What is torque?

Short Answer:

Torque is the turning or twisting effect produced by a force acting on a body about an axis. It is the product of the force and the perpendicular distance from the axis of rotation to the line of action of the force. Torque is a vector quantity and determines how effectively a force can cause rotational motion.

In simple terms, torque measures how much a force can rotate an object around a pivot point or axis. For example, when we tighten a bolt using a spanner, the turning effect we apply on the bolt is called torque. Its unit is Newton-metre (N·m) in the SI system.

Detailed Explanation :

Torque

Torque is one of the most fundamental concepts in mechanics and plays a vital role in the study of rotational motion. It represents the rotational effect of a force applied on a body around a particular axis. When a force acts on a lever arm at some distance from a fixed point, it tends to rotate the body about that point. The measure of this tendency to rotate is called torque.

Mathematically, torque () is expressed as:

where,
= Torque (N·m)
= Force applied (N)
= Perpendicular distance from the axis of rotation to the line of action of force (m).

If the force is applied at an angle  to the lever arm, then the torque is given by:

The direction of torque is determined using the right-hand rule — if the fingers of the right hand curl in the direction of rotation, the thumb points in the direction of torque.

Concept of Torque

The concept of torque is similar to the concept of force in linear motion. Just as force causes a linear acceleration in a body, torque causes an angular acceleration in a rotating body. When torque acts on a body, it creates rotational motion around a fixed axis. The amount of rotation depends on the magnitude of torque and the moment of inertia of the body.

Torque can be positive or negative depending on the direction of rotation it produces:

  • Clockwise Torque is usually considered negative.
  • Anticlockwise Torque is usually considered positive.

This convention helps in solving rotational equilibrium problems easily.

Types of Torque

Torque can be classified into the following types based on its nature of action:

  1. Static Torque:
    It is the torque that does not produce angular acceleration because the body does not rotate. For example, when tightening a bolt with a wrench, before the bolt starts moving, the torque applied is static torque.
  2. Dynamic Torque:
    It is the torque that produces angular acceleration in the rotating body. For instance, the torque generated by the crankshaft in an engine while running is a dynamic torque.

Unit of Torque

In the SI system, the unit of torque is Newton-metre (N·m).
In the CGS system, it is dyne-centimetre (dyne·cm).
1 N·m = 10⁷ dyne·cm.

Factors Affecting Torque

The magnitude of torque depends upon three main factors:

  1. Magnitude of Force: Greater the force applied, greater the torque produced.
  2. Perpendicular Distance (Lever Arm): The longer the lever arm, the larger the torque for the same force.
  3. Angle of Application: The torque is maximum when the force acts perpendicular to the lever arm (i.e., at 90°).

Thus, torque can be increased either by applying a larger force or by using a longer arm to apply the same force.

Physical Meaning of Torque

Torque is a measure of the effectiveness of a force in producing rotational motion. It is analogous to force in linear motion. If a force is applied through the axis of rotation, it produces no torque because the perpendicular distance is zero. Only the component of the force that acts perpendicular to the radius causes torque.

For example:

  • When opening a door, if you push near the hinges, it’s difficult because the lever arm is small.
  • If you push near the edge (farther from hinges), it becomes easy due to the longer lever arm and hence higher torque.

This clearly shows that torque depends both on force and on the point of application.

Torque in Rotational Motion

In rotational dynamics, torque plays the same role as force in linear motion. According to Newton’s second law for rotation:

where,
= Moment of inertia of the body (kg·m²)
= Angular acceleration (rad/s²)

This means the angular acceleration of a rotating body is directly proportional to the applied torque and inversely proportional to its moment of inertia.

Applications of Torque

  1. Automobiles: The torque generated by an engine determines the ability of the vehicle to accelerate and move loads.
  2. Wrenches and Levers: Longer handles are designed to produce more torque with the same force.
  3. Electric Motors: The torque determines the power output and load-carrying capacity of motors.
  4. Bicycles: Pedal length affects torque generation, influencing how easily a rider can move the bicycle.
  5. Rotating Machines: Torque is used in turbines, pumps, and compressors to measure mechanical output.

Torque and Power Relation

Power is related to torque in rotational systems by the formula:

where,
= Power (W),
= Torque (N·m),
= Angular velocity (rad/s).

This equation shows that for a given speed, more torque means more power.

Conclusion:

Torque is the twisting or rotational effect of a force acting on a body about a fixed axis. It is a key concept in rotational motion, determining how effectively a force can produce rotation. The magnitude of torque depends on the force applied, its perpendicular distance from the axis, and the angle of application. It plays a crucial role in all mechanical systems involving rotation, such as engines, motors, gears, and levers, making it one of the most important quantities in mechanical engineering.