Key Equations
Newton's Laws & Momentum — AQA A-Level Physics
On Data Sheet
Not on Data Sheet
Newton's second law
$$F = ma$$
- Where:
- $F$ = resultant force (N)
- $m$ = mass (kg)
- $a$ = acceleration (m s⁻²)
Only valid for constant mass. Acceleration is in the same direction as the resultant force.
Momentum
$$p = mv$$
- Where:
- $p$ = momentum (kg m s⁻¹)
- $m$ = mass (kg)
- $v$ = velocity (m s⁻¹)
Vector quantity. Direction same as velocity.
Newton's second law (momentum form)
$$F = \frac{\Delta p}{\Delta t}$$
- Where:
- $F$ = resultant force (N)
- $Δp$ = change in momentum (kg m s⁻¹)
- $Δt$ = time interval (s)
More general form. Equivalent to F = ma when mass is constant.
Conservation of momentum (two objects)
$$m_A u_A + m_B u_B = m_A v_A + m_B v_B$$
- Where:
- $m_A, m_B$ = masses of objects A and B (kg)
- $u_A, u_B$ = initial velocities (m s⁻¹)
- $v_A, v_B$ = final velocities (m s⁻¹)
Valid only in closed systems with no external resultant force.
Kinetic energy
$$E_k = \frac{1}{2}mv^2$$
- Where:
- $E_k$ = kinetic energy (J)
- $m$ = mass (kg)
- $v$ = speed (m s⁻¹)
Used to test whether a collision is elastic (KE conserved) or inelastic (KE not conserved).
Impulse
$$\begin{aligned}
F \Delta t &= \Delta p \\
&= mv - mu
\end{aligned}$$
- Where:
- $F$ = resultant force (N)
- $Δt$ = time interval (s)
- $Δp$ = change in momentum (kg m s⁻¹)
- $m$ = mass (kg)
- $v$ = final velocity (m s⁻¹)
- $u$ = initial velocity (m s⁻¹)
Impulse has units N s, equivalent to kg m s^-1.