Motion and Measurement
Category : 6th Class
Learning Objectives
— Distance
— Displacement
— Speed
— Velocity
— Acceleration
INTRODUCTION
We observe in our daily life various moving objects like cars, buses, water flowing down etc. We also often talk of how fast or slow, an object is moving by comparing the distances travelled by the objects in a given time interval. In this chapter we shall learn to describe moving objects and measure various physical quantities.
REST AND MOTION
If the position of an object does not change with time with respect to its surroundings, it is said to be at rest. For e.g., a box lying on the table, a baby lying in his cot, a PC lying on the table etc.
If the position of an object changes with time relative to its surroundings, it is said to be in motion. A bird flying in the air, and a ball rolling on the ground are a few examples of objects in motion.
Rest and Motion are Relative Terms
The same object can be at rest or in motion at a time. A person sittings in a' moving train is at rest with respect to the other passengers in the train but he is in motion w.r.t. a man standing on the ground.
Distance covered by a moving body can never be zero or negative but displacement of a moving body can be zero or negative.
For e.g., a person goes to the market which is 1 km away
from his home (assume path is straight line) then the distance and d is placement both are 1 km but when he reaches back to home the distance covered by him is 1km + 1 km = 2 km while the displacement is 1 km- 1 km= zero as he comes back to his initial point.
Another example can be consider, a body moving in a circle of radius r. Then the distance covered by the body after completing one revolution is 2pr which is the length of a complete circular path while displacement is zero.
TYPES OF MOTION
(1) Rectilinear motion: Motion along a straight line is called rectilinear motion. The motion of a train along a straight track and a ball falling vertically downwards are examples of rectilinear motion.
(2) Translatory motion: When a body moves as a whole such that every point on it moves through the same distance per unit time, it is said to be in translator/motion. For e.g., a ball rolling down an inclined plane is intranslatory motion.
(3) Curvilinear motion: Motion of a body along a curved path is called curvilinear motion. For e.g., A racing car speeding on a race track, throwing of javelin etc.
(4) Circular motion: Motion of a body in a circular path is called circular motion. The body moves such that its distance from the center of the circular path remains same. For e.g., revolution of earth around the sun, a car following a round about etc.
(5) Rotatory motion: If a body moves in a round path without changing its position from one point to another, then its motion is called rotatory motion. For e.g., a spinning top, rotation of earth etc.
(6) Periodic motion: The motion which repeats itself after a fixed interval of time is called periodic motion. The revolution of moon around the earth and oscillations of a pendulum are examples of periodic motion.
(7) Oscillatory / Vibratory motion: The to and fro motion of an object about a mean position is known as oscillatory or vibratory motion. Motion of a swing, movement of pendulum of a clock are examples of oscillatory motion.
Do You Know?
Every oscillatory motion is periodic but every periodic motion is not oscillatory.
Uniform and non-uniform motion can be rectilinear or circular
OBJECTS HAVING MORE THAN ONE TYPE OF MOTION
UNIFORM AND NON-UNIFORM MOTION
Uniform motion: An object is said to have uniform motion if it travels equal distances in equal intervals of time.
Example: The motion of the earth about its axis, the motion of watch hands etc.
Non-uniform motion: An object is said to have non-uniform motion, if it travels unequal distances in equal intervals of time.
Example: Motion of a train, when it approaches towards a station.
IMPORTANT PARAMETERS OF MOTION
Not Distance covered by a moving body can never be zero or negative but displacement of a moving body can be zero or negative.
For e.g., a person goes to the market which is 1 km away
from his home (assume path is straight line) then the distance and displacement both are 1 km but when he reaches back to home the distance covered by him is 1 km + 1 km = 2 km while the displacement is 1 km- 1 km = zero as he comes back this initial point.
Another example can be consider, a body moving in a circle of radius r. Then the distance covered by the body after completing one revolution is 2pr which is the length of a complete circular path while displacement is zero.
Distance
The actual length of the path covered by an object is called distance. Its S.I unit is meter (m).
Displacement
The shortest distance between the initial and final position of a body is called displacement. Its S.I. unit is meter (m)
If a body reaches from position A to B via C then the distance travelled by the object = AC + CB
Distance travelled
= AC + AB
And displacement = AB
Speed
Distance covered by a body per unit time is called speed.
\[\text{Speed=}\frac{\text{distance}}{\text{time}}\]
\[\therefore \text{S}\text{.I}\,\text{unit}\,\text{=}\frac{\text{m}}{\text{s}}\]
Velocity
It is the displacement per unit time
\[\text{Velocity=}\frac{\text{displacement}}{\text{time}}\]
\[\therefore \text{S}\text{.I}\,\text{unit}\,\text{=m/s}\]
Acceleration
The rate of change of velocity of a body is called acceleration.
If 'u' is the initial velocity of a body and after a time interval 't', it acquires a final velocity 'v', then change in velocity
\[Accleration,\text{ }\left( a \right)\,\,=\frac{change\,in\,velocity}{time}=\frac{v-u}{t}\]
\[\therefore S.I.unit=\frac{m/s}{s}\]
\[\,=m/{{s}^{2}}\]
Acceleration due to gravity: When a body falls freely under the effect ofgravity of earth, then its acceleration is called acceleration due to gravity.
It is denoted by 'g'. The value ofg on earth is taken to be 9.8 m/s^{2}.
g = 9.8 m/s^{2} for a body falling vertically downwards.
g = -9.8 m/s^{2} for a body rising vertically upward.
