1.1-1.2P - Units for motion and force

The unit tells the quantity

A unit tells you what kind of measurement a number represents. The number $5$ could mean $5 \mathrm{kg}$, $5 \mathrm{m}$, $5 \mathrm{s}$, $5 \mathrm{N}$, or something else entirely; the unit gives the number its physics meaning.

In this cluster, Pearson expects you to use these units:

The safest exam habit is to read the quantity first, then choose the unit. For example, a mass is measured in $\mathrm{kg}$, but a force such as weight is measured in $\mathrm{N}$. Those two are often confused because everyday speech says "weighs 50 kg", but in physics $\mathrm{kg}$ is mass, not force.

Kilogram, metre and second

The simplest units in this lesson are $\mathrm{kg}$, $\mathrm{m}$, and $\mathrm{s}$.

These units are the building blocks for the compound units you meet later. For example, a speed in $\mathrm{m/s}$ is built from metres and seconds. An acceleration in $\mathrm{m/s^2}$ is also built from metres and seconds, but it has a different meaning because the seconds appear twice.

Use the exact symbol. Write $\mathrm{kg}$, not $Kg$ or $kgs$; write $\mathrm{m}$, not $M$; write $\mathrm{s}$, not $sec$ unless the question has already accepted that wording. Give the unit when it has not already been supplied in the question. When a question asks for the unit, or the answer line has no unit printed on it, a mark is usually given for the correct unit, so a correct number with a missing or wrong unit loses that mark. An explicitly wrong unit changes the meaning of the answer.

Units for motion

Two motion units in this lesson are made from metres and seconds.

Speed uses $\mathrm{m/s}$ for distance per time; velocity uses the same unit for displacement per time, with a direction. A speed of $4 \mathrm{m/s}$ means the object covers 4 metres each second, if the speed is steady.

Acceleration uses $\mathrm{m/s^2}$ because it is about how velocity changes each second. An acceleration of $3 \mathrm{m/s^2}$ means the velocity changes by $3 \mathrm{m/s}$ every second: an object starting from rest with this acceleration is moving at $3 \mathrm{m/s}$ after 1 second, $6 \mathrm{m/s}$ after 2 seconds and $9 \mathrm{m/s}$ after 3 seconds. Acceleration is a change in velocity, in $\mathrm{m/s}$, divided by a time, in $\mathrm{s}$. That gives metres per second, per second, which is written $\mathrm{m/s^2}$. The extra "per second" is why acceleration has the squared second in the unit.

Do not shorten $\mathrm{m/s^2}$ to $\mathrm{m/s}$. That changes the quantity from acceleration to speed or velocity. In the same way, do not use $\mathrm{m/s^2}$ for a speed just because the object is moving quickly.

Newtons and newtons per kilogram

The unit of force is the newton, symbol $\mathrm{N}$. The unit is named after Isaac Newton, so its symbol is a capital $\mathrm{N}$, but the unit name is written in lower case: newton. Forces can change an object's speed, direction, or shape, but in this lesson the key point is the unit: if the quantity is a force, its unit is $\mathrm{N}$.

The unit $\mathrm{N/kg}$ means newtons per kilogram. It is used for gravitational field strength: the force due to gravity on each kilogram of mass. On Earth, the gravitational field strength is about $10 \mathrm{N/kg}$ ($9.8 \mathrm{N/kg}$ more precisely). This means each kilogram of mass experiences a gravitational force of about $10 \mathrm{N}$. So a student with a mass of $50 \mathrm{kg}$ has a weight of about $500 \mathrm{N}$: in physics, the student's mass is $50 \mathrm{kg}$ and their weight is $500 \mathrm{N}$.

The slash in $\mathrm{N/kg}$ matters. It means "per kilogram". $\mathrm{N/kg}$ is not the same as $\mathrm{N}$, and it is not the same as $\mathrm{kg}$. A common mistake is to write a gravitational field strength as $10 \mathrm{N}$, but $10 \mathrm{N}$ is a force, not force per kilogram.

Keep these pairs separate:

Separate Physics: Nm and kg m/s

Separate Physics students also need two extra units in this cluster: $\mathrm{N\,m}$ and $\mathrm{kg\,m/s}$.

$\mathrm{N\,m}$ is newton metre. It is used for the moment of a force, which is the turning effect of a force about a pivot. The unit combines a force unit, $\mathrm{N}$, with a distance unit, $\mathrm{m}$, because a moment is found by multiplying a force by a distance from the pivot. At this stage, you only need the unit and its meaning; later work covers how moments are calculated and balanced.

$\mathrm{kg\,m/s}$ is kilogram metre per second. It is used for momentum. The unit combines mass, $\mathrm{kg}$, with velocity, $\mathrm{m/s}$, because momentum is found by multiplying mass by velocity. At this stage, you only need to recognise and use the unit; later work covers momentum calculations and changes in momentum.

These two units look similar to other units in the course, so read them carefully:

Exam unit habits

Units are quick marks when you handle them carefully. Before you write a final answer, check three things:

1. Does the unit match the quantity asked for?
2. Does the symbol use the correct capital letters, such as $\mathrm{N}$ for newton?
3. Have you kept the full compound unit, such as $\mathrm{m/s^2}$, $\mathrm{N/kg}$, or $\mathrm{kg\,m/s}$?

Here are some typical corrections:

A good check is to say the unit out loud in full: "newtons per kilogram" is not the same as "newtons"; "kilogram metre per second" is not the same as "metres per second"; "metres per second squared" is not the same as "metres per second".

Quick recap

• Mass, length and time use kilograms (kg), metres (m) and seconds (s).
• Speed and velocity use $\mathrm{m/s}$; acceleration uses $\mathrm{m/s^2}$ because it measures velocity change each second.
• Force and weight use newtons (N); gravitational field strength uses $\mathrm{N/kg}$.
• Moment uses $\mathrm{N\,m}$; momentum uses $\mathrm{kg\,m/s}$. These compound units describe different quantities.