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Torque

physical science Maturity 9-11 Next article →

In physics and mechanics, torque is the rotational equivalent of linear force. While a linear force is a simple push or pull that moves an object in a straight line, torque is a twist applied to an object around a specific axis.

moment arm
moment arm

This concept is essential for understanding how machines function and how objects rotate. In the field of physics, this twisting effect is typically called torque. However, in engineering, it is often referred to as the "moment of force" or simply the "moment."

Torque, position, and force
Torque, position, and force

This distinction in terminology often depends on a person's geographical location or their specific field of study.

To understand how torque works, you must look at three specific quantities. The first is the magnitude of the force being applied. The second is the lever arm, which is the distance from the axis of rotation to the point where the force is applied.

moment arm
moment arm

The third factor is the angle at which the force hits the lever arm. To produce the maximum amount of torque, the force must be applied perpendicularly, or at a right angle, to the lever arm. If a force is directed parallel to the position vector, it produces no torque at all. Therefore, only the perpendicular component of a force contributes to the rotation.

Torque, position, and force
Torque, position, and force

Mathematically, torque is described as a cross product between a position vector and a force vector. In three dimensions, torque is considered a pseudovector. This means it has both a magnitude and a specific direction. You can find the direction of the torque vector using the right-hand grip rule. If you curl the fingers of your right hand from the lever arm toward the direction of the force, your thumb points in the direction of the torque.

Torque, position, and force
Torque, position, and force

This resulting vector is perpendicular to both the position and the force vectors, defining the plane in which they lie.

The history of the word "torque" can be traced back to the Latin word meaning "to twist." The term was suggested by James Thomson and appeared in print in April 1884. That same year, Silvanus P. Thompson used the term in his book, *Dynamo-Electric Machinery*. While the specific word "torque" is relatively recent, the underlying scientific principles are much older. The terminology for these rotational ideas can be traced back to at least 1811 in the work of Siméon Denis Poisson. An English translation of Poisson's research was eventually published in 1842.

Measuring torque requires specific scientific units. In the International System of Units (SI), the standard unit is the newton-meter (N⋅m). It is important to note that while the newton-meter is dimensionally equivalent to the joule, the joule is never used to express torque. This is because torque is assigned to a vector, while energy is assigned to a scalar.

Torque Curve
Torque Curve

In the United States, industrial settings often use imperial units. These include the pound-foot (lbf-ft) or the pound-inch (lbf-in). Some practitioners in the US also use the foot-pound (ft-lb) or inch-pound (in-lb) to describe torque.

Torque has a deep connection to the concept of angular momentum. The net torque acting on a body determines the rate at which that body's angular momentum changes over time. This relationship serves as the rotational version of Newton's second law.

PrecessionOfATop
PrecessionOfATop

Additionally, torque is closely linked to the concepts of work and power. If a torque acts through an angular displacement, it performs mechanical work. This work is equal to the change in the rotational kinetic energy of the body. The power produced by a torque depends on the instantaneous angular speed of the object.

Torque Curve
Torque Curve

Finally, the principle of moments, also known as Varignon's theorem, helps explain how multiple forces interact. This principle states that the total torque resulting from several forces applied around a single point is equal to the sum of the individual torques. When these various torques are balanced, the object will not undergo rotational acceleration. This principle is vital for engineers when designing stable structures or mechanical systems. From spinning tops to heavy industrial machinery, the laws of torque govern almost every rotating movement in our world.

PrecessionOfATop
PrecessionOfATop
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🖼️ Images & Media (4)
File:Torque, position, and force.svg
Torque, position, and force.svg
File:moment arm.svg
moment arm.svg
File:PrecessionOfATop.svg
PrecessionOfATop.svg
File:Torque Curve.svg
Torque Curve.svg
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