Difference Between Torque and Moment

Torque is defined as the measure of the force that can cause an object to rotate about an axis. Force is the thing that causes an object to accelerate in linear kinematics. Like in that way, torque causes an angular acceleration. So, torque can be defined as the rotational equivalent of linear force. And the point where the object rotates is called the axis of rotation. Basically, according to physics, torque is simply the tendency of a force to turn or twist. Different terms like moment or moment of force are widely used to describe torque. Generally, torque refers to the twisting force that causes motion and it also refers to the turning effect. 

Basically, the point of the rotation of the object is called the axis of rotation. Everyone is making use of this force without realizing this fact. And also the Torque is a vector quantity. So, the direction of the torque vector depends on the direction of the force on the axis. Torque can either be defined as static or dynamic.

Static torque: A static torque is the type of torque that does not produce an angular acceleration. For Example, If Someone is pushing on a closed-door they are applying a static torque to the door because the door is not rotating about its hinges, despite the force applied. If someone is pedaling a bicycle at a constant speed they are also applying a static torque because they are not accelerating.

Dynamic torque: A dynamic torque is the type of torque that produces an angular acceleration. For Example, the drive shaft in a racing car accelerating from the start line is carrying a dynamic torque because it must be producing an angular acceleration of the wheels given that the car is accelerating along the track.

Measurement of Torque

The unit of torque for measuring the value is Newton–meter (N-m). This equation can be represented as the vector product of force and position vector.

て = r x F

So, this equation is defined as a vector product hence torque also must be a vector.

Introduction to Moment 

The Moment of a force is a type of measure of its tendency to cause a body to rotate about a specific point or axis. This force is different from the tendency for a body to move, or translate, in the direction of the force. For developing a moment, the force must act upon the body in such a manner that the body would begin to twist and this will occur every time a force is applied so that it does not pass through the centroid of the body. A moment basically generates due to a force not having an equal and opposite force directly along its line of action.

Elements of a Moment

In the Elements of a moment, it is described that the magnitude of the moment of a force acting about a point or axis is directly proportional to the distance of the force from the point or axis. So, the Moment is defined as the product of the force (F) and the moment arm (d). The moment arm is the perpendicular distance between the line of action of the force and the center of moments. 

Moment = Force x Distance 

M = (F)(d)

So basically, the turning effect of a force is called the moment. The moment is the result of the force multiplied by the perpendicular distance from the line of action of the force to the pivot or point where the object will turn.

Measurement of Moment 

The SI unit of moment of a force is Newton-meter (Nm) and It is a vector quantity. Moment’s direction is given by the right-hand grip rule perpendicular to the plane of the force and pivot point which is parallel to the axis of rotation.

て=F×d

In this particular moment concept, the moment arm is defined as the distance from the axis of rotation. This perpendicular distance plays an important role. For Example, The lever, pulley, gear, and most other simple machines create mechanical advantage by changing the distance and that is the moment arm.

Torque Formula derivation

て = F × r × sinθ

て = torque

F = linear force

r = distance measured from the axis of rotation to the point where the application of linear force takes place

theta = the angle between F and r

In this particular formula, sin(theta) has no units, r has units of meters (m), and F happens to have units of Newtons (N). 

Combining all these units together, it can be seen that a unit of this force is a Newton-meter (Nm).

The Formula Derived as: The SI unit for torque is newton-meter (N⋅m).

Now to find out the formula or expression.

Rate of change of Angular Momentum in relation to time = \[\frac {\Delta L} {\Delta T}\]

Now,\[\frac {\Delta L} {\Delta T} = \frac {\Delta\lgroup I\omega\rgroup} {\Delta T} = \frac {I.\Delta\omega} {\Delta T}\] ……. (1) 

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

Now \[\frac {\Delta \omega} {\Delta T}\] refers to the rate of change of angular velocity with the time that is angular acceleration (α).

So from equation 4, \[\frac {\Delta L} {\Delta T}\] = I α …………………(2)

I i.e, a moment of inertia, refers to the rotational equivalent of mass(inertia) of linear motion.

Similarly, the angular acceleration α (alpha) refers to the rotational motion equivalent of linear acceleration.

So from equation 5, \[\frac {\Delta L} {\Delta T}\] = τ ……………………. (6) 

This describes the rate of change of angular momentum with time called Torque.

Torque refers to the moment of force. 

Torque (て) = 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 vector and the lever arm vector. ‘x’ certainly denotes the cross product.

て = r F sin θ = r ma sinθ = r m αr sinθ =

𝑚r2.

α sin θ = I α sinθ = I X α ……………………… (4)

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

て = I α (from equation 4)

or, て= \[\frac {I\lgroup \omega2-\omega1\rgroup} {t}\] (here α = angular acceleration = time rate of change of the important angular velocity = \[\frac {\lgroup \omega2-\omega1\rgroup} {t}\] where ω2 and ω1 happen to be the final and initial angular velocities and t is the time gap)

or, て t = I (ω2-ω1) ……………………(5)

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

I (ω2-ω1) = 0

i.e., I ω2=I ω1 ………….. (6)

Difference between Torque and Moment