Torque

Also known as: moment, τ

definition

The rotational equivalent of force; a measure of how much a force tends to cause an object to rotate about an axis. Torque governs every rotational system — from opening doors and tightening bolts to engine design and robotic arms.

💡 Intuition

How hard you're twisting something. Depends on force AND distance from pivot.

Core Idea

Torque = force \times lever arm (perpendicular distance to the axis).

Formal View

Torque is defined as the cross product of the position vector and the force vector: \vec{\tau} = \vec{r} \times \vec{F}, with magnitude \tau = rF\sin\theta. The net torque on a rigid body equals I\alpha, where I is the moment of inertia and \alpha is the angular acceleration.

🔬 Example

Opening a door: push far from the hinge (more torque), push near the hinge (less torque).

🎯 Why It Matters

Torque governs every rotational system — from opening doors and tightening bolts to engine design and robotic arms. Understanding torque is critical for mechanical engineering and structural analysis.

⚠️ Common Confusion

Torque is not force—same force at different distances produces different torques.

💭 Hint When Stuck

When solving a torque problem, first identify the pivot point (axis of rotation) and each applied force. Then calculate each torque as \tau = rF\sin\theta, where r is the distance from the pivot and \theta is the angle between the force and the lever arm. Finally, assign positive/negative signs for counterclockwise/clockwise and sum all torques.

Related Concepts

Prerequisites

force circular motion

Next Steps

angular momentum

How Torque Connects to Other Ideas

To understand torque, you should first be comfortable with force and circular motion. Once you have a solid grasp of torque, you can move on to angular momentum.

Go Deeper

Worked Examples

Step-by-step solved problems

Practice Problems

Test your understanding

Formula Explained

Notation, derivation, and common mistakes

Frequently Asked Questions

What is Torque in Physics?

The rotational equivalent of force; a measure of how much a force tends to cause an object to rotate about an axis.

Why is Torque important?

What do students usually get wrong about Torque?

Torque is not force—same force at different distances produces different torques.

What should I learn before Torque?

Before studying Torque, you should understand: force, circular motion.

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