Units and Measurements
Motion in a Plane
Laws of Motion
- Introduction to Laws of Motion
- Aristotle’s Fallacy
- Newton’s Laws of Motion
- Inertial and Non-inertial Frames of Reference
- Types of Forces
- Work Energy Theorem
- Principle of Conservation of Linear Momentum
- Concept of Collisions
- Impulse of a Force
- Rotational Analogue of a Force - Moment of a Force Or Torque
- Couple and Its Torque
- Mechanical Equilibrium
- Centre of Mass
- Centre of Gravity
Mechanical Properties of Solids
Thermal Properties of Matter
Electric Current Through Conductors
Electromagnetic Waves and Communication System
- Projection of Satellite
- Weightlessness in a Satellite
- Time Period of a Satellite
- Binding Energy of an orbiting satellite
Any object revolving around the earth.
Satellite created by nature.
Example: - Moon is the only natural satellite of the earth.
Humans built objects orbiting the earth for practical uses. There are several purposes which these satellites serve.
Example:- Practical Uses of Artificial satellites are
Determining the Time period of Earth Satellite:-
Time taken by the satellite to complete one rotation around the earth is known as the time period of the satellite.
As satellites move in circular orbits there will be a centripetal force acting on it.
`"F"_c = "mv"^2/("R"_e + h)` it is towards the centre.
h = distance of the satellite from the earth
`"F"_c` = centripetal force.
`"F"_G = ("GM"_e"m")/("R"_e + "h")^2`
`"F"_g` = Gravitational force
m = mass of the satellite.
`"M"_e` = mass of the earth
`"F"_c = "F"_G`
`"mv"^2/("R"_e + "h")=("GM"_e"m")/("R"_e + "h")^2`
`"v"^2 = "GM"_e/("R"_e + "h")`
`"v" = sqrt("