Key Equations
Newton's Laws & Momentum - OCR A-Level Physics
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Newton's second law
$$F = ma$$
- Where:
- $F$ = N
- $m$ = kg
- $a$ = m \(s^{-2}\)
F is the resultant force. Special case of F = dp/dt for constant mass.
Impulse
$$\begin{aligned}
F\Delta t &= \Delta p \\
&= mv - mu
\end{aligned}$$
- Where:
- $F\Delta t$ = N s
- $\Delta p$ = kg m \(s^{-1}\)
Impulse equals the area under a force-time graph. Used to explain safety features: longer contact time means smaller force.
Linear momentum
$$p = mv$$
- Where:
- $p$ = kg m \(s^{-1}\) (or N s)
- $m$ = kg
- $v$ = m \(s^{-1}\)
Momentum is a vector. Assign positive/negative signs for direction.
Conservation of momentum (two-body)
$$m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$$
- Where:
- $m$ = kg
- $u, v$ = m \(s^{-1}\)
Applies to all collisions and explosions in a closed system. For objects that stick together: (m_1 + m_2)v = m_1 u_1 + m_2 u_2.
Newton's second law (momentum form)
$$F = \frac{\Delta p}{\Delta t}$$
- Where:
- $F$ = N
- $\Delta p$ = kg m \(s^{-1}\)
- $\Delta t$ = s
The full form of Newton's second law. Needed when mass changes (rockets, conveyor belts).
Kinetic energy
$$E_k = \frac{1}{2}mv^{2}$$
- Where:
- $E_k$ = J
- $m$ = kg
- $v$ = m \(s^{-1}\)
Used to determine whether a collision is elastic (KE conserved) or inelastic (KE not conserved). Momentum is always conserved regardless.