Short Answer:

Torque is the turning or twisting effect produced by a force when it acts at a distance from the axis of rotation of a body. It is the tendency of a force to cause rotation rather than linear motion. Torque depends on two factors — the magnitude of the force and the perpendicular distance between the line of action of the force and the axis of rotation. Mathematically, torque is given by T = F × r, where F is the applied force and r is the perpendicular distance (moment arm). The SI unit of torque is Newton-meter (N·m).

Detailed Explanation :

Torque and its Units

In Engineering Mechanics, torque is one of the most important concepts used to describe rotational motion. It can be defined as the rotational effect of a force applied to a body about an axis or point. Just as a force causes linear motion, torque causes rotational motion. When a force is applied at some distance from the axis of rotation, it tends to twist or turn the body — this turning effect is called torque.

For example, when you use a wrench to loosen a bolt, the force applied on the handle of the wrench at a distance from the bolt creates torque that rotates the bolt. Similarly, when opening a door, you apply a force at the handle, away from the hinges; this force causes the door to rotate — an example of torque in action.

Thus, torque is a measure of the tendency of a force to rotate a body about an axis. The greater the distance from the axis of rotation, the greater the torque for the same amount of force.

Mathematical Expression of Torque

Torque is calculated as the product of the magnitude of the force and the perpendicular distance from the axis of rotation to the line of action of the force.

Mathematically,

Where:

• T = Torque (N·m)
• F = Force applied (N)
• r = Perpendicular distance from the line of action of force to the axis of rotation (m)

Here, r is also known as the moment arm or lever arm.

The direction of torque depends on the direction in which the force tends to rotate the body:

• If the force tends to rotate the body clockwise, the torque is said to be clockwise torque.
• If the force tends to rotate the body anticlockwise, the torque is said to be anticlockwise torque.

Vector Form of Torque

In vector form, torque is expressed as the cross product of the position vector and the force vector:

Where:

• r is the position vector of the point where the force is applied, measured from the axis of rotation.
• F is the applied force vector.

The magnitude of the torque is given by:

where θ is the angle between r and F.

This equation shows that torque is maximum when the force acts perpendicular (90°) to the lever arm because sin 90° = 1.

Units of Torque

The SI unit of torque is Newton-meter (N·m).

This means that when a force of 1 Newton acts at a perpendicular distance of 1 meter from the axis of rotation, it produces a torque of 1 N·m.

In other systems:

• CGS Unit: Dyne-centimeter (dyne·cm)
• FPS Unit: Pound-foot (lb·ft) or pound-inch (lb·in)

However, in engineering and physics, the SI unit N·m is most commonly used.

Dimensional Formula of Torque

The dimensional formula of torque can be derived from its definition:

The dimensional formula of force, , and that of distance, .
Therefore,

Hence, the dimensional formula of torque is [M L² T⁻²].

Factors Affecting Torque

1. Magnitude of Force (F):
   The larger the applied force, the greater the torque produced.
2. Distance from Axis (r):
   Torque increases with an increase in the perpendicular distance between the line of action of the force and the axis of rotation.
3. Angle of Application (θ):
   Torque depends on the angle between the force and lever arm. The maximum torque occurs when the force acts perpendicular to the lever arm (θ = 90°).

Difference between Force and Torque

Although both force and torque are related to motion, they are different in nature:

• Force causes linear motion.
• Torque causes rotational motion.
  Force acts along a line, while torque acts around a point or axis.

For instance, pushing a door at its hinge does not open it because the torque produced is zero (distance = 0). But pushing it at the handle (farther from the hinge) produces maximum torque and opens the door easily.

Examples of Torque in Daily Life

1. Opening or Closing a Door:
   The force applied at the door handle creates torque that rotates the door about its hinges.
2. Using a Spanner:
   Torque is produced when a wrench is used to tighten or loosen a nut.
3. Turning a Steering Wheel:
   Torque allows the wheel to rotate and change the direction of the vehicle.
4. Rotating a Screw or Bolt:
   Applying a twisting force creates torque, causing rotation.
5. Bicycle Pedaling:
   When you push the pedal, torque is applied on the crank that rotates the chain wheel.

Applications of Torque in Engineering

Torque is widely used in mechanical and automotive engineering for analyzing and designing machines involving rotation. Some applications include:

• Engines: Torque measures the engine’s ability to do rotational work.
• Gears and Shafts: Torque helps in determining strength and power transmission capacity.
• Machine Tools: Torque analysis ensures proper functioning of rotating tools like drills and lathes.
• Braking Systems: Torque helps in calculating the braking force required to stop rotating parts.
• Robotics and Control Systems: Torque is crucial for controlling rotational joints and actuators.

Importance of Torque

Torque is an essential concept for understanding mechanical systems that involve rotation. It is used to determine the efficiency, performance, and safety of mechanical devices. Without torque, rotational motion cannot occur, and machines such as engines, turbines, and pumps would not function. Torque also helps in understanding the balance between force and distance in levers and rotational equilibrium systems.

Conclusion

In conclusion, torque is the rotational effect of a force acting at a distance from the axis of rotation. It is given by T = F × r, where r is the perpendicular distance between the line of action of the force and the axis. The SI unit of torque is Newton-meter (N·m), and its direction is determined using the right-hand rule. Torque plays a vital role in mechanical and engineering applications, as it governs the design and performance of rotating systems like engines, machines, and levers.