## Definition of Linear Momentum

The definition of linear momentum follows the formulation of impulse presented before, . In this expression an impulse changes the velocity multiplied by the mass of the object from where the definition of momentum is extended, .

 That is, the linear momentum of an object with respect to a frame of reference is the product of the mass of the object times the velocity of the object in the frame of reference. From this definition, the linear momentum of the object depends on the frame of reference where the velocity is measured. Also, it should be noticed that the linear momentum of distinct objects moving at the same velocity can be different because of their masses; for example, a truck and a car moving at the speed limit in the highway have different linear momentum. In addition, linear momentum is a vector quantity; thus, the direction of motion of an object is important when establishing its linear momentum.

Also, it should be noticed that because masses are always positive, the direction of the vector velocity and that of the vector linear momentum are the same. In the MKS unit system, there is not a special name for the unit of linear momentum, the units associated to this quantity are the unit of mass times the unit of velocity .

 As an illustration of the vector nature of linear momentum, the two identical trucks (respect to their masses) shown at the left drawing are moving at the same speed, let us say 60 mph, but the blue truck is moving due West (or left) while the red truck is moving toward East (or right). For both trucks the magnitude of theirs linear momentum are the same. However, following the convention established before about the sign of vectors, the direction of motion of the blue truck is specified by assigning to its linear momentum a negative sign while for the red truck the direction of motion is specified by indicating that its linear momentum is positive. Of course, for objects moving in two or three dimension, the vector nature of their linear momenta is described using the rigorous analysis of vectors presented before.

Therefore, in general for the three dimensional case and for the two dimensional case.

 Show Linear Momentum The animation on the left shows a basketball through toward a rigid wall. For the purpose of this animation, it is assumed that there is not gravity affecting the motion of the ball. Thus, the ball will move horizontally in a straight line. The collision with the wall is such that the basketball does not change at all its speed. Can you calculate the change in linear momentum under the previous conditions?

 1) Question a) 0 Kg m/s N b) –3.6 Kg m/s c) –1.8 Kg m/s d) 1.8 Kg m/s e) None of the above.

### Relation between Linear Momentum and Impulse

Since the impulse is and the linear momentum is , the following relation between the impulse and the linear momentum can be established,

Thus, the later relation indicates that an impulse given to an object results in a change of the linear momentum of the object. Conversely, if an object changes its linear momentum, it is because an impulse has acted on the object.

The Impulse on an object is equal to the change in Linear Momentum of the object.

The following question is a direct application of the previous formula.

 1) Question a) 36 N b) 5.9 N c) –18 N N d) –36 N e) None of the above.

 by Luis F. Sáez, Ph. D. Comments and Suggestions: LSaez@dallaswinwin.com
 by Luis F. Sáez, Ph. D. Comments and Suggestions: LSaez@dallaswinwin.com