Motion
Motion is a change in position of an object with respect to time. Motion is typically described in terms of displacement, distance, velocity, acceleration, time and speed.
The branch of physics which deals with the study of motion of material objects is called mechanics.
Mechanics is divided into following branches.
(i) Statics : Statics is the branch of mechanics which deals with the study of motion of objects under the effect of forces in equilibrium.
(ii) Kinematics :
It is that branch of mechanics which deals with the study of motion of object without taking into account the factors (i.e. nature of forces, nature of bodies etc.) which cause motion. Here time factor plays an essential role.
(iii) Dynamics :
It is that branch of mechanics which deals with the study of motion of objects taking into account the factors whichcause motion.
Rest : An object is said to be at rest if it does not change its position with time, with respect to its surroudings.
A book lying on a table, a person sitting in a chair are the examples of rest.
Motion : An object is said to be in motion if it changes its position with time, with respect to its surroundings.
Example : A bird flying in air, a train moving on rails, a ship sailing on water, a man walking on road are some of the examples of motion, visible to the eye. Motion of gas molecules is an example of motion, invisible to the eye.
Rest & Motion are relative terms :
When we say that an object is at rest or in motion,then this statement is incomplete and meaningless. Basically, rest & motion are relative terms. An object which is at rest can also be in motion simultaneously. This can be illustrated as follows.
The passengers sitting in a moving bus are at rest with respect to each other but they are also in motion at the same time with respect to the objects like trees, buildings on the road side. So the motion and rest are relative terms.
Rectilinear motion :
If a particle moves in a fixed direction, the motion of this type is called rectilinear motion or one dimensional motion.For example the motion of an ant on a wire is a rectilinear motion.
Two dimensional motion :
If the motion of a particle is in such a way that its position remains on a fixed plane, then the motion of a particle is called two dimensional motion.
Laws Of Motion
First Law of Motion
A body continue to be in its state of rest or of uniform motion along a straight line, unless it is acted upon by some external force to change the state
(1) If no net force acts on a body, then the velocity of the body cannot change i.e. the body cannot accelerate.
(2) Newton‟s first law defines inertia and is rightly called the law of inertia. Inertia are of three types :Inertia of rest, Inertia of motion, Inertia of direction
(3) Inertia of rest : It is the inability of a body to change by itself, its state of rest. This means a body atrest remains at rest and cannot start moving by its own.
Second Law of Motion
(1) The rate of change of linear momentum of a body is directly proportional to the external force appliedon the body and this change takes place always in the direction of the applied force.
(2) If a body of mass m, moves with velocity v then its linear momentum can be given by p= mv and if force is applied on a body, then Force = mass ? acceleration
Third Law of Motion
To every action, there is always an equal (in magnitude) and opposite (in direction) reaction.
(1) When a body exerts a force on any other body, the second body also exerts an equal and opposite forceon the first.
(2) Forces in nature always occurs in pairs. A single isolated force is not possible.
(3) Any agent, applying a force also experiences a force of equal magnitude but in opposite direction. Theforce applied by the agent is called „Action‟ and the counter force experienced by it is called „Reaction‟.
(4) Action and reaction never act on the same body. If it were so the total force on a body would have always been zero i.e. the body will always remain in equilibrium.
(5) If F (AB)= force exerted on body A by body B (Action) and F(BA)= force exerted on body B by body A (Reaction) Then according to Newton‟s third law of motion F (AB) = F(BA)
(6) Example : (i) A book lying on a table exerts a force on the table which is equal to the weight of the book. This is the force of action.
Linear motion
Linear motion, also called uniform motion or rectilinear motion, motion in one spatial dimension. According to Newton’s first law (also known as the principle of inertia), a body with no net force acting on it will either remain at rest or continue to move with uniform speed in a straight line, according to its initial condition of motion. In fact, in classical Newtonian mechanics, there is no important distinction between rest and uniform motion in a straight line; they may be regarded as the same state of motion seen by different observers, one moving at the same velocity as the particle, the other moving at constant velocity with respect to the particle. A body in motion may be said to have momentum equal to the product of its mass and its velocity. It also has a kind of energy that is entirely due to its motion, called kinetic energy. The kinetic energy of a body of mass m in motion with velocity v is given by K = (1/2)mv2.
