11Gmomentum


 * Momentum**


 * Momentum is the property which makes a moving object difficult to stop or make change direction.

so
 * Momentum (vector) = mass × velocity (vector)
 * {We use __p__ for momentum}
 * __p__ = m__v__


 * An elephant walking has a lot of momentum because of its large mass.
 * A bullet shot out of a gun has a lot of momentum because of its high velocity.
 * A bullet travelling at walking speed would only have a very small amount of momentum and be very easy to stop.
 * The momentum of an elephant fired out of a gun would be astonishingly large and very hard to stop.


 * Change in Momentum = Mass x (Change in Velocity)

math \\ . \qquad \Delta \underline{p} = m \times \Delta \underline{v} \\. \\ . \qquad \Delta \underline{p} = m \times \Big( v - u \Big) \\. \\ . \qquad \Delta \underline{p} = m\underline{v} - m\underline{u} math

**Example** A car with mass 900kg is being towed at 12 m/s. Find the momentum.

math . \qquad p = 900 \times 12 = 10,800 \; \; \text{kg.m/s} math

b) If the car then slows to 10 m/s, Find the new momentum

math . \qquad p=900 \times 10 = 9,000 \; \; \text{kg.m/s} math

c) Find the change in momentum

math . \qquad \Delta p = 9,000-10,800=-1,800 \; \; \text{kg.m/s} math

**Newton's 2nd Law and Momentum**

Isaac Newton actually stated his 2nd Law as:
 * Resultant Force is proportional to the rate of change of momentum.

using notation, this becomes: math . \qquad \underline{R} \propto \dfrac{d\underline{p}}{dt} math OR math . \qquad \underline{R} = k\dfrac{d\underline{p}}{dt} math

Provided we use standard units (Newtons, kg, m, s) the constant of proportionality, k, is 1, so: math . \qquad \underline{R} = \dfrac{d\underline{p}}{dt} math

But __p__ = m__v__ math . \qquad \underline{R} = \dfrac{d(m\underline{v})}{dt} \qquad \text{but m is constant, so:} math . math . \qquad \underline{R} = m \dfrac{d\underline{v}}{dt} math and dv/dt is acceleration, so we get the more familiar version of Newton's 2nd Law:
 * __R__ = m__a__