Mechanics: Mechanics is the branch of physics that deals with the motion of objects and the forces that change it.
Generally, mechanics is divided into two branches.
1. Kinematics
2. Dynamics
Kinematics is the study of motion of objects without referring to forces. In our everyday life, we observe many objects in motion. Or example, cars, buses, bicycles, motor cycles moving on the roads, aeroplanes flying through air, water flowing in canals or some object falling from the table to the ground.
Kinematics is the study of motion of objects without referring to forces on the other hand, Dynamics deals with forces and their effects on the motion of objects.
Scalar: A Scalar is that physical quantity which can be described completely by its magnitude only.
Examples: Mass, distance, length, time, speed, energy and temperature are scalar quantities.
A vector is that physical quantity which needs magnitude as well as direction to describe it completely.
Examples: The examples of vector quantities are displacement, velocity. acceleration, force and weight.
Origin: The point where x axis and y axis meet is known as origin.
It is denoted by O.
These axes are also called reference axes.
The direction is usually given by an angle (theta) with x-axis. The angle with x-axis is always measured from the right side of x-axis in the anti-clockwise direction.
Resultant vector: We can add two or more vectors to get a single vector. This is called as resultant vector.
It has the same effect as the combined effect of all the vectors to be added.
We have to determine both magnitude and direction of the resultant vector, therefore it is quite different from that of scalar addition.
One method of addition of vectors is the graphical method.
Addition of vectors by graphical Method:
Head to tail rule: To add these vectors, we apply a rule called head-to-tail rule which states that: To add a number of vectors, redraw their representative line such that the head of one coincides with the tail of the other. The resultant vector is given by a single vector which is directed from the tail of the first vector to the head of the last vector.
Rest: A body is said to be at rest if it does not change it position with respect to its surroundings.
Examples:
(i) A book, placed on the table is an example of rest. Because it does not change its position.
(ii) Trees and streetlights around the roads are the examples of rest. Both do not change their positions.
Motion: A body is said to be in motion, if it changes its position with respect to its surroundings.
Examples:
(i) A bus moving on a road is an example of motion.
(ii) A running boy in the street is an example of motión.
Meaning of surroundings: Surrounding are the places in neighbourhood of any object, where various objects are present.
The state of rest or motion of a body is relative.
Explanation: A passenger sitting in a moving bus is at rest because he/she is not changing his/her position with respect to other passengers or objects in the bus. But to an observer outside the bus, the passenger and the objects inside the bus are in motion.
Motion: A body is said to be in motion, if it changes its position with respect to is surroundings.
Types of motion: The motion of bodies can be divided into three types.
(i) Translatory motion (linear, random and circular)
(ii) Rotatory motion.
(iii) Vibratory motion (to and fro motion)
Translatory motion: If the motion of a body is such that every particle of the body moves in the same manner, it is called tanslatory motion. For example, the motion of a train or a car is tanslatory motion (Fig.2.6).
Examples:
(i) A car or train moving in a straight line has translational motion.
Rotatory Motion: If each point of a body moves around al fixed point (axis), the motion of this body is called rotatory motion.
Example: The motion of an electric fan and the drum of a washing machine dryer is rotatory motion. The motion of a top is also rotatory motion.
To and fro motion of a body about its mean position is known as vibratory motion.
Examples:
(i) Consider the motion of a baby in a swing as shown in the given figure. It moves back and forth about its mean position. The motion of the baby repeats from one extreme to the other extreme with the swing.
Linear motion: Straight line motion of a body is known as its linear motion.
Examples: (i) The object falling vertically down is an example of linear motion.
Circular motion:
The motion of an object in a circular path is known as circular motion.
Examples:
(1) A ball tied at the end of a string can be made to whirl. The stone as shown in given figure moves in a circle and thus has circular motion.
(ii) A Ferris wheel is also an example of circular motion.
Random motion: The disordered or irregular motion of an object is called random motion.
Examples:
(i) The motion of insects and birds is random motion.
(ii) The motion of dust or smoke particles in the air is also random motion.
(iii) Zig zag motion of the molecules of gases and liquids is called random. It is also called Brownian motion. This movement is also shown in figure.
Distance:
(1) The distance is the length of actual path of the motion.
(ii) It can be found out by given formula S = vt
(iii) It is a scalar quantity because it needs only magnitude to describe.
(iv) Its unit is meter (m).
Displacement:
(1) Displacement is the shortest distance between two points which has magnitude and direction.
