Newton's Laws & Momentum

Newton's three laws of motion, linear momentum, conservation of momentum, impulse, elastic and inelastic collisions, and safety applications.

Spec Points Covered
  • State Newton's three laws of motion and apply them to real-world situations.
  • Apply $F = ma$ to calculate resultant force, mass or 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..
  • Express Newton's second law in terms of rate of change of momentum.
  • Define momentum and apply conservation of momentumIn a closed system (no external forces), the total momentum before an event equals the total momentum after. to collisions and explosions.
  • Define impulseThe product of force and the time for which it acts. Equal to the change in momentum. and calculate it from force-time data.
  • Distinguish between elastic and inelastic collisions using 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..
  • Explain how vehicle safety features use impulseThe product of force and the time for which it acts. Equal to the change in momentum. to reduce injury.
Notes
01 Newton's first law: no resultant force means no change in motion Newton's first law 3.4.1.5 → 02 Newton's second law: F = ma relates resultant force to acceleration Newton's second law 3.4.1.5 → 03 Newton's second law in terms of momentum: F = rate of change of momentum $F = \frac{\Delta p}{\Delta t}$ 3.4.1.5 → 04 Newton's third law: forces arise in equal and opposite pairs on different objects Newton's third law 3.4.1.5 → 05 Momentum is the product of mass and velocity Linear momentum 3.4.1.6 → 06 Total momentum is conserved in all collisions when no external force acts Conservation of momentum 3.4.1.6 → 07 Impulse equals the change in momentum Impulse 3.4.1.6 → 08 Elastic collisions conserve kinetic energy; inelastic collisions do not Elastic collision 3.4.1.6 → 09 Safety features reduce injury by increasing the time over which momentum changes 3.4.1.6 →
Σ Key Equations Full Reference →
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.
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.
Momentum
$$p = mv$$
  • Where:
    • $p$ = momentum (kg m s⁻¹)
    • $m$ = mass (kg)
    • $v$ = velocity (m s⁻¹)
Vector quantity. Direction same as velocity.
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.
Q Retrieval Practice All 12 Questions →
Q1. State Newton's first lawAn object remains at rest or moves with constant velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹. unless acted on by a resultant force. of motion.
An object remains at rest or moves with constant velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹. unless acted on by a resultant force.
Q2. State Newton's second lawThe resultant force on an object is equal to its rate of change of momentum. For constant mass, F = ma. in two forms.
  • F = ma (force equals mass times accelerationThe rate of change of velocity. A vector quantity. Measured in m s⁻².).
  • F = delta-p / delta-t (force equals rate of change of momentum).
Q3. State Newton's third lawWhen two objects interact, the forces they exert on each other are equal in magnitude, opposite in direction, and act on different objects. of motion.
If object A exerts a force on object B, then object B exerts an equal and opposite force on object A.
Q4. What four conditions must a Newton's third lawWhen two objects interact, the forces they exert on each other are equal in magnitude, opposite in direction, and act on different objects. pair satisfy?
Same type of force, same magnitude, opposite direction, acting on different objects.
Q5. Define momentum and state its unit.
  • Momentum = mass times velocity.
  • Unit: kg m s^-1.