Newton’s Laws of Motion: MDCAT Physics notes
Newton’s Laws of Motion notes for MDCAT: inertia, mass as a measure of inertia, F = ma, apparent weight in lifts, rope-sliding problems and key traps.
First law: the law of inertia
A body at rest stays at rest, and a body in uniform motion keeps moving with constant velocity, unless an unbalanced (net) external force acts on it. The first law is therefore called the law of inertia.
Inertia is the natural tendency of a body to keep its state of rest or uniform motion. Mass is the quantitative measure of inertia: the more massive a body, the harder it is to change its velocity.
- When a stationary bus starts suddenly, a standing passenger falls backward: the feet move with the bus, the upper body stays at rest (inertia of rest).
- When a moving bus brakes, passengers lurch forward. In the bus frame this feels like a pseudo (fictitious) force pushing forward; really, the body is just continuing its motion.
Second law
The acceleration of a body is directly proportional to the net force and inversely proportional to its mass, in the direction of the net force:
$$\vec F_{net} = m\vec a$$
If several forces act but they balance, the net force is zero and the body does not accelerate (it may still move at constant velocity). So a body can have many forces on it and still have zero acceleration.
Third law
To every action there is an equal and opposite reaction, acting on a different body. All three laws are about force: the first defines it qualitatively, the second measures it, the third says forces come in pairs.
Apparent weight in a lift
A scale reads the normal (contact) force $R$, which is what you feel as your weight.
| Lift motion | Scale reading | Feels |
|---|---|---|
| At rest or constant velocity | $R = mg$ | Normal |
| Accelerating upward (a) | $R = m(g+a)$ | Heavier |
| Accelerating downward (a) | $R = m(g-a)$ | Lighter |
| Free fall ($a = g$) | $R = 0$ | Weightless |
Example: a 50 kg man in a lift accelerating downward at $1.3\ \text{m s}^{-2}$: $R = 50(9.8 - 1.3) = 425\ \text{N}$.
Sliding down a weak rope
If a rope can bear at most tension $T_{max}$, the man must slide down with an acceleration large enough that $T \le T_{max}$. From $mg - T = ma$: $a = g - T/m$. For $T_{max} = \tfrac34 mg$, the minimum acceleration is $a = g/4$.
Closed systems
A bird flying inside a closed cage on a scale: the air transmits the bird's weight to the cage, so the system mass (bird + cage) is unchanged. A 4 kg bird in a 2 kg cage is still a 6 kg system.
Variation of g
Because the Earth bulges at the equator, a point on the equator is farther from the centre, so $g$ is least at the equator and greatest at the poles.
Key formulas
- $F_{net} = ma$; $\quad W = mg$
- Lift: $R = m(g \pm a)$
- Rope: $a = g - T/m$
Common MDCAT traps
- Mass measures inertia, not weight.
- Zero acceleration does not mean zero forces; it means zero net force.
- Braking pushes you forward (pseudo force), starting pushes you backward.
- Upward acceleration increases apparent weight whether the lift moves up or down.
- $g$ is least at the equator, not at the poles.
Quick revision
- First law = law of inertia.
- SI unit of force: newton, $1\ \text{N} = 1\ \text{kg m s}^{-2}$.
- Free fall: apparent weight zero.
- Rope with breaking load $\tfrac34 mg$: slide with $g/4$.
- All three laws involve force.