(ii) It can be found out by given formula d = vt
(iii) It is a vector quantity because it needs magnitude and direction to describe.
(iv) Its unit is meter (m).
Definition: The distance covered in unit time is known as speed.
Unit time: It may be a sec an hour, a day and a year.
Examples:
Falcon can fly at a speed of 200km * h ^ - 1 Cheetah can run at a speed of 70km * h ^ - 1 , Formula: Speed can be found out by following formula. Speed = distance covered time taken v = s/t In this formula S is the distance covered by the object, v is its speed and t is the
time taken by it. Unit: Sl unit of speed is metre per second (m * s ^ - 1)
Sealar quantity: Speed is a scalar quantity because it needs magnitude only to describe.
Velocity: The rate of displacement of a body is called its velocity.
Example: A body covers 2km distance towards north it is its velocity. The velocity tells us not only the speed of a body but also its direction of motion.
Formula:
Velocity= displacement time taken
d t V= Here d is the displacement of the body moving with velocity v in time taken t.
Unit: SI unit of velocity is the same as speed i.e. metre per second (ms-1).
Vector quantity: Velocity is a vector quantity because it needs magnitude and direction for complete description.
Variable speed: A body has variable speed if it covers equal distances in unequal intervals of time however short the interval may be.
Example: Suppose a body covers 2km distance in half hour and again it covers 2km distance in one hour. It is clear, that this body covers equal distances in unequal intervals of time so its speed is called variable speed.
Uniform Speed: A body has uniform speed if it covers equal distances in equal intervals of time however short the interval may be. (OR)
If the speed of the body does not vary and has the same value then the body is said to posses uniform speed.
Example: Suppose a body covers 2km distance in half hour and again it covers 2km distance in next half hour it is clear, that body covers equal distances in equal intervals of time so its speed is called uniform speed.
Variable Velocity: A body has variable velocity if its speed or direction is changing.
Example: Suppose a car is moving on a linear road, it covers 2km distance in 20 minutes and again covers 3km distance in 20 minutes. The speed of the body varies therefore having variable velocity.
Uniform velocity: A body has uniform velocity if it covers equal displacement in equal intervals of time however short the interval may be. (OR)
If the speed and direction of a body does not change, then it posses uniform velocity.
Example No 1: A paratrooper attains a uniform velocity also called terminal velocity with which it comes to ground.
Example No 2: Suppose a body covers 2km distance towards north in 10 minutes. It again covers 2km distance towards north in next 10 minutes. It is clear that the speed and direction of the body do not change so body has uniform velocity.
Acceleration: Acceleration is defined as the rate of change of velocity of a body.
Reason of acceleration: In many cases the velocity of a body changes due to a change either in its magnitude or direction or both. The change in the velocity of a body causes acceleration in it.
Example No 1: Acceleration of a moving object is in the direction of velocity if its velocity is increasing.
Example No 2: Acceleration of the object is opposite to the direction of velocity if its velocity is decreasing.
Formula: Acceleration can be found out by given formula. Acceleration = Acceleration = Change in velocity time taken final velocity-initial velocity time taken a=
Here a is the acceleration, vi is the initial velocity, ve is the final velocity and t is the time taken.
Negative Acceleration, is called decelaration or retardation.
Positive acceleration: Acceleration of a body is positive if its velocity increases with time: The direction of this acceleration is the same in which the body is moving without change in its direction.
Negative Accelerationz: Acceleration of a body is negative if velocity of the body decreases. The direction of negative acceleration is opposite to the direction in which body is moving.
"Negative acceleration is also called deceleration or retardation."
Graph: A graph is a pictorial diagram in the form of a straight line or a curve which shows the relationship between two physical quantities.
Variables: The quantities between which a graph is ploted are called variable.
Independent Variables: A quantity which we can change with our wishes is called independent variable. Dependent Variables: The quantity which changes due to change in independent variable is called dependent variables: The quantity whose value varies with the independent quantity
Distance-time graph: It is useful to represent the motion of objects relation between distance S and time taken t by a moving body.
The axis of time: In the distance time graph, time is taken along horizontal axis. Axis of distance: In the distance time graph vertical axis shows the distance covered by the object.
Gradient of the distance-Time graph is equal to the average speed of the body.
Gradient: The gradient is the measure of slope of a line.
The graph between speed v versus time t. This is called speed-time graph.
