What is Torque? Definition, Formula, Equation, Units, Deviation, Types


In this article, we will learn what is torque, definition, formula, equation, units, deviation, types, etc.

Let’s explore!

What is Torque? Defintion

Torque Basics

The word toque is derived from the Latin word ‘torquere’, which means “to twist or turn.” The word was also used since 1834, when ancient Romans used this term for metal necklaces, which were twisted or turned from ends.

For an object to move in a linear direction, we need some force to apply to it.  Similarly, torque is what is required to move an object around its axis. So, in simple words, we can put that, in physics, torque is the amount of force necessary to move an object around its axis. Hence, we can define torque as the angular equivalent of linear force on an object.

Definition of Torque

All the objects on these planets, when they move, they are the result of some force or energy. Further, the type of energy or force they possess can be determined by their movement.

  • Anything which causes an object to move in a specific direction is known as force. Not always, but an object moves in a linear direction due to force most of the time. But if force causes an object to move in an angular motion around its axis, we call it a torque.
  • In simple words, we can expect that force causes an object to move because it produces acceleration, but torque causes an object to move because it causes rotation.
  • Torque is a vector quantity because it has both magnitude and direction, and the direction of the torque vector depends on the direction of the force on the axis.  A slight change in the torque can cause an effect on the whole result. The symbol of torque is T.

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Important Terms about Torque

Pivot

The rotational point in any lever system is called a pivot. It is referred to as the central point of the whole system. For example, the point where the gears rotate is the main point or pivot in a cycle.

Moment arm

The moment arm or lever arm is the perpendicular distance taken from the center or pivot of the system or object. Torque is always defined from the pivot point. In other words, we would say that torque increases with the rise in angular acceleration.

Fulcrum

Fulcrum is the supporting or resting point of the whole lever system.

Non-Concurrent forces

When different forces act on several points such that it produces turning movement, or generally stating, torque in the body is called concurrent forces.

Concurrent forces

When different forces act on a body to pass through one common point, they are shown as one net force and are termed concurrent forces.

Line-of-action

The path along which resultant forces are likely to act is known as line-of-action.

Rotational equilibrium

Rotational equilibrium is the situation in which the body’s angular and linear accelerations are zero. Hence, in such a case, the body is said to be in rotational equilibrium.

Couple

Two forces acting on a body in different directions such that they don’t pass through a common point are known as a couple. The couple produces a turning effect in the body.

Role of Torque in Rotational Kinematics

The place of force in linear kinematics is taken by torque in rotational kinematics. So, there is an equivalent of Newton’s second law of motion (F=ma) in rotational kinematics.

Τ = I. α

Here,

  • α is the angular acceleration, and
  • ‘I’ is the rotational inertia.

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Eqation Relation between Torque, Power, & Energy

The three terms torque, power, and energy have always been confused as torque is usually described or considered as turning power. 

As for energy, it has the same dimension as torque, but still, they are not the same. It is used to measure different things. They are different in that torque is a vector quantity, and power can be derived using a system’s torque if the system’s speed is known.

Their relationship is:

  • P =   Force.  Distance

Force

  • P = F. 2πr

Time

  • t= 2πτω (ω in revolutions/sec)
  • t= τω (ω in radian/sec)

Units of Torque

The SI unit of torque is Newton-meter equal to the torque resulting from a force of one newton applied perpendicularly to the end of a moment arm one meter long.

Most often, Foot-pound is also used in imperial units. The pound is mainly used for mass and sometimes for force. But here pound is used for force and can be defined as the force due to earth gravity on a one-pound object.

  • Torque = Force X Distance
  • Torque = N X m
  • Torque = Nm
  • Nm = N X m
  • Nm = Kgmsec-2 X m
  • Nm = kgm2sec-2

The other units used for measuring Torque are listed below:

  • Millinewton Meter
  • Micronewton Meter
  • Pound inch
  • Foot-poundal
  • Kilopond Meter
  • Pound-foot
  • Ounce-foot
  • Meganewton Meter
  • Kilonewton Meter
  • Kilogram Meter
  • Dyne centimeter
  • Gram centimeter
  • Newton centimeter
  • Kilogram centimeter

Equation & Formula of Torque

Mass and acceleration are required to find a linear force. As rotation is involved in torque, hence it is a bit different from it. Think about opening a door.