Do You Know?
Speed of sound in air is 332 m/s and speed of light in air is 3x10^{8} m/s.
In a good vacuum where air friction is legible the paper and coin truly fall with the same acceleration, regardless of the shape or weight of the paper.
MEASUREMENT AND ITS NEED
To buy a piece of cloth, to buy vegetables, to know the amount of sugar to be added to a cup of coffee, we need measurements. A quantity which can be measured is known as Physical quantity.
Measurement is the comparison of unknown physical quantity -with a known standard quantity of same kind.
The result of measurement is expressed as the numerical value 'n' and the unit 'u'.
i.e. Q = nu
For e.g., length of a cloth is expressed as L = 2m. The numerical value tells that how many times a standard quantity is contained in a given physical quantity.
STANDARD UNIT OF MEASUREMENT
A standard unit is a standard measure of some definite and suitable quantity which remains the same at all times and all places.
The system of units which is internationally accepted for measurement is abbreviated as SI (International system) units. The SI system was developed by General conference on weight and measures in 1960 for international usage.
Physical Quantity |
S.I. unit |
Symbol |
Length |
Metre |
M |
Mass |
Kilogram |
Kg |
Time |
Second |
S |
Temperature |
Kelvin |
K |
Electric current |
Ampere |
a |
MULTIPLES AND SUBMULTIPLES OF UNITS
Length: (Distance between two points)
1 decametre (dam) = 10 m
1 hectometre (hm) = 100 m
1 kilometre (km) = 1000 m
1 decimetre (dm) \[={{10}^{-1}}\]
1 centimetre (cm) \[={{10}^{-2}}\]
1 millimetre (mm) \[={{10}^{-3}}\]
1 micrometre (mm) = 10^{–6}
1 Angstrom (Å) = 10^{–10}
Mass: (Total matter present in a body)
1 Quintal (qt) = 100 kg
1 Tonne (t) = 1000kg
1 Decagram (dag) = 10^{–2} kg
1 gram (g) = 10^{–3} kg
1 milligram (mg) = 10^{–6} kg
Time: (Interval between two events)
1 minute = 60 seconds
1 hour = 60 minutes
1 day = 24 hours
1 year = 365 \[\frac{1}{4}\]days
1 century = 100 years
1 millennium = 1000 years
1 mean solar day = 24 hours
= 24 x 60 min
= 1440 x 60 seconds
= 86400 seconds
Do You Know?
The second is defined as the 9192631770 times the period of oscillation of radiation from the cesium atom.
Temperature: (Hotness or coldness of a body)
The units of temperature are Celsius (°C), Fahrenheit (°F), Kelvin (K)
To convert °C to °F or vice-versa, the following relation is used:
\[\frac{C}{5}=\frac{F-32}{9}\]
And to convert °C into Kelvin (K) K=°C+273
MEASUREMENT OF LENGTH
Length is defined as the distance between any two points.
The S.I. unit of length is meter.
Smaller lengths are measured in centimeter (cm) or millimeter (mm). Larger lengths like distance between two cities is measured in kilometers (km).
Very large distances like distance between stars or distance between sun and earth are measured in Light years (ly).
One light year is the distance travelled by light in vacuum in one year.
\[11y=9.46\times {{10}^{15}}m\]
Note
For accurate measurement the eye of the observer must be in front of the point of measurement. If the position of eye is wrong, then the parallax error tends to occur.
Length of a curved line can be measured with the help of a thread. A knot is tied at one end of the thread & placed at one point the starting point of a curved line. Then go on stretching the thread along the curve keeping the thread taut. Then tie another knot on reaching the endpoint of the curved line. Now the length of thread can be measured using a meter scale. This length of thread gives the length of the curved line.
Instruments Used for Measuring Length
Most commonly used instruments for measuring lengths are met rescale, measuring tape and metre rod.
For measuring the length, breadth or height of a cuboidal box metre scale can be used.
Metre rod is usually used by the cloth merchant to measure the length of a piece of cloth.
Tailor use a tape to take the measurements of different parts of body of a person.
For correct measurement, zero (0) mark of the scale must be coincides with the one edge of the object whose length is to be measured.
Note
Accuracy of physical balance is not affected by gravity.
Do You Know?
Kilogram is defined as the mass of a specific platinum-iridium alloy cylinder kept at the international Bureau of weights and measures at Severs France.
MEASUREMENT OF VOLUME
Volume is the space occupied by an object. An object of regular shape like cube or cuboid will have length (1), breadth (b) and height (h). Therefore volume can be measured by determining the length of each side and using the formula volume \[=l\times b\times h\]
Volume of an irregular object can be determined by immersing it in water.
The volume of water displaced by the irregular object can be measured with the help of a measuring cylinder. Thereby using the principle that volume of object immersed is equal to the volume of water displaced by the object, volume of irregular object can be determined.
MEASUREMENT OF MASS
Mass is the quantity of matter contained in a body. The S.I. unit of mass is kilogram (kg).
Mass is measured by a beam balance or a physical balance.
Physical balance measures the mass of a body by comparing it with a known standard mass.
Both arms of the physical balance are of equal length. So using the principle of moments, in equilibrium masses in both the pans of the balance should be equal. Hence with the help of a known mass in one pan, mass of an object in the other pan can be determined.
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