Newton's Laws & Momentum

Newton's laws, conservation of momentum, impulse, and elastic and inelastic collisions.

Spec Points Covered
  • I can state Newton's three laws of motion and apply each to physical situations.
  • I can define linear momentumThe product of an object's mass and its velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.. A vector quantityA quantity that has both magnitude and direction.. Measured in kg m s⁻¹. and calculate it for objects in one dimension.
  • I can apply $F = ma$ to problems involving resultant force and accelerationThe rate of change of velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.. A vector quantity. Measured in m s⁻²..
  • I can express Newton's second law in terms of momentum: $F = \Delta p / \Delta t$.
  • I can define impulseThe product of force and the time for which it acts. Equal to the change in momentum. and relate it to the change in momentum and the area under a force-time graph.
  • I can state and apply the principle of conservation of linear momentumThe product of an object's mass and its velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.. A vector quantityA quantity that has both magnitude and direction.. Measured in kg m s⁻¹..
  • I can distinguish between elastic and inelastic collisions by comparing kinetic energyThe capacity to do work. Measured in joules (J).The energyThe capacity to do work. Measured in joules (J). an object possesses due to its motion. before and after.
  • I can solve collision and explosion problems in one dimension, including recoil.
  • I can explain how safety features (crumple zones, airbags, seatbelts) use impulseThe product of force and the time for which it acts. Equal to the change in momentum. to reduce force.
Notes
01 Newton's First Law Newton's First Law → 02 Linear momentum Linear momentum → 03 This is the full (general) form of Newton's second law $F = \frac{\Delta p}{\Delta t}$ → 04 Impulse Impulse → 05 Conservation of momentum Conservation of momentum → 06 Elastic collision Elastic collision → 07 In an explosion $0 = m_1 v_1 + m_2 v_2$ → 08 Crumple zones →
Σ Key Equations Full Reference →
On Data Sheet
Not on Data Sheet
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.
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.
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). NOT on the data sheet -- must derive from F = ma and p = mv.
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.
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.
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.