Where do you push on it when you want it to open? You push on the side of the door with no hinges because pushing on the side with the hinges would make it much harder to open.

So, for torque, we need to know not only the mass and acceleration of a linear force but also how far that force is from the axis of rotation since we can get different results depending on that. We can see this in the equation of torque;

  • T = F * r * sinθ
  • T = torque
  • F = linear force
  • r = distance measured from the axis of rotation to where the linear force is applied
  • θ = the angle between F and r

Here, sin(theta) has no units, r is in meters (m), and F has SI units of Newtons (N). Combining these, we get that a unit of torque is a Newton-meter (Nm).

If the force is at right angles (90 degrees) to the moment arm, so the sine term becomes 1 and

T = F. r 

The direction of the torque vector is found by convention using the right-hand grip rule. If a hand is curled around the axis of rotation with fingers pointing in the direction of the force, then the torque vector points in the direction of the thumb, as shown in Figure.

Derivation of Torque Formula & Equation

Formula derivation for torque is:

Rate of change of Angular Momentum with time = ΔL/ΔT

  • Now, ΔL/ΔT = Δ (I ω)/ΔT = I. Δω/ΔT ……. (1)

Here ‘I’ is undoubtedly the constant when the mass and shape of the object are unchanged

Now Δω/ΔT refers to the rate of change of angular velocity with time, i.e., angular acceleration (α).

  • So, from equation 4, one can write, ΔL/ΔT = I α ………………… (2)

I (moment of inertia) refers to the rotational equivalent of mass(inertia) of linear motion. Similarly, angular acceleration α (alpha) indeed refers to the rotational motion equivalent of linear acceleration.

From equation 5, one can get, ΔL/ΔT = τ ……………………. (6) this indeed states that the rate of change of angular momentum with time is called Torque.

  • Torque (T) refers to the moment of force. Τ = r x F = r F sinθ ……………. (3)

F is the force Vector, and r refers to the position vector

θ happens to be the angle between the force and lever arm vector. ‘X indeed denotes the cross product.

  • Τ = r F sin θ = r ma sinθ = r m αr sinθ = mr2. α sinθ = I α sinθ = I X α ……………………… (4)

[α is angular acceleration, I refers to the moment of inertia, and X denotes cross product.]

  • T = I α (from equation 4)

or, T = I (ω2-ω1)/t [here α = angular acceleration = time rate of change of the essential angular velocity = (ω2 – ω1)/t where ω2 and ω1 happen to be the final and initial angular velocities and t is the time gap]

  • or, T t = I (ω2-ω1) …………………… (5)

when, T = 0 (i.e., net torque is zero),

  • I (ω2-ω1) = 0
  • i.e., I ω2=I ω1 …………… (6)

Difference Between Torque and Moment

The moment is the turning effect of the force. It moves the body around the axis in a clockwise or anticlockwise direction. At the same time, torque is the force that causes the body to rotate or move around its axis.

Types of Torqe

There are two types of torque. These are;

Static torque

When the torque does not produce angular acceleration or motion, then it is called static torque. It happens because the torques adding together cancel out each other and cause an object to remain stationary.

As an example, let’s consider ourselves pushing on the closed door. We notice that the closed-door does not move any further on pushing the door 

Another example of this type of force can be paddling on the bicycle at a constant speed because it won’t allow the bike to accelerate any further.

Dynamic torque

When the applied torque produces an angular acceleration in an object, it is called dynamic torque. We can say that this type of torque produces a change in rotational motion.

For example, the wheels of the moving car produce this type of torque which causes the vehicle to move forward upon wheels.

Dependency of Torque

Torque is also known as a moment of force. The concept of this phenomenon is very similar to force. The force causes pushing and pulling objects, while torque results in twisting and turning. Torque is dependent upon a few parameters. They are listed below:

  • Magnitude of force
  • Distance between the point where force is applied and the rotation axis
  • The orientation of force in association with displacement from the point of applied force to the axis.

