Whether you walk on the road, slide on a marble, or push a sofa, everything is physics and physical components. Indeed force and momentum are one of the important concepts on which half of the physics laws lean on. But the force and the momentum are different from each other.

**Force vs Momentum**

The difference between force and momentum is that the force is the multiplication of mass of the body and acceleration applied on the body, while Momentum is a multiplication of mass of the body and the velocity. For any stationary object, the force can exist while the momentum of that same stationary object is zero.

The force means the external action of pushing or pulling something that changes the momentum of a body. The formula of force is MA, where M is the mass of the body and A is the acceleration applied. An unbalanced force changes the place of an object while a balanced one doesn’t since it equalises the force of the body too.

The momentum, on the other hand, is the quantitative analysis of motion in the body—momentum changes with the constant acceleration. Also, momentum increases with time for an applied force. The momentum is always zero for any object at rest. Also, the formula for momentum is M=mass*velocity.

**Comparison Table Between Force and Momentum**

Parameters of Comparison | Force | Momentum |

Definition | Force is the external action on the body that either shifts the body or not. | Momentum is the amount of motion in a moving body that instigates the movement. |

Direction | The direction depends upon acceleration. | The direction of momentum depends on velocity. |

Time | The increase in time eventually decreases the force amount if momentum is constant. | The increase in time increases the momentum. |

Contact with objects | It happens when the body comes in contact or not in contact. | It’s a result of an unbalanced force acting on a body. |

Formula | The formula of force is force = mass*acceleration. | The formula of momentum is momentum = mass*velocity. |

**What is Force?**

Force is an external action that changes the motion of the object. Like you push a sofa or push a car from behind, these types of forces that act on a body is a force. With force, an object with some mass can change its velocity that includes the state of being rest. Any push or pull action is a force.

Thus Newton’s law is one of the important concepts in the physics world. It makes more than half of the physics. According to Newton, this law says that the net force applied to the object is equal to the rate at which its momentum changes with time. If mass remains constant, then acceleration is directly proportional to the net force applied.

The formula of force is force= mass*acceleration. It’s to be pushed it pulled so that it overrules the mass of the body to break the object state, which is on rest. Concepts like thrust, which accelerates the velocity, drag, that decreases, torque, pressure, mechanical stress, deformation, flow in fluids, equilibrium, gravitational force, rolling balls on inclined declined or on a plane surface is supported by this Newton’s law.

Force is a vector quantity. It means it will have a magnitude and direction both. Since acceleration is a vector quantity and mass is constant, it makes the force a vector quantity. Like if you have to push a table, you will accelerate according to the direction. And if you’re pulling, you will have to go in a negative direction.

**What is Momentum?**

According to Newtonian mechanics, momentum or describing linear momentum, translational momentum or simply momentum is the multiplication of mass with velocity. Since velocity is a vector quantity and mass is a constant body, it makes momentum to be a vector quantity as well.

The formula of momentum is Momentum = mass * velocity. Newton’s 2nd law states that the body’s momentum is equal to the force applied to it. It depends upon the frame of reference. Momentum is conserved in special relativity and, in modified formation, in the case of electrodynamics, quantum mechanics general relativity, and quantum field theory.

Suppose you are playing pool. When you hit the cue ball to destroy the formation of those stripes and solids, it happens when the cue ball transfers its energy to those coloured balls—the momentum changes from zero to some value. Similarly, the momentum is only visible when the velocity is more than the mass to break its inertia.

Formulas like Lagrangian, Hamiltonian mechanics allows one to choose a coordinate system that has symmetries and constraints. Here the general Momentum is a conserved quantity. Well, momentum is an important concept in the field of physics. Indeed it either supports many other important formulas.

**Main Differences Between Force and Momentum**

- The direction of the force depends on the acceleration of the body, while the direction of momentum depends on the velocity.
- The increase in time decreases the amount of force, whereas the increase in time increases the momentum.
- A force can exist on a stationary object, while a Momentum is zero for a stationary object.
- Force can be a result of when objects come in contact and even without coming in contact, while Momentum always an unbalanced force acting.
- The formula for force is force= mass* acceleration, while the formula for momentum is momentum= mass*velocity.

**Conclusion**

Isaac Newton was one of the greatest scientists who changed the working of world. No doubt a brilliant and a genius mind had contributed to such a great extent in physics. His concepts, his formulas have been in such wide use.

The concept of force and momentum makes many portions of the physics and derived various important formulas. From gravitational formulas to thrust and pressure, force and momentum plays a vital role and lays the very, but this slight difference in quantities makes them different from each other.

**References**

- https://books.google.com/books?hl=en&lr=&id=KemaBQAAQBAJ&oi=fnd&pg=PR7&dq=force&ots=EiyKMBPuS3&sig=VBFZhw0ZxIf_Y82FPO0JO4OpDyc
- https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1540-6261.1996.tb05222.x

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