Torque

Introduction

Have you ever had a tough time unscrewing the cap off of something? Maybe a bottle or even a jar? Perhaps you were trying to open a jar of pickles or olives, and you used way too much force, and the resulting torque screwed the lid tighter. Just when you think you are going to break the cap open to get the contents of that jar, it starts turning smoothly until it eventually comes right off. This force is exactly what torque is.

What is torque? 

Torque is a measure of the tendency of a force to rotate an object about an axis, fulcrum, or pivot. As a force is a push or a pull on an object, a torque can be a twist on the object. It is denoted by . The torque formula is 

=rF

=rF sin

= Torque vector

r = position vector about which the torque is measured

F = Force vector 

= Angle between the force vector and level arm vector

A force applied at a right angle to a lever multiplied by the distance from its point of application to the lever’s pivotal point typically produces a torque. The SI unit of torque is the newton metre(N-m).

Dimensional Analysis 

The dimensional formula of torque is [ML2T−2], as the torque formula is derived from force and position. For force, the dimensions are [MLT-2], and the dimensions are [L] for position vectors. So, calculating them, we get [ML2T−2].

Measurement of Torque 

For the explanation and measurement of torque, let’s consider the situation given below and see how the forces act on any object.

• Suppose there is a rod with endpoints A and B. Let two opposite forces, F1 and F2,  act on the given rod in a circular manner. However, the magnitude of both forces are equal, so the object has been balanced. So, we can conclude that the net force is zero.
• But somehow, the rod is rotating, and hence we can assume that even after being in translational equilibrium, the rod still can rotate because of the factor we call torque or moment of force.
• Here the most important thing to note is that torque is always perpendicular to the force acting on it. 
• Apart from it, we can see some other examples of how torque is calculated. When someone opens a door, he is applying force on the door, and the position vector will be perpendicular to it. 
• Therefore, we take a cross product between Force and the position vector, which comes into play as sinQ.

So, we see that torque is a vector. This means that it has both magnitude and direction. 

Torque Formula 

Torque formula depends on the angular momentum as for a single point particle, we can write it as :

L=rp

Here, “p” is the particle’s linear momentum, and “r” is the particle’s position vector. After this, the time derivative will be :

dL/dt=rdp/dt+dr/dtp

Now with the product rule in vectors, the result can be obtained. Besides this, we will use the previous results like dp/dt=F and dr/dt=v. So we can write it as :

dL/dt=(rF)+(vp)

When we do the cross-product between velocity and momentum, we will get zero because both the terms are parallel to get cancelled. So, now only two terms will be left, and they will be Force and position vector.

dL/dt=rFnet=net

The above proof can be generalised to any distribution of masses numerically. For example, if you have a continuous mass of points, and each point has a mass m, the static equilibrium is provided by the sum of forces over each point.

How are we able to increase or decrease torque?

To maintain healthy unique applications, it is frequently necessary to increase or decrease the torque produced by a motor. Remember that the length of a lever can increase or decrease the pressure on an item depending on the amount of space through which the lever must be pushed. Similarly, gearing can be used to increase or decrease the torque produced by a motor. An increase in torque is accompanied by a proportionate decrease in rotational speed.

Adjustable gearing is essential for achieving appropriate overall performance in motors powered by combustion engines. These engines create the most torque at a small number of high rotational speeds. Adjustable gearing allows enough torque to be delivered to the wheels at any engine rotational speed.

Bicycles require gearing because humans are unable to pedal at a cadence high enough to maintain a useful speed when utilising a wheel directly (until one is biking a penny-farthing).

Adjustable gearing isn’t usually necessary in motors driven by steam engines or electric motors. Excessive torque is available at low speeds in both circumstances, and it is extremely consistent throughout a wide range of speeds.

Conclusion:

When the term ‘torque’ is mentioned, it is almost always in the context of automobiles. Torque is a term that is frequently used to describe the efficiency of a vehicle, but what exactly does it imply? Torque is the force exerted by pistons on the crankshaft, causing it and the wheels to turn in an automobile.

Torque is a widely used physics term that has many uses, despite its association with automobiles. Torque is defined as a twisting pressure with a proclivity towards rotation. The axis of rotation is named after the factor that causes the item to rotate. Every day, you use torque without realising it. You notice torque while obviously opening a locked door. Torque is used in a variety of ways, including turning the key, twisting the doorknob, and pushing the door open, so it swings on its hinges.

Torque is an important aspect of generating power from a car’s engine since it represents the maximum weight that an engine can handle while still creating enough electricity to revolve the engine on its axis.