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Prerequisite Materials:

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Newton's Three Laws of Motion.

Newton's 1^st Law

Every body continues at constant velocity, unless acted upon by an external force.

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Newton's 2^nd Law $$\mathbf{F}=\frac{d\mathbf{p}}{dt}$$

The change of momentum of an object is proportional to the force impressed and is made in the direction of the straight line in which the force is impressed. If the mass is constant, then $\mathbf{F}=m\mathbf{a}$

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Newton's 3^rd Law

To every action there is always opposed an equal reaction; or the mutual actions of two bodies upon each other are always equal and directed to contrary parts.

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Further reading:

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Momentum

Momentum is a physical quality of moving objects defined thus:

$\text{momentum}=\text{mass}\times \text{velocity}$

or

$$p=mv$$

• where
• $p$ is the momentum of the object, $\mathit{kg}m{s}^{-1}$ [or $Ns$];
• $m$ is the mass of the object, $\mathit{kg}$;
• and
• $v$ is the velocity on the object, $m{s}^{-1}$

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The Rearrangements:

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Questions and other materials:

Momentum Revision
(Care of mmerevise.co.uk)

Exam Questions
(Care of www.savemyexams.com)

Questions
(Care of www.cyberphysics.co.uk)

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Conservation of momentum

When two objects interact the force between them are given by Newton's third law

$$F_1=-F_2$$

These forces are proportional to the rate of change of momentum

$$\frac{\Delta p_1}{\Delta t}=-\frac{\Delta p_2}{\Delta t}$$

As the contact time for both objects is the same then this simplifies to

$$\phantom{\text{\hspace{1em}\hspace{1em}[1]}}\Delta p_1=-\Delta p_2\text{\hspace{1em}\hspace{1em}[1]}$$

The change in momentum is given by

$$\Delta p=mv-mu$$

So [1] becomes

$$m_1{v}_1-m_1{u}_1=-(m_2{v}_2-m_2{u}_2)$$

$$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$$

That is, the momentum before is equal to the momentum after the collision. This is the conservation of momentum.

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Other Sources and Questions

Exam Questions
(care of www.savemyexams.com)

Practice Problems with Conservation of Momentum [with Ans]
(care of www.mrstapleton.com)

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Friction

$$\text{force}=\text{coefficient of friction}\text{normal reaction force}$$

$$f=\mu R$$

• where
• $f$ is the frictional force, in newtons, $N$;
• $\mu$ is the coefficient of friction, unitless or dimensionless;
• and
• $R$ is the normal reaction force, in newtons, $N$.

Exam Questions
(Care of www.examsolutions.net)

Questions
(Care of savemyexams.com)

Revision
(Care of mmerevise.co.uk)

... search for more ...
(Care of duckduckgo.com)

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Resultant Force

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