recall F = ma and solve problems using it, understanding that acceleration and resultant force are always in the same direction

Momentum & Newton’s Laws of Motion

What You’ll Learn

Recall the key equation \$F = ma\$ and solve problems using it. Understand that acceleration and the resultant force are always in the same direction. 🚀

Newton’s Three Laws (Quick Recap)

  1. First Law (Inertia): An object stays at rest or moves in a straight line unless acted on by an external force. 🛑

  2. Second Law (Force & Acceleration): The net force on an object is equal to its mass times its acceleration.
    \$F_{\text{net}} = ma\$ ⚡️

  3. Third Law (Action & Reaction): For every action, there is an equal and opposite reaction. 🤝

Momentum: The “Carry‑On” of Motion

Momentum \$p\$ is the product of mass and velocity:

\$p = mv\$

Think of a soccer ball: the heavier it is or the faster it rolls, the more “push” it has to change its motion. ⚽️

The Core Equation: \$F = ma\$

When a net force acts on an object, it changes the object’s momentum. The change in momentum per unit time equals the net force.

\$F_{\text{net}} = \frac{dp}{dt} = ma\$

Direction Note: The direction of acceleration is always the same as the direction of the net force. If you push a car to the right, it accelerates to the right. 🏎️

Exam Tip

When solving for acceleration, always write the equation as \$a = \dfrac{F_{\text{net}}}{m}\$ and check the sign (positive = same direction as the force).

Example Problem 1: Pushing a Box

A 10 kg box is pushed with a horizontal force of 50 N. What is its acceleration?

StepCalculation
Given\$m = 10\,\text{kg}\$, \$F_{\text{net}} = 50\,\text{N}\$
Formula\$a = \dfrac{F_{\text{net}}}{m}\$
Result\$a = \dfrac{50}{10} = 5\,\text{m/s}^2\$

Exam Tip

Always state the units of force (N) and mass (kg) before calculating. Check that the acceleration unit comes out as m/s².

Example Problem 2: Direction Check

A 5 kg toy car is pulled to the left with a force of 20 N. What is its acceleration and direction?

Since the force is to the left, the acceleration will also be to the left.

\$a = \dfrac{20\,\text{N}}{5\,\text{kg}} = 4\,\text{m/s}^2 \text{ (to the left)}\$

Exam Tip

When the problem states a direction (left/right/up/down), keep that direction in mind when writing the final answer. Use arrows or words to clarify.

Momentum Conservation (Quick Peek)

If no external forces act, the total momentum of a system stays constant. Think of two ice skaters pushing off each other: they move in opposite directions with equal and opposite momenta.

Exam Tip

When a problem involves collisions, check if the system is isolated (no external forces). If yes, use the conservation of momentum: \$m1v1 + m2v2 = m1v'1 + m2v'2\$.

Key Takeaways

  • Remember \$F = ma\$ and that acceleration is in the direction of the net force.

  • Use the formula \$a = \dfrac{F_{\text{net}}}{m}\$ to solve for acceleration.

  • Check units: N for force, kg for mass, m/s² for acceleration.

  • When directions are involved, explicitly state them in your answer.

  • For collisions, think about whether the system is isolated to apply momentum conservation.

Final Exam Tip

Read the question carefully, identify all forces, sum them vectorially, then apply \$F = ma\$. Write every step clearly; examiners love tidy work! ??