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Momentum Simplified Revision Notes

Revision notes with simplified explanations to understand Momentum quickly and effectively.

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Momentum

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Momentum: All moving objects have momentum. If an object is not moving, the momentum is zero.

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Formula

p=m×vp = m \times vMomentum(kgm/s)=mass(kg)×velocity(m/s)Momentum (kg m/s) = mass (kg) × velocity (m/s)

Where pp is the momentum in kilograms meters per second kgms1kgms^-1, mm is the mass in kilograms (kg), and (v v) is the velocity in meters per second ms1ms^-1.

Conservation of Momentum

  • In a closed system, the total momentum before an event is equal to the total momentum after an event.
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Example: The backwards momentum of a cannon is equal to the forward momentum of the cannonball.

  • Momentum is always conserved in a collision or explosion (where there are no external forces like friction, air resistance, electrostatic attraction, etc.).
  • In collisions: total momentum before=total momentum after\text{total momentum before} = \text{total momentum after}
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Example: Two marbles colliding; each will have momentum before and after the collision.

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Remember, momentum is a vector.

Changes in Momentum (Physics Only)

Newton's Second Law

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Force is equal to the rate of change of momentum.

Force=change in momentumtime F=(mvmu)t\text{Force} = \frac{\text{change in momentum}}{\text{time}}\ F = \frac{(mv - mu)}{t}

Where FF is the force, mvmv is the final momentum, mumu is the initial momentum, and tt is the time.

Conservation of Momentum

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In a closed system, the total momentum before an event is equal to the total momentum after the event. This principle is known as the conservation of momentum.

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Example:

Consider two footballs with the same mass, mm. One football is stationary, while the other is moving at a velocity of vv.

The momentum before they collide is just the sum of the momentum of each ball:

total momentum before = (m×v)+(m×0)(m×v)+(m×0)

Total momentum before = mv mv

So the total momentum before the collision is just the momentum of the moving ball because the other ball is not moving and so has no momentum.

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After the collision, the total momentum remains mv.mv. Ball B, which was initially stationary, now has velocity and momentum, while ball A moves with a reduced velocity. The sum of these two momentums after the collision will still equal the total momentum before the collision, mv.mv.

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