** Moment vs Momentum **

Moments and momentum are concepts found in physics. Momentum is a defined physical property while moment is a broad concept applied in many cases to obtain a measure of the effect of a physical property around an axis and its distribution around the axis.

**Moment**

Moments generally refers to a measure of the effect of some physical quantity around an axis. This measure is computed by the product of the physical quantity and the perpendicular distance from the axis. Moment of force, moment of inertia, and polar moment of inertia are examples found in mechanics for the application of this concept. This concept is further extended to the fields such as statistical theory, where moments of random variables are discussed.

If not specified, moment generally refers to the moment of a force, which is a measure of the turning effect of a force. Moment of force is measured in Newton meters (N_{m}) in the SI system, which looks similar to the unit of mechanical work but carries a completely different meaning.

When a force is applied it creates a turning effect about a point other than on the line of action of the force. The amount of this effect or the moment is directly proportional to the magnitude of the force and the perpendicular distance to the force from the point.

*Moment of a force=Force × Perpendicular distance from the point to force*

**Moment τ = F × x**

If a force system has no resultant moments, i.e. ∑τ = 0 , the system is in * rotational equilibrium*. When the moment of a force has a physical sense it is often called “

**”.**

*torque** Moment of inertia* is a measure of the distribution of mass of a body around an axis. It is computed by the sum of the products of mass at each point and the distance to that point from the axis.

If m_{i} is the mass at point i and r_{i} is the distance to that point from the axis concerned, the moment of inertia is given by,

*Discrete point mass system I = ∑m _{i}*

*For a rigid body I = ∫m _{i} r_{i}^{2} *

It is an important factor when considering the rotational motion of the physical systems.

The concept of moment is applied in many instances of physics, especially in mechanics, but in all the cases it determines the effect of some physical property around an axis at a distance.

*• Electric dipole moment is a measurement of the charge difference and direction between two or more charges.*

*• Magnetic moment is a measure of the strength of a magnetic source.*

*• Moment of inertia is a measure of an object’s resistance to changes in its rotation rate.*

*• Torque or moment is the tendency of a force to rotate an object about an axis.*

*• *Bending moment is a moment that results in the bending of a structural element.

*• *First moment of area is a property of an object related to its resistance to shear stress.

*• *Second moment of area is a property of an object related to its resistance to bending and deflection.

*• *Polar moment of inertia is a property of an object related to its resistance to torsion

*• *Image moment is a statistical property of an image.

*• *Seismic moment is quantity used to measure the size of an earthquake.

**Momentum**

Momentum (Linear momentum) is defined as the product of mass and velocity. It is one of the most important physical quantities of a system, and it is a conserved property in the universe, both at microscopic and macroscopic levels.

**Momentum = mass × velocity ↔ P = mv**

Mass is a scalar and velocity is a vector. The product of a vector and a scalar is a vector. Therefore, momentum is a vector quantity and has a magnitude and a direction.

The momentum is directly related to the state of motion of a particle, a body, or a system and often used to describe the changes in the physical systems. Momentum is used in following key physical concepts;

**Universal Law of Conservation of Momentum:**

If unbalanced external forces are not acting on a system, the total momentum of the system is a constant.

*If ∑F _{external,system} = 0, then ∑mv_{system} = constant ↔ ∆mv_{system }= 0*

**Newton’s Second Law:**

Resultant force acting on a body is proportional to the rate of change of momentum of the body, and it is in the direction of the change of momentum.

*F _{resultant }∝ dmv/dt ≈ ∆mv/∆t*

And from the definition of the impulse (I)

*I = F∆t = ∆mv*

The moment of linear momentum around an axis is defined as the angular momentum. It can be shown that angular momentum is equal to the product of the angular velocity and the moment of inertia of the body/system around the considered axis.

*Angular momentum = ∑mv _{i} r_{i}^{2} = Iω*

**What is the difference between Moment and Momentum?**

• Momentum is the product of mass and the velocity of a body. Moment is a concept that gives a measure of the effect of a physical property around an axis. It also gives a measure of the distribution.

• Momentum is a vector while moments can be either vector or scalar.

• Momentum is a conserved property in the universe, and independent of the frame of reference. Moments are dependent on the axis considered.

• Moment of linear momentum around an axis is the angular momentum about that axis.