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So this is more of a clarifying question. A lot of online definitions state that momentum is a measure of how hard it is to stop or swerve an object, which makes sense. However, the formula for momentum is mass times velocity, and I'm just wondering how the individual components (mass and velocity, that is) make the object harder to stop. Also, are objects with more mass harder to stop because they have more inertia, or is there another reason? Thanks.

Qmechanic
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user386598
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3 Answers3

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A force induces a change in momentum. Because momentum is mass multiplied by velocity, that basically means that the faster an object is, or the more mass it has, then the larger the momentum and then the more force you will need to slow it down a given amount. Or, alternatively, use the same force for a longer time.

Pato Galmarini
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I think a better description for momentum is, how much "oomph" an object has.

A non moving object clearly has zero oomph.

A heavier(faster) object has more important than a lighter(slower) one. This is all reflected on the formula $\vec p=m \vec v$.

To change how much oomph an object has, a force is required. $\vec F= \frac{\mathrm{d}}{\mathrm{d}t}\vec p=m \vec a$.

Since velocity is a vector quantity, it has a magnitude and a direction. To stop an object, you decrease the magnitude. The force required is proportional to the mass of the object and the change in magnitude, as can be seen from the formula.

To deflect an object, your change the direction. Same as above, the required force is proportional to the mass and change in velocity direction.

infinitezero
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Momentum is a measure of the "quantity" of motion there is in a system. It is oriented and proportional to velocity (obviously!). It is also proportional to the amount of matter in motion, i.e mass. So by definition, momentum is simply mass times velocity: $$\vec{p} = m \vec{v}. $$ By inertia (Newton's first law), a body tries hard to keep its momentum constant. You need a force to change the "amount of motion". So by definition, the total force applied on the moving body is the rate of change of the momentum: $$ \vec{F}_{tot} = \frac{d\vec{p}}{dt}. $$ So stoping a massive body in fast motion will be "hard" since its "momentum" is large. You'll need to apply a strong force to change its velocity and stop it.