Speed and Velocity
Both speed and velocity tell us how far something is travelling in unit time. As velocity is a vector it must also tell us what direction the object is travelling in.
average velocity v̅ = Δs / Δt
Acceleration
Acceleration tells us how rapidly something is changing velocity – for instance, the change in velocity in unit time.Deceleration is the same thing, but has a negative sign as the velocity if decreasing.
Velocity-time graphs
These are similar to displacement-time graphs, but this time velocity is on the y-axis. Here are the only possibilities that you’ll come across at A-level.
gradient = change in V (or ΔV) / change in t (or Δt) = the acceleration at any time.
Circular motion
When an object moves in a circle at a constant speed its velocity (which is a vector) is constantly changing. Its velocity is changing not because the magnitude of the velocity is changing but because its direction is. This constantly changing velocity means that the object is accelerating (centripetal acceleration). For this acceleration to happen there must be a resultant force, this force is called the centripetal force.
Angular Speed
The angular speed (w) of an object is the angle (q) it moves through measured in radians (rad) divided by the time (t) taken to move through that angle. This means that the unit for angular speed is the radian per second (rad s-1).
v is the linear velocity measured in metres per second (ms-1).
r is the radius of the circle in metres (m).
f is the frequency of the rotation in hertz (Hz).
Centripetal Acceleration
Centripetal acceleration (a) is measure in metres per second per second (ms-2). It is always directed towards the center of the circle.
Centripetal Force
When an object moves in a circle the centripetal force (F) always acts towards the centre of the circle. The centripetal force, measured in newtons (N) can be different forces in different settings it can be gravity, friction, tension, lift, electrostatic attraction etc.
Vibrationational motion
periodic back-and-forth motion of the particles of an elastic body or medium, commonly resulting when almost any physical system is displaced from its equilibrium condition and allowed to respond to the forces that tend to restore equilibrium.
Vibrations fall into two categories: free and forced. Free vibrations occur when the system is disturbed momentarily and then allowed to move without restraint. A classic example is provided by a weight suspended from a spring. In equilibrium, the system has minimum energy and the weight is at rest. If the weight is pulled down and released, the system will respond by vibrating vertically.
The vibrations of a spring are of a particularly simple kind known as simple harmonic motion (SHM). This occurs whenever the disturbance to the system is countered by a restoring force that is exactly proportional to the degree of disturbance. In this case, the restoring force is the tension or compression in the spring, which (according to Hooke’s law) is proportional to the displacement of the spring. In simple harmonic motion, the periodic oscillations are of the mathematical form called sinusoidal.
Most systems that suffer small disturbances counter them by exerting some form of restoring force. It is frequently a good approximation to suppose that the force is proportional to the disturbance, so that SHM is, in the limiting case of small disturbances, a generic feature of vibrating systems. One characteristic of SHM is that the period of the vibration is independent of its amplitude. Such systems therefore are used in regulating clocks. The oscillation of a pendulum, for instance, approximates SHM if the amplitude is small.
A universal feature of free vibration is damping. All systems are subject to frictional forces, and these steadily sap the energy of the vibrations, causing the amplitude to diminish, usually exponentially. The motion is therefore never precisely sinusoidal. Thus, a swinging pendulum, left undriven, will eventually return to rest at the equilibrium (minimum-energy) position.
Forced vibrations occur if a system is continuously driven by an external agency. A simple example is a child’s swing that is pushed on each downswing. Of special interest are systems undergoing SHM and driven by sinusoidal forcing. This leads to the important phenomenon of resonance. Resonance occurs when the driving frequency approaches the natural frequency of free vibrations. The result is a rapid take-up of energy by the vibrating system, with an attendant growth of the vibration amplitude. Ultimately, the growth in amplitude is limited by the presence of damping, but the response can, in practice, be very great. It is said that soldiers marching across a bridge can set up resonant vibrations sufficient to destroy the structure. Similar folklore exists about opera singers shattering wine glasses.
Electric vibrations play an important role in electronics. A circuit containing both inductance and capacitance can support the electrical equivalent of SHM involving sinusoidal current flow. Resonance occurs if the circuit is driven by alternating current that is matched in frequency to that of the free oscillations of the circuit. This is the principle behind tuning. For example, a radio receiver contains a circuit, the natural frequency of which can be varied. When the frequency matches that of the radio transmitter, resonance occurs and a large alternating current of that frequency develops in the circuit. In this way, resonating circuits can be used to filter out one frequency from a mixture.
