1. What is Torque?
Torque is the turning or twisting effect produced by a force. While a force makes an object move in a straight line, torque makes it rotate. You experience torque whenever you open a door, turn a wrench, or twist a bottle cap.
The effectiveness of a force in producing rotation depends not only on how strong the force is but also on where and how it is applied.
1.1. Understanding Through Daily Life
Torque appears in many familiar situations:
- Pushing a door near the hinges is harder than pushing it near the handle.
- Using a long wrench makes it easier to loosen tight bolts.
- A child on the seesaw needs to sit farther from the pivot to balance an adult.
These examples show that both force and distance from the rotation point matter.
1.1.1. When Do We Get More Rotation?
You get a stronger turning effect when the applied force is:
- Larger in magnitude
- Applied farther from the pivot
- Applied at a right angle to the lever arm
2. Definition and Formula of Torque
Torque is defined as the product of the applied force and the perpendicular distance from the axis of rotation. This perpendicular distance is called the moment arm or lever arm.
The magnitude of torque is given by:
\( \tau = r F \sin \theta \)
Here:
- \( r \) is the distance from the pivot to the point where the force acts
- \( F \) is the applied force
- \( \theta \) is the angle between the force and the lever arm
2.1. Vector Form of Torque
Torque is a vector quantity. It is given by the cross product of the position vector and the force vector:
\( \vec{\tau} = \vec{r} \times \vec{F} \)
The direction of torque is perpendicular to the plane formed by \( \vec{r} \) and \( \vec{F} \), determined using the right-hand rule.
3. Clockwise and Counterclockwise Torques
When analysing rotation, it is important to identify whether a torque tends to rotate an object clockwise or counterclockwise about its pivot. These two directions are considered opposite and may cancel each other if acting simultaneously.
3.1. Choosing the Sign Convention
Typically:
- Counterclockwise torque is taken as positive.
- Clockwise torque is taken as negative.
This helps solve problems systematically, especially when multiple torques act on a body.
4. Factors Affecting Torque
The amount of torque produced depends on three main factors. Understanding them helps in solving rotational motion problems efficiently.
4.1. Magnitude of the Force
A larger force produces more torque. For example, pushing harder on a wrench increases the turning effect.
4.2. Length of the Lever Arm
The farther the force is applied from the pivot, the larger the torque. This is why tools like wrenches and crowbars are designed with long handles.
4.3. Angle of Application
Torque is maximum when the force is applied at \( 90^\circ \) to the lever arm because \( \sin 90^\circ = 1 \). If the force is applied parallel to the arm, torque becomes zero.
5. Examples Illustrating Torque
Torque plays a vital role in understanding how rotational motion occurs in real-world situations.
5.1. Opening a Door
You push at the handle, far from the hinge, to produce greater torque and open the door easily.
5.2. Tightening or Loosening Bolts
A long wrench provides a larger lever arm, increasing torque with the same applied force.
5.3. Balancing on a Seesaw
Children sitting farther from the pivot can balance adults by generating equal and opposite torque.
6. Why Torque is Important
Torque is a fundamental concept in rotational mechanics. It helps us understand how forces cause angular acceleration, balance objects, operate machines, and predict the motion of rotating systems.
In upcoming topics, concepts like moment of inertia, angular acceleration, and rotational dynamics build directly on the idea of torque.