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 β from opening doors and tightening bolts to engine design and robotic arms.
Definition
The rotational equivalent of force; a measure of how much a force tends to cause an object to rotate about an axis.
π‘ Intuition
How hard you're twisting something. Depends on force AND distance from pivot.
π― Core Idea
Torque = force \times lever arm (perpendicular distance to the axis).
Example
Formula
Notation
\tau (tau) is torque in newton-metres (NΒ·m), r is the distance from the axis of rotation to the point of force application, F is the applied force, and \theta is the angle between \vec{r} and \vec{F}.
π Why It Matters
Torque governs every rotational system β from opening doors and tightening bolts to engine design and robotic arms. Understanding torque is critical for mechanical engineering and structural analysis.
π 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.
Formal View
Related Concepts
π§ Common Stuck Point
Torque is not forceβsame force at different distances produces different torques.
β οΈ Common Mistakes
- Using the total length of the object instead of the perpendicular distance (lever arm) from the pivot to the line of action of the force.
- Forgetting to include the \sin\theta factor when the force is not perpendicular to the lever arm, which overestimates the torque.
- Confusing torque with force β a large force applied at the pivot produces zero torque because the lever arm is zero.
Go Deeper
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.
What is the Torque formula?
When do you use Torque?
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.
Prerequisites
Next Steps
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 and rotational equilibrium.
π§ͺ Interactive Playground
Drag to explore. Click to commit changes.