In musical instruments, the motion of strings, membranes, and air columns consists of a superposition of SHM’s; in engineering structures, vibrations are a common, though usually undesirable, feature. In many cases, complicated periodic motions can be understood as the superposition of SHM at many different frequencies.
SPEED
An object is said to be in motion if it changes its position with time, with respect to its surroundings.Speed is defined as the distance moved per unit time,
i.e Speed =Distance /Time
When we say that an object is at rest or in motion,then this statement is incomplete and meaningless. Basically, rest & motion are relative terms.
An object which is at rest can also be in motion simultaneously. This can be illustrated as follows.
The passengers sitting in a moving bus are at rest with respect to each other but they are also in motion at the same time with respect to the objects like trees, buildings on the road side. So the motion and rest are relative terms.
VELOCITY
Velocity indicates the rate of change of the object’s position (r ); i.e., velocity tells you how fast the object’s position is changing. The magnitude of the velocity (|| v || ) indicates the object’s speed. The direction of the velocity (dir v ) indicates the object’s direction of motion. The velocity at any point is always tangent to the object’s path at that point. Thus, the velocity tells you how the object is moving. In particular, the velocity tells you which way and how fast the object is moving.
MASS
It is the measure of the quantity of matter in an object and its unit is kilogram (kg) in SI units. It depends on the number of molecules in the matter and their masses and does not depend on gravity. Therefore an object would have same mass on Earth and on the Moon but different weight because of the change of gravity. Gravity on the moon is 1/6th of the gravity on earth. Mass of an object can be measured by using spring balance (newton-meter), top pan balance or lever balance. The international definition of mass is It is equal to the mass of the international prototype of the kilogram made up of platinum-iridium alloy kept at international bureau of weights and measurements in Paris.
Mass is the amount of matter in an object. It can also be defined as the property of a body that causes it to have weight in a gravitational field. It is important to understand that the mass of an object is not dependent on gravity. Bodies with greater mass are accelerated less by the same force.
WEIGHT
The weight of an object is defined as the force of gravity on the object and may be calculated as the mass times the acceleration of gravity, w = mg. Since the weight is a force, its SI unit is the newton.
For an object in free fall, so that gravity is the only force acting on it, then the expression for weight follows from Newton’s second law.
FORCE
Force is any interaction that, when unopposed, will change the motion of an object. A force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate.
IMPACT
Impact is a high force or shock applied over a short time period when two or more bodies collide. Such a force or acceleration usually has a greater effect than a lower force applied over a proportionally longer period.
WORK
Work is said to be done when a force applied on the body displaces the body through a certain distance in the direction of force.Mathematically, work is the force-displacement product
W = F x s cos a
or the force-displacement path integral
dW = F · ds
Positive work means that force (or its component) is parallel to displacement. Negative work means that force (or its component)is opposite to displacement i.e. In conservative field work done by the force over a closed loop is zero.
POWER
Power is defined as the rate at which work is done. Its unit is watt Power is said to be one watt, when one joule of work is said to be done in one second.
If work is being done by a machine moving at speed v against a constant force, or resistance, F, then since work done is force times distance, work done per second is Fv, which is the same as power.
Power = Fv
ENERGY
Energy is the capacity for doing work. Energy can manifest itself in many forms like mechanical energy, thermal energy, electric energy, chemical
energy, light energy, nuclear energy, etc.
The energy possessed by a body due to its position or due to its motion is called mechanical energy. The mechanical energy of a body consists of potential energy and kinetic energy.
Potential energy is the energy of a body or a system with respect to the position of the body or the arrangement of the particles of the system.For example, gravitational potential energy is associated with the gravitational force acting on object’s mass; elastic potential energy with the elastic force (ultimately electromagnetic force) acting on the elasticity of a deformed object; electrical potential energy with the coulombic force; strong nuclear force or weak nuclear force acting on the electric charge on the object; chemical potential energy, with the chemical potential of a particular atomic or molecular configuration acting on the atomic/molecular structure of the chemical substance that constitutes the object; thermal potential energy with the electromagnetic force in conjunction with the temperature of the object.
Kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.
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