Chapter 8: Measurement of Time and Motion

Early people noticed that some events in nature repeat after fixed intervals: the Sun rises and sets, the Moon changes its shape, and the seasons come back. They used these cycles to make calendars, and one rising-to-rising of the Sun became a day. To measure shorter intervals inside a day they invented devices: the sundial (the moving shadow of an object), the water clock (water flowing out of or into a vessel), the hourglass (sand trickling through a narrow neck) and the candle clock (a candle burning down at a steady rate). In India, the Ghatika-yantra was a floating bowl with a tiny hole; it filled and sank in about 24 minutes, and a day was divided into 60 such ghatis.

A simple pendulum is a small heavy ball, called the bob, hung from a rigid support by a long thread. When it is left alone it hangs straight down at its mean position. If the bob is pulled slightly to one side and released, it swings to and fro on both sides of the mean position. This repeated to and fro motion is called oscillatory motion, and since it repeats again and again it is also periodic. One oscillation is complete when the bob goes from one extreme position to the other extreme position and comes back to where it started. Counting from the mean position, one oscillation is also complete when the bob returns to the mean position moving in the same direction as before.

The time taken by a pendulum to complete one oscillation is its time period. To measure it accurately, count the time for 10 oscillations with a watch and divide by 10. This is better than timing one swing, because a small error in starting or stopping the watch is shared among 10 swings. Experiments show that the time period depends on the length of the pendulum: a longer pendulum has a longer time period. It does not depend on the mass of the bob. All pendulums of the same length have almost the same time period at a place, so a pendulum can be used to keep time. Galileo noticed this regularity, and Huygens made the pendulum clock in the 17th century.

The SI unit of time is the second, with the symbol s. Larger units are the minute (min) and the hour (h): 60 s = 1 min and 60 min = 1 h. So 1 h = 3600 s. Rules for writing: unit names such as second, minute and hour start with a small letter unless they begin a sentence; the symbols s, min and h are small letters, are the same for one or many, and have no full stop after them; leave a space between the number and the symbol (write 5 s, not 5s); and sec and hrs are wrong forms. A wall clock can show a smallest interval of 1 second, but sports timers, ECG machines and computers measure milliseconds (one-thousandth of a second) and even microseconds (one-millionth of a second).

When objects cover the same distance, the one that takes less time is faster. When the distances are different, we compare how much distance each covers in one unit of time. This is called speed. Speed = total distance covered divided by total time taken. The SI unit of length is the metre (m) and of time the second (s), so the SI unit of speed is metre per second (m/s). Other common units are kilometre per hour (km/h) for vehicles. A speed of 5 m/s means 5 metres are covered every second.

The speed formula can be rearranged. If any two of speed, distance and time are known, the third can be found. Distance = speed times time, and time = distance divided by speed. The units must match: if speed is in km/h, time must be in hours and distance in km. To change km/h to m/s, multiply by 1000 and divide by 3600, which means divide by 3.6. To change m/s to km/h, multiply by 3.6. For example, 36 km/h = 10 m/s, and 5 m/s = 18 km/h.

Objects seldom move at the same speed all the time. The average speed is the total distance covered divided by the total time taken, whatever happened in between. Average speed = total distance divided by total time. In this book, 'speed' normally means average speed. Note that the average speed is not always the simple average of two speeds. Vehicles carry two instruments: the speedometer shows the speed of the vehicle at that moment in km/h, and the odometer shows the total distance travelled in km. Subtracting an earlier odometer reading from a later one gives the distance covered between the two readings.

Motion along a straight line is called linear motion. If an object moves along a straight line with a constant speed, its motion is uniform linear motion; it covers equal distances in equal intervals of time. If its speed keeps changing, the motion is non-uniform linear motion; it covers unequal distances in equal intervals of time. To decide, make a table of distances covered in equal time intervals and compare them. True uniform motion is an idealisation, because real objects seldom keep exactly the same speed for long, which is why we use average speed.