Contents
Physics Topics cover a broad range of concepts that are essential to understanding the natural world.
What are the Units of Measurement for Time? What is the New Definition of 1 Second?
A screw gauge can measure lengths smaller than those measured with a vernier. Normally screw gauges can measure lengths upto 0.01 mm, i.e., 10 micrometer (µm), and as such are know as micrometer screw gangs. The working principle is-when a screw is turned, it travels uniformly in a direction perpendicular to the plane of rotation. On one complete rotation, the screw travels a distance equal to its pitch, i.e., the distance between two consecutive threads on the screw.
Description: A screw gauge essentially consists of [Fig.] a thick U-shaped metal frame with a flat end on its left arm A, called stud. Its right arm ends in a long, hollow, cylindrical nut C whose inner side is threaded. A screw S, having one flat end B, can be moved inside the nut C by rotating a hollow cylinder D, called thimble, attached at the other end of the screw. The main scale (L) usually graduated
in mm is marked on a base line on the surface of C. The thimble is also graduated and usually is divided into 100 or 50 divisions. It is called the circular scale (R) . A rachet E is attached to the screw, by a spring. When the flat end B of the screw is in contact with the stud A, any further movement of the rachet does not press B against A . The rachet, therefore, helps to hold the object to be measured gently, without any deformation, between A and B.
Example: In an experiment if c = 0.001 cm, the main scale reading is 0.7 cm and the circular scale reading is 37, then d = 0.7 cm + 37 × 0.001 cm = 0.737 cm.
Pitch and least count of a screw gauge The distance advanced by the thimble along the baseline (L) on one complete rotation of the circular scale, is called pitch or screw pitch. To determine the pitch, the 0 mark on the circular scale is aligned with the baseline and the reading on the main scale is recorded.
The thimble or circular scale is rotated once to coincide the 0 mark of the circular scale with the baseline again and then the new reading is taken. The difference between the two readings along the main scale is the pitch. Usually, the pitch equals the value of the smallest main scale division, 0.5 mm or 1 mm. The ratio between the pitch and the number of divisions on the circu-lar scale is the least count (c).
Thus, least count,
c \(=\frac{\text { pitch }}{\text { no. of divisions on the circular scale }}\)
Least count of a screw gauge is the smallest length that can be measured with it.
For example, if the screw pitch is 0.1 cm, i.e., 1 m and the cir-cular scale has 100 divisions, then,
c = \(\frac{0.1}{100}\) = 0.001 cm
Method of measurement: The object whose thickness is to be measured, like a thin wire or a thin metal sheet, is placed between the stud A and the flat end B of the screw such that the two surfaces of the object touch A and B [Fig.]. In this situation both the readings on
1. the main scale and
2. the circular scale are noted. Then, the thickness of the object (d) = reading on the main scale + reading on the circular scale × c.
Example- In Fig., if c = 0.001 cm (say), the main scale reading is 0.7 cm and the circular scale reading is 37.
∴ d = 0.7 cm + 37 × 0.001 cm = 0.737 cm
Numerical Examples
Example 1.
Find the screw pitch of a screw gauge having 100 circular scale divisions and a least count of 0.002 cm.
Solution:
Screw pitch
= least count × number of divisions on circular scale
= 0.002 cm × 100 = 0.2 cm
Example 2.
A screw gauge has 50 circular scale divisions and a pitch of 0.1 cm. When this is used to measure the thickness of a plate, the main scale reading is 0.2 cm and the circular scale reading is 35. What is the thickness of the plate?
Solution:
Least count (c) for the screw gauge = \(\frac{0.1}{50}\)
= 0.002 cm
So the thickness of the plate,
t = 0.2 cm + 35 × 0.002 cm = 0.27 cm
Measurement of Mass
The principle of moments is applied to measure the unknown mass of a body by comparing it with a standard mass using a beam balance or common balance.
Standard mass: The mass of a platinum-iridium cylinder kept at the International Bureau of Weights and Measures near Paris is taken as the standard mass and is 1 kilogram.
Spring balance and weighing machines can be used to find the weight of a body; the mass can be calculated from these measurements also.
Some indirect methods are employed for the measurement of the mass of practically inaccessible bodies like planets and atomic particles :
- measurement of the gravitational pull of a planet on a known mass;
- mass spectroscopy, when an atomic particle is charged.
Measurement of Time
The concept of time measurement is always based on some periodic event in nature. An event is periodic if it repeats itself over and over again consuming the same amount of time.
Example:
i) The earth completes a full rotation about its axis in a day. This event repeats itself over and over again and is, thus, periodic. So the time period of the earth’s diurnal motion is a day. This period—a day—can be used as a unit in this measurement of time. For convenience, a day is subdivided to get other units like an hour, a minute and a second.
ii) The earth completes a full revolution around the sun in a year. So the time period of the earth’s annual motion is a year. This period—a year—can also be taken as a unit of time. It can be subdivided to get units like a month and a day; or can be multiplied to get longer units like a decade, a century or a millennium.
The instrument for the measurement of time is a clock. Clocks of different forms are used for time measurements of different types. A clock should always be calibrated initially in any of the time units discussed above.
However, a day or a year has noticeable uncertainties in its value and cannot provide a reliable and accurate measure of the units used in clocks. For example, a second, defined from a day or from a year, is highly uncertain and not at all reliable.
At present, universally accepted high precision time measurement techniques are provided by atomic clocks. This is not actually a clock of practical use; rather the frequencies of electromagnetic radiations emitted by atoms are utilised for a high precision definition of the standard unit of time—one second. Cesium clock is the particular atomic clock used in SI to define a second. Since cesium-133 atom emits electromagnetic radiation of a precise and constant frequency, it was chosen as the atomic clock standard. This definition is given below:
Definition of 1 second: Standard time, 1 second in SI, is defined as 9192631770 periods of radiation from cesium- 133 atom, at a fixed wavelength. The clock has a least count of about 10-10 s and has a precision of 1 s in 1 × 1018 s.
Clocks in day-to-day use: The cesium clock is the primary clock that defines the unit of time—a second. But actual day-to-day use employs secondary clocks, which are calibrated as per the predefined second, and the time to be measured is directly obtained from the calibrations.
- A pendulum has a definite period of oscillation. This is used in pendulum clocks.
- A periodically vibrating coiled spring is utilised in winding-type wrist watches.
- A quartz crystal oscillator vibrates at a natural frequency of 32768 Hz, i.e., the period of vibration is 1/32768 sec-ond. This is the source of modern high-precision quartz clocks.