagram of a wrench turning a nut, illustrating the pivot point, lever arm (r), and applied force (F). Lever Arm (r) Force (F) τ

The Torque Formula

The effectiveness of a force in causing rotation depends on three things: how hard you push, where you push, and at what angle you push.

\[\tau = r F \sin(\theta)\]
  • $\tau$ (tau): Torque (measured in Newton-meters, N·m).
  • $r$: The distance from the pivot point to where the force is applied (the lever arm).
  • $F$: The magnitude of the applied force.
  • $\theta$: The angle between the force vector and the lever arm.

Note: Torque is maximized when the force is applied perpendicularly ($\theta = 90^\circ$), because $\sin(90^\circ) = 1$.

Interactive Torque Lab

Try to balance the seesaw! Adjust the mass of the objects and their distance from the center (the fulcrum). Notice how a smaller weight can balance a larger weight if it is placed further from the center.

Seesaw Equilibrium

10 kg
2 m

Left Torque:

--- N·m

Right Torque:

--- N·m

Rotational Equilibrium

An object is in rotational equilibrium when the sum of all torques acting on it is zero. This is the rotational version of Newton’s First Law.

\[\sum \tau = 0\]
  • Clockwise (CW) Torques: Usually treated as negative.
  • Counter-Clockwise (CCW) Torques: Usually treated as positive.

If the torques balance out, the object will not change its state of rotation.

Interactive Match: Torque Concepts

Can you match the action to its effect on torque?

Why Should I Care?

Torque is the principle behind every simple machine that involves rotation:

  • Tools: Wrenches and crowbars use long handles to increase $r$, allowing you to produce massive torque with relatively small force.
  • Biometrics: Your muscles create torque around your joints to move your limbs.
  • Automotive: An engine’s “torque” rating tells you how much pulling power it has to get a heavy load moving.

💡 Quick Concept Check:

Why is the door handle always located on the opposite side of the hinges?

Click to Reveal Answer
To maximize the **lever arm ($r$)**. By placing the handle as far from the hinges (the pivot) as possible, you minimize the amount of force ($F$) required to produce the torque needed to rotate the door open.
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