Applications of Torque

Any object that tends to move in angular motion with applied force has some torque. There are many applications of torque that we observe in our daily life. Some of these applications are:

  • Hinged door (As you get closer to the hinge, you must apply a larger force to make the door swing. As you get farther from the hinge, you can use a smaller force to make the door swing. The product of force and the perpendicular distance to pivot (hinge) is called the torque or the moment arm.
  • Seesaw (Torque is defined as force times distance, where the force acts perpendicular to the distance about a point of rotation. If the sum of the torques that cause rotation in a clockwise direction equals the sum of the torques that cause it to rotate counter-clockwise, the seesaw remains balanced).
  • Wrench (A torque wrench is a tool used to tighten nuts and bolts to a predetermined torque value. This instrument allows fasteners to be tightened to the proper tension, helping avoid damage from over-tightening of joints coming apart from under-tightening).
  • Moving bicycle or any wheel bearing object
  • Flag flying on the mast
  • Steering wheel (Steering wheel torque is the influence of engine loads on the steering due to which driver will fill sudden shocks on the steering while driving)
  • Gyroscopes (A gyroscopic torque will result if the flywheel axis is rotated and acts perpendicular to the rotor axis. The magnitude of the torque is the product of the flywheel rotor moment of inertia, the flywheel angular velocity, and the angular velocity of the flywheel axis).
  • A pendulum or a parachute applies torque when swinging
  • Bottle opener
  • turning the key
  • turning the doorknob

Torque is a fundamental phenomenon. From seesaws to heavy machinery, it is applicable and of great use.

Advantages of Torque

There are so many applications of torque in our daily life. If we look at the torque which I being used in our car engines, we can pick out some of the advantages and disadvantages it has. So, the benefits of torque in the machine are that it provides;

More power

If there is more torque in an engine, it will provide more power to work.

Better acceleration

Torque is also directly proportional to acceleration which means more torque in the engine will produce more acceleration.

More efficient engine

With the increase of torque in the engine, it will work more efficiently and smoothly.

Torque sensors

Torque sensors are gadgets used for measuring the twisting and turning forces. They may be static torque or dynamic torque and can measure forces either in the clockwise or anti-clockwise direction. They are small, compact, and powerful devices that serve as essential applications. It is an industrial application of torque.

Torque aids in determining the direction and magnitude of rotational force applied to an entity. It also helps you find out whether the applied force will cause clockwise or counterclockwise motion. Moreover, the angular acceleration of the body causing rotation can also be predicted with it.

Disadvantages of Torque

Just like having advantages of different things that use the principle of torque to work, some things also have disadvantages.  For example, a torque converter works using the principle of torque; when it moves into any malfunction, it delivers vibrating and slipping effects.

So, some of the disadvantages of using it are;

Overheating

Due to a faulty torque converter, the engine of the vehicle can overheat in a brief period.

Transmission slipping

An issue with the torque converter will probably show itself fairly immediately because fluid flow cannot be adequately handled. When there is insufficient flow or overflow of fluid in the transmission, it causes a slippery nature in the gears and reduces the feel of acceleration. With this, there will also be a loss in the vehicle’s fuel economy.

Shuddering

Torque converter issue can cause the vehicle to shudder at the speed of 30-45 MPH. It can cause the car to feel bouncy or like on a rough surface.

Fluid Contaminants

Malfunctioning a torque converter can become the reason for fluid like oil and petroleum’s contamination, so it needs to work correctly.

Weird sounds

Due to any malfunctions in the torque converter, the engine can make weird sounds that can be uncomfortable for the driver or anyone.

Conclusion

Torque is the amount of force required to move a body in an angular motion around its axis. The SI unit of torque is Nm. There are two types of it which are static torque and dynamic torque. One talks about the torque, which doesn’t cause the body to move, but the other one would make it move in angular motion. Torque is a vector quantity as it has both magnitude and direction.

Torque has many advantages in terms of power and acceleration because more torque leads to more power, and more power leads to more acceleration. Torque also has disadvantages in the overheating and weird sound inside the engine.

The blog gives an in-depth insight into the concept of torque. It states the definition, derivation, advantages, disadvantages, types, and unit of torque.

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