The axis of speed is taken along y-axis, and the axis of time in speed time graph is taken along x-axis.
Gradient of the speed-Time graph is equal to the average aceleration of the body.
The area under speed-time graph up to the time axis is numerically equal to the distance covered by the object.
Galileo was the first scientist who, notice that all the freely falling objects have the same acceleration, independent of their masses.
Equations: vrvi + at S=vit+ 1 at 2aS = vi-v
Points of applying these equation, while applying these equation:
1. Motion is always considered along a straight line
ii. Acceleration is assumed to be uniform.
iii. Only the magnitudes of vector quantities are used.
iv. the direction of initial velocity is taken as positive. Other quantities which are in the direction of initial velocity are taken as positive. The quantities in the direction opposite to the initial velocity are taken as negative.
Gravitational acceleration: The acceleration of a freely falling bodies is called gravitational acceleration. It is denoted by g.
Value of g: On the surface of the Earth, the value of g is approximately 10ms-2,
1. vv+gt
2. h=vt+gt 2
3. 2gh-v-v
In 1905, famous scientist Albert Einstein proposed his revolutionary theory of special relativity which changed many of the basic concepts of physics.
Speed of light is a universal constant. Its value is approximately 3×108ms-1. Speed of light remains the same for all motions.
Any object with mass cannot achieve speeds equal to or greater than that of light this is known as universal speed limit.
Distance is a scalar quantity because it only measures the magnitude while displacement is a vector quantity because it measures both magnitude and direction.
Speed is a scalar quantity because it measures the magnitude only while velocity is a vector quantity because it measures both magnitude and direction.
The acceleration is positive when the velocity is increasing and it is negative when the velocity is negative. 1
The equations of acceleration are derived from the definitions of average velocity and average acceleration, and they are used to calculate an objects position, velocity and acceleration is a function of time. When the acceleration is not constant, more complex techniques need to be employed.
Graph line becomes horizontal when the object is at rest.
Acceleration is taken as negative when it opposes the direction of motion, such as in deceleration or when an object slows down.
In circular motion the point about which a body goes around, is outside the body. In
rotatory motion the line about which a body moves is passing through the body itself.
Riders in a ferris wheel have rotatory motion because the axis about which a rider moves is passing through the rider itself.
Yes, a body moving at a constant speed have acceleration if it changes its direction a moving in a circular path.
v = 36km * h ^ - 1 v = (36 * 1000)/3600 * m * s ^ - 1 v = m * s ^ - 1
Total distance = 80m Total time = 10 sec Average speed = Total distance Total time
Average speed = 80m 10 sec
Average speed = 8m * s ^ - 1 .
Ans. Least count of Vernier Caliper: 0.01, cm.
Least count of Screw Gauge: 0.001, cm.
Importance: It determines the smallest measurement of an instrument can make ensuing higher accuracy.
Ans. Dimensional analysis uses dimensions [e.g., (L) for length] to check to correctness of physical equations and convert units.
Ans. Systematic Errors: Consistent errors caused by faulty equipment or incorre methods.
Example: A miscalibirated scale always showing 2 kg extra.
Example: Fluctuations in stopwatch readings.
Random Errors: Unpredictable errors due to environmental factors or human
Ans. Significant figures indicate the precesion of a measurement.
Rules:
(i) Non-zero digits are significant.
(ii) Zeros between non-zero digits are significant.
(iii) Leading zeros are not significant.
(iv) Trailing zeros in a decimal are significant.
Example: 0.00450 has 3 significant figures.
Ans. Scientific notation simplifies working with very large or small numbers by expressing them in the form a x 10".
Example: 3000 = 3.0 × 103.
Ans. Accuracy: How close a measured value is to the true value.
Precesion: How consistently measurements can be operated.
Exampel: A clock showing the correct time is accurate, If it always shows the same time (even if wrong) it precise.
Ans. The Sl system provides a standarized, universally accepted system of measurement, ensuring consistency and accuracy across all scientific and engineering fields worldwide.
Ans. ✩ Base Quantities: Fundamental quantities not derived from others., (e.g., length, time).
Example: length (meter), Time (second).
Example: Speed = distance/time (m/s).
Derived Quantities: Formed by combining base quantities mathematically.
Ans. Physical quantities are measurable aspects of nature used to describe physical phenomena
They are classified into:
B. Base Quantities: Fundamental and independent (e.g., length, mass and time).
b. Derived Quantities: Demental and
