# What is the formula for momentum in physics?

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bandmanjoe | Middle School Teacher | (Level 2) Senior Educator

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In classical physics, momentum is the product of an object's mass times it's velocity, so the formula would be written like this:

p = m x v, or momentum = mass times velocity.

Momentum is a characteristic that can be applied lots of different ways, but in physics, an object that has a larger mass and a velocity constant will produce more momentum.  Or, you can increase the other quantity, and increase the velocity to produce a larger momentum.   Momentum is closely associated with inertia, the tendency of objects to resist changes in motion.  An object with a larger mass tends to have a larger inertia, a larger tendency to resist changes in motion, whether it is moving, or sitting still.  So objects with mass and velocity create a certain amount of momentum while they are moving, and that momentum is directly related to how much mass there is and how fast that mass is moving.

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chandrachaks | Elementary School Teacher | (Level 1) Adjunct Educator

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Momentum can be defined as "mass in motion." All objects have mass; so if an object is moving, then it has momentum - it has its mass in motion.

Momentum depends upon two variables mass and velocity. In terms of an equation, the momentum of an object is equal to the mass of the object times the velocity of the object.

momentum = mass * velocity

In physics, the symbol for the quantity momentum is the lower case p. Thus, the above equation can be rewritten as

p=mv

where m is the mass and v is the velocity. The equation illustrates that momentum is directly proportional to an object's mass and directly proportional to the object's velocity.

momentum is also a conserved quantity, meaning that if a closed system is not affected by external forces, its total linear momentum cannot change.

The momentum of any object that is at rest is 0. Objects at rest do not have momentum - they do not have any "mass in motion." Both variables - mass and velocity - are important in comparing the momentum of two objects.

let us understand the concept with the help of an example:

Consider a 0.5-kg physics cart loaded with one 0.5-kg brick,  moving with a speed of 2.0 m/s. The total mass of loaded cart is 1.0 kg and its momentum is 2.0 kg•m/s. If the cart was instead loaded with three 0.5-kg bricks, then the total mass of the loaded cart would be 2.0 kg and its momentum would be 4.0 kg•m/s. A doubling of the mass results in a doubling of the momentum.

Similarly, if the 2.0-kg cart had a velocity of 8.0 m/s (instead of 2.0 m/s), then the cart would have a momentum of 16.0 kg•m/s (instead of 4.0 kg•m/s). A quadrupling in velocity results in a quadrupling of the momentum.

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