Short on time? This page is the recap. For diagrams, derivations and worked examples, use the full study guide. This is the algebra-based course: no calculus is needed.
Recap
- Unbalanced forces: the net force on the system is not zero. The system’s velocity then changes.
- Newton’s second law: the centre-of-mass acceleration has size proportional to the net external force and points the same way.
- Only external forces count. Internal forces come in third-law pairs and cancel, so they cannot change the centre-of-mass velocity.
- Forces can balance along one axis and not along another. Velocity changes only along the unbalanced axis.
- Choose the system first. The whole system gives the acceleration; a single part gives an internal force such as a tension.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| a = ΣF / m | a in m/s², ΣF in N, m in kg | find acceleration from forces |
| ΣF_x = m a_x, ΣF_y = m a_y | signs from your axes | apply the law along each axis |
| 1 N = 1 kg·m/s² | check units | |
| a ∝ ΣF (fixed m) | predict factor-of-change | |
| a ∝ 1/m (fixed ΣF) | predict factor-of-change | |
| slope of a–ΣF graph = 1/m | kg⁻¹ | measure a mass from data |
Assumptions behind the numbers
- The frame of reference is inertial (not accelerating) unless stated.
- Strings are light and do not stretch; pulleys are light and frictionless. Then the tension is the same all along a string, and joined objects share the same size of acceleration.
- Near Earth’s surface, F_g = mg with g = 9.8 m/s² (10 m/s² where stated).
- Air resistance is negligible unless stated.
Mistakes to avoid
- Using one force instead of the net force. Add every external force with signs first.
- Drawing ma on the free-body diagram. It is not a force.
- Assuming acceleration is along the velocity. It is along the net force.
- Counting internal forces. For a whole system, string tensions between its parts cancel.
- Setting tension equal to the hanging weight when the hanging object accelerates.
- Using weight in newtons as the mass. m goes in kg.
Quick self-check
- A net force of 15 N acts on a 3.0 kg block. What is its acceleration? (5.0 m/s², in the direction of the net force)
- The same net force acts on a block with three times the mass. By what factor does the acceleration change? (It becomes one third.)
- A 1200 kg car accelerates at 2.5 m/s². What net force acts on it? (3.0 × 10³ N, forward)
Next: practice questions.