Measurement of Length and Motion
Standard Units of Measurement (the SI System)
To measure something is to compare it with a fixed amount and find how many times that amount it contains. Every measurement has two parts: a number and a unit (for example, ‘5 metres’ — 5 is the number, metre is the unit). Without the unit, the number has no meaning.
Long ago people measured length using body parts — the handspan, the cubit (elbow to fingertip) and the foot. The problem is that these differ from person to person, so the same wall might measure a different number of handspans for two people. To avoid confusion, the whole world agreed on fixed standard units that never change.
The accepted system is the SI system (from the French Système International). Its basic units include:
- Length — the metre (m).
- Mass — the kilogram (kg).
- Time — the second (s).
Larger and smaller units are related to the metre in tens: 1 metre = 100 centimetres (cm); 1 centimetre = 10 millimetres (mm); and 1 kilometre (km) = 1000 metres. We choose a convenient unit for each job — kilometres for the distance between cities, metres for a room, centimetres for a book and millimetres for the thickness of a coin.
A standard unit must be the same for everyone.
- The handspan differs from person to person.
- So the same object would give different measurements, causing confusion.
Use 1 m = 100 cm and 1 km = 1000 m.
- (a) 3 m = 3 × 100 = 300 cm.
- (b) 2000 m = 2000 ÷ 1000 = 2 km.
Choose a unit that gives a convenient number.
- (a) A large distance → kilometre (km).
- (b) A very small length → millimetre (mm).
Key Points
- A measurement has a number and a unit; the unit gives it meaning.
- Body-part units (handspan, cubit, foot) vary, so we use fixed standard units.
- The SI units: length = metre (m), mass = kilogram (kg), time = second (s).
- 1 m = 100 cm, 1 cm = 10 mm, 1 km = 1000 m; choose a convenient unit for each job.
Methods for Measuring Length
The most common tool for measuring length is a ruler (scale); a longer flexible measuring tape is used for bigger lengths like a room or a person’s height. To get a correct reading, we must use these tools carefully. There are three important rules.
- Place the scale correctly. Lay the scale along the object touching it. Many rulers are worn at the zero end, so start measuring from the 0 mark (or any full mark) rather than the very edge.
- Take the reading from the right position. If the object does not begin at 0, the length = (reading at the other end) − (reading at the start). For example, if an object lies between the 2 cm and 7 cm marks, its length is 7 − 2 = 5 cm.
- Keep your eye in the correct position. Look at the mark straight on, directly above the point being read. If you look from an angle, you read a wrong value — an error called parallax error.
Some objects are not straight. To measure a curved line, lay a thread along the curve, mark where it begins and ends, then straighten the thread against a ruler. To measure the length of a curved or large object fairly, always use a suitable tool and these careful steps.
When the object does not start at 0, subtract the readings.
- Length = 9 cm − 2 cm.
- Length = 7 cm.
Parallax error comes from the position of the eye.
- It is the wrong reading you get when you look at the scale from an angle.
- Avoid it by keeping your eye directly above (straight in line with) the mark.
A straight ruler cannot follow a curve directly.
- Lay a thread carefully along the curved line.
- Mark the start and end on the thread, then straighten it against a ruler to read the length.
Key Points
- Use a ruler for small lengths and a measuring tape for larger ones.
- Place the scale touching the object; if it does not start at 0, length = end reading − start reading.
- Keep the eye straight above the mark to avoid parallax error.
- Measure a curved line using a thread, then straighten it against a ruler.
Types of Motion
An object is said to be in motion when its position changes with time compared to a fixed point around it. If its position does not change, it is at rest. Whether something is moving is judged with respect to its surroundings — a tree is at rest with respect to the ground, but appears to move when you watch it from a running train.
Motion is of several kinds, and an object may show more than one at a time:
- Rectilinear (straight-line) motion — movement along a straight line. Examples: a car on a straight road, a falling stone, a marching soldier.
- Circular motion — movement along a circular path. Examples: the hands of a clock, a stone tied to a string and whirled, the blades of a fan.
- Periodic (or oscillatory) motion — movement that repeats after equal intervals of time. Examples: a swinging pendulum, a child on a swing, the vibrating string of a guitar.
Some everyday motions combine types. The wheel of a moving bicycle rotates (circular motion) while the bicycle as a whole moves forward in a straight line (rectilinear motion). Recognising the type of motion helps us describe and study how things move.
Match the path to the type of motion.
- (a) Clock hands move along a circle → circular motion.
- (b) A falling stone moves in a straight line → rectilinear motion.
Periodic motion repeats at equal time intervals.
- The pendulum swings to and fro.
- It returns to the same position after equal time gaps, so the motion repeats.
Look at the wheel and the bicycle as a whole.
- The wheel turns round and round → circular motion.
- The whole bicycle moves forward in a line → rectilinear motion.
Key Points
- An object is in motion when its position changes with time relative to its surroundings; otherwise it is at rest.
- Rectilinear motion is along a straight line (a falling stone).
- Circular motion is along a circular path (clock hands, a fan).
- Periodic motion repeats after equal time intervals (a pendulum).