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Momentum & Impulse

01Momentum & Impulse

Momentum

This section covers linear momentum as the product of mass and velocity, including its vector nature and units.

Mass in motion

Momentum is the product of an object's mass and velocity:

p=mvp=mv

where pp is momentum, mm is mass and vv is velocity.

The SI unit of momentum is:

kg m s−1\text{kg m s}^{-1}

Momentum is a vector quantity. Its direction is the same as the object's velocity, so a sign convention must be used in one-dimensional calculations.

v>0;p>0positive directionv<0;p<0motion reversed

If motion to the right is chosen as positive, an object moving to the right has positive velocity and positive momentum.

If the same object reverses direction, its velocity becomes negative and its momentum is also negative.

The choice of positive direction is arbitrary, but it must be used consistently throughout a calculation.

Worked example: A 60 g60\,\text{g} tennis ball moves at 75 m s−175\,\text{m s}^{-1}. A 3.0 kg3.0\,\text{kg} object moves in the same direction at 1.5 m s−11.5\,\text{m s}^{-1}. Compare their momenta.

For the ball:

p=(0.060)(75)=4.5 kg m s−1p=(0.060)(75)=4.5\,\text{kg m s}^{-1}

For the larger object:

p=(3.0)(1.5)=4.5 kg m s−1p=(3.0)(1.5)=4.5\,\text{kg m s}^{-1}

They have the same momentum even though their masses and speeds are very different.

Exam Tip: Convert mass to kilograms before using p=mvp=mv, and include the sign of the velocity when direction matters.

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