The scientific definition of linear momentum is consistent with most people’s intuitive understanding of momentum: a large, fast-moving object has greater momentum than a smaller, slower object. Linear momentum is defined as the product of a system’s mass multiplied by its velocity. In symbols, linear momentum is expressed as

Momentum is directly proportional to the object’s mass and also its velocity. Thus the greater an object’s mass or the greater its velocity, the greater its momentum. Momentum

**Linear Momentum: **

Linear momentum is defined as the product of a system’s mass multiplied by its velocity:

### Example 1: **Calculating Momentum: A Football Player and a Football**

(a) Calculate the momentum of a 110-kg football player running at 8.00 m/s. (b) Compare the player’s momentum with the momentum of a hard-thrown 0.410-kg football that has a speed of 25.0 m/s.

*Strategy*

No information is given regarding direction, and so we can calculate only the magnitude of the momentum,

when only magnitudes are considered.

*Solution for (a)*

To determine the momentum of the player, substitute the known values for the player’s mass and speed into the equation.

*Solution for (b)*

To determine the momentum of the ball, substitute the known values for the ball’s mass and speed into the equation.

The ratio of the player’s momentum to that of the ball is

*Discussion*

Although the ball has greater velocity, the player has a much greater mass. Thus the momentum of the player is much greater than the momentum of the football, as you might guess. As a result, the player’s motion is only slightly affected if he catches the ball. We shall quantify what happens in such collisions in terms of momentum in later sections.

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