Chapter Notes

Measurement of Time

Humans have been interested in tracking time for a long time. They noticed that many natural events repeat themselves regularly, like the rising and setting of the Sun, the phases of the Moon, and the changing seasons. They used these cycles to keep time and developed calendars. A day was defined by the cycle of the Sun's rising and setting. Then, they looked for ways to know the time of day.

To measure shorter periods within a day, they created devices like sundials, water clocks, hourglasses, and candle clocks.

• Sundial Time is determined by the position of the shadow cast by the Sun's light on an object.
• Water Clock Time is measured by the flow of water either out of or into a vessel.
  • In one type, water flows out of a vessel with markings.
  • In another type, a bowl with a small hole is floated on water. It fills gradually and sinks after a certain time.
• Hourglass Time is measured by the flow of sand from one bulb to another.
• Candle Clock Candles with markings indicate the passage of time as the candle burns.

Activity 8.1: Let us construct

A simple water clock can be made using a plastic bottle, a drawing pin, and some water. Cut the bottle in half, make a hole in the cap, invert the top half into the bottom half, and fill it with water. Mark the water level every minute as the water drips.

As civilization advanced and people travelled long distances, accurate time measurement became essential. This led to better mechanical clocks driven by weights, gears, and springs from the fourteenth century. The invention of the pendulum clock in the seventeenth century was a significant breakthrough.

Know A Scientist

The pendulum clock was invented in 1656 and patented in 1657 by Christiaan Huygens (1629-1695). He was inspired by Galileo Galilei's (1564-1642) investigations of pendulums. Galileo noticed a lamp swinging in a church and found that the time for each swing was the same, using his pulse to measure time. He concluded that the time to complete one oscillation was constant for a pendulum of a specific length.

8.1.1 A simple pendulum

A simple pendulum consists of a small metallic ball, called the bob, suspended from a rigid support by a long thread.

When the bob is moved to one side and released, it begins oscillatory motion. This motion is periodic because it repeats its path after a fixed time.

One oscillation is completed when the bob moves from its mean position (O) to one extreme position (A), then to the other extreme position (B), and back to O. It also completes one oscillation when it moves from A to B and back to A. The time period is the time taken to complete one oscillation.

Activity 8.2: Let us experiment

To measure the time period of a pendulum, collect a string, a bob, a stopwatch, and a ruler. Tie the bob to the string, fix the other end to a support, and let the bob come to rest. Move the bob slightly to one side and release it. Measure the time for 10 oscillations and repeat the activity several times. Divide the time taken for 10 oscillations by 10 to find the time period.

The time period of a pendulum is almost the same every time.

The time period of a simple pendulum depends on its length but not on the bob's mass. All pendulums of the same length have the same time period at a given location.

The time period of a simple pendulum of a given length is constant at a place. This property is used in the measurement of time.

All clocks, old or modern, are based on a continuously repeating process that marks equal time intervals.

Modern clocks use tiny, rapid vibrations from a quartz crystal (quartz clocks) or atoms (atomic clocks). Huygens' early pendulum clocks could lose 10 seconds per day, but today's atomic clocks lose only one second in millions of years. Scientists are always seeking more accurate ways to measure time.

8.1.2 SI unit of time

The SI unit of time is the second, with the symbol s. Larger units are the minute (min) and the hour (h).

$60 \text{ s} = 1 \text{ min} \quad 60 \text{ min} = 1 \text{ h}$

Units of time (second, minute, hour) begin with a lowercase letter, except at the beginning of a sentence. Their symbols ('s', 'min', 'h') are also lowercase and singular. A full stop is not written after the symbol, except at the end of a sentence. "sec" for second and "hrs" for hour is incorrect.

Activity 8.3: Let us identify

The smallest interval of time that can be measured with a typical wall clock is one second.

Science and Society

Measuring tiny fractions of a second is crucial in today's world. In sports, timekeeping devices record events to one-hundredth or one-thousandth of a second (a millisecond). In medicine, heart monitors like Electrocardiogram (ECG) machines measure millisecond variations in heartbeats. In music, digital recordings capture sound thousands of times per second. Smartphones and computers process signals in microseconds (one-millionth of a second). Scientists develop more precise time-measuring tools for space exploration, medicine, and advanced science experiments.

