Mechanics 1 Flashcards
Define angular displacement
Angular displacement is defined as the angle described by the radius vector in a given time at the centre of the circle.
Define radius vector
A vector drawn from the centre of a circle to the position of a particle on the circumference of the circle is known as the radius vector.
Define one radian
One radian is the angle subtended by and arc equal to the radius of the circle.
State the right hand rule
Imagine the axis of rotation to be held in the right hand with the fingers curled around it and the thumb outstretched. If the curled fingers give the direction of motion of a particle performing circular motion, then the direction of outstretched thumb gives the direction of angular displacement vector.
Define angular velocity
Angular velocity of a particle performing circular motion is defined as the time rate of change of limiting angular displacement.
What is the direction of angular velocity?
Same as that of angular displacement
Define angular acceleration
The average angular acceleration is defined as the time rate of change of angular velocity.
Define instantaneous angular acceleration
Instantaneous angular acceleration is defined as the limiting rate of change of angular velocity.
Define uniform circular motion
Uniform circular motion (UCM) is defined as the periodic motion of particle along the circumference of the circle with constant angular speed.
Define periodic time of a particle performing circular motion
The time taking by a particle performing UCM to travel a distance equal to the circumference of the circle is called as periodic time or period (T).
Define frequency of a particle performing uniform circular motion
Frequency of revolution is defines as the number of revolutions performed by a particle performing UCM in unit time.
Define centripetal force
Centripetal force is a force acting on a particle performing circular motion, which is along the radius of the circle and directed towards the centre of the circle.
Define centrifugal force
Centrifugal force is a pseudo force in UCM which acts along the radius and directed away from the centre of the circle.
What force provides centripetal force for a car moving along a curved road?
Friction
Maximum safety speed for a car to be driven around a curved horizontal road
V= root(μrg)
Define banking of road.
The process of raising the outer edge of a road over the inner edge through a certain angle is know as banking of road.
Why is banking of roads necessary?
Force of friction provides centripetal force
Define the angle of banking
The angle made by the surface of a banked road with the horizontal surface is called the angle of banking.
Maximum safe speed if a vehicle on a banked road
Vo= root(Rgtan(θ))
What is the dependence of angle of banking on mass of the vehicle?
Independent
Define conical pendulum
A conical pendulum is a simple pendulum given such a motion that the bob describes a horizontal circle and the string describes a cone.
Speed of bob of conical pendulum
V= root(rgtan(θ))
Time period of conical pendulum
T= 2π*root(l/g)
What does the time period of a conical pendulum depend on?
- Length of pendulum
- Angle of inclination to the vertical
- Acceleration due to gravity at a given place
- Independent of theta if small
- Independent of mass of bob
Tension in the string of conical pendulum
T= mg*root(1+ (r/h)^2)
Linear velocity of a particle performing vertical circular motion at highest position
Va= root(rg)
Linear velocity of a particle performing vertical circular motion at lowest point
Vb= root(5rg)
Linear velocity of a particle performing vertical circular motion at a midway point
Vc= root(3rg)
Energy of a particle performing vertical circular motion
E=(5/2) mgr
State Newtons law of Gravitation
Newton’s law of of Gravitation states that every particle of matter attracts every other particle of matter with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Value of universal gravitational constant
G = 6.63(10^(-11)) Nmm/(kg*kg)
Define satellite
And object which revolves in an orbit around a planet is called as a satellite.
Define artificial satellite
The man made satellites revolving round the Earth are known as artificial satellites.
Explain two stage rocket.
Satellite kept at tip of rocket.
Initially, fuel in the first stage of the rocket is ignited on the surface of the earth so that the rocket rises to desired height above the surface of the earth.
First stage detached by remote control and rocket is rotated through 90deg.
Second stage ignited. Satellite projected in horizontal direction.
When fuel in second stage completely burnt empty second stage also detached. Resultant motion from velocity of projection given to it.
Discuss possible case of projection of satellite
- VVe
Hyperbolic orbit. Will escape Earths gravitational field and continue to travel infinitely.
Define Critical velocity of a a satellite
The minimum horizontal velocity of projection that can be given to a satellite at a certain height so that it can revolve in a circular orbit around the earth is called the critical velocity.
How does critical velocity depend on height?
Orbital velocity of a satellite decreases with increase in height.
Define periodic time of a satellite
The time taken by a satellite to complete one revolution around the Earth is known as the periodic time of satellite.
Equation for periodic time or a satellite
T^2 = 4 * (π^2) * (r^3) / (GM)
Or
T= 2π root(r/g)
What is the relation between time period of a satellite and the radius of its orbit?
Square of Time period of a satellite is directly proportional to the cube of the radius of its orbit.
How does the time period of satellite vary with height of satellite?
Period of satellite increases as height of projection is increased.
Kepler’s first law
Aka law of orbit
Every planet revolves around the sun in and elliptical orbit with the sun situated at one if the foci of the ellipse.
Kepler’s second law
Aka law of equal areas
The radius vector drawn from the sun to any planet sweeps out equal areas in equal intervals of time.
Kepler’s third law
Aka law of period or harmonic law
The square of the period of revolution of the planet around the sun is directly proportional to the cube of the semi major axis of the elliptical orbit.
Define binding energy of the satellite
The minimum energy required for a satellite to escape from Earth’s gravitational influence is called as the binding energy of the satellite.
Equation for binding energy of a satellite revolving in a circular orbit round the Earth.
B.E. = (1/2) GMm / r
Binding energy of satellite at rest on the surface of the earth
B.E. = GMm /R
Define escape velocity
The minimum velocity with which a body should be projected from the surface of the Earth so that it escapes Earth’s gravitational field is called the escape velocity of the body.
Equation for escape velocity
Ve= root(2GM/r)
Or
Ve= root(2gR)
Why is there a feeling of weightlessness in a satellite?
Feels weight due to normal.
In satellite both man and satellite falling towards the earth with acceleration ‘g’. So, he can’t exert weight on floor and satellite does not provide normal reaction.
Variation of g with altitude
g at height h = g [1-(2h/R)]
Variation of g with depth
g at depth d= g[1- (d/r)]
Variation of g with latitude
g’ = g - Rwwcos(φ)cos(φ)
Where is the maximum reduction in acceleration due to gravity?
Equator
Where us there no reduction in acceleration due to gravity
Poles
Define geostationary satellite
An artificial satellite revolving in a circular orbit round the earth in an equatorial plane in the same sense as rotation of the earth and having the same period of revolution as rotation of the Earth is called a geostationary satellite.
Why is a geostationary satellite called so?
Relative velocity = 0
Appears stationary from earths surface
Uses of satellites
- Transmission of telephone and radiowave signals over large areas of earths surface
- Broadcasting telecommunications
- Military purposes
- Weather forecasting and meteorological purposes
- Astronomical observations
- Study of solar and cosmic radiations
- Relay distress signals from ships
- Transmit cyclone warnings to coastal villages.
- For Geoposition Systems (GPS)