8.2 Slow or Fast

When we say something is moving fast or slow, we are comparing how much distance it covers in a certain amount of time.

In a race, the person who is ahead at any moment is running faster. This means they have covered more distance in the same amount of time.

The distances moved by objects in a given interval of time determine which one is faster or slower. The faster runner has a higher speed.

8.3 Speed

By comparing the distances that two or more objects move in a unit time, we can find out which one is moving faster. The unit time can be one second, one minute, or one hour. The speed of an object is the distance it covers in a unit of time.

To determine the speed of an object, we need to know the total distance it covered and the time it took to cover that distance. The speed of an object is calculated as:

$\text{Speed} = \frac{\text{Total distance covered}}{\text{Total time taken}}$

The SI unit of speed is metre per second, expressed as $\text{m/s}$. Speed can also be expressed in other units, such as kilometre per hour ($\text{km/h}$).

Given

• Distance covered = $3.6 \text{ km}$
• Time taken = $15 \text{ min}$

To Find

Speed of the bicycle in $\text{m/s}$

Formula

$\text{Speed} = \frac{\text{Distance covered}}{\text{Time taken}}$

Solution

$\text{Speed} = \frac{3.6 \text{ km}}{15 \text{ min}}$

Convert km to m and min to s:

$\text{Speed} = \frac{3.6 \text{ km} \times 1000 \frac{\text{m}}{\text{km}}}{15 \text{ min} \times 60 \frac{\text{s}}{\text{min}}}$

$\text{Speed} = \frac{3.6 \times 1000 \text{ m}}{15 \times 60 \text{ s}}$

$\text{Speed} = 4 \text{ m/s}$

Final Answer $4 \text{ m/s}$

Activity 8.2: Finding the speed of trains

To find the speed of trains, look up the railway timetable on the internet. Identify a train stopping at the nearest railway station, find the next station and the distance to it in the timetable. Note the departure and arrival times and calculate the time taken. Repeat for different types of trains.

Compare the speeds of the trains to see which is the fastest.

8.3.1 Relationship between speed, distance, and time

We can calculate speed using the formula:

$\text{Speed} = \frac{\text{Total distance covered}}{\text{Total time taken}}$

If we know the speed and time, we can calculate the distance:

$\text{Total distance covered} = \text{Speed} \times \text{Total time taken}$

If we know the distance and speed, we can calculate the time:

$\text{Total time taken} = \frac{\text{Total distance covered}}{\text{Speed}}$

Given

• Speed = $50 \text{ km/h}$
• Time = $2 \text{ h}$

To Find

Distance

Formula

$\text{Distance} = \text{Speed} \times \text{Time}$

Solution

$\text{Distance} = 50 \frac{\text{km}}{\text{h}} \times 2 \text{ h} = 100 \text{ km}$

Final Answer $100 \text{ km}$

Given

• Distance = $360 \text{ km}$
• Speed = $90 \text{ km/h}$

To Find

Time

Formula

$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$

Solution

$\text{Time} = \frac{360 \text{ km}}{90 \frac{\text{km}}{\text{h}}} = 4 \text{ h}$

Final Answer $4 \text{ h}$

The speed calculated using the formulas above is the average speed, because the object might not have travelled at the same speed during the entire time.

Science and Society

Vehicles like scooters, motorbikes, cars, and buses have a speedometer, which measures and displays the vehicle's speed in $\text{km/h}$. They also have an odometer, which measures the distance travelled by the vehicle in kilometres.

8.4 Uniform and Non-uniform Linear Motion

Linear motion is when an object moves along a straight line. Imagine a train on a straight track between two stations. The train starts slowly, speeds up, slows down, and stops. In between the two stations, the train may move at a constant speed for some distance.

Uniform linear motion is when an object moves along a straight line with a constant speed. Non-uniform linear motion is when the speed of an object moving along a straight line keeps changing.

An object in uniform linear motion covers equal distances in equal intervals of time. An object in non-uniform linear motion covers unequal distances in equal intervals of time.

Uniform linear motion is an idealization. In everyday life, objects seldom move with a constant speed over long distances or for long periods. That is why we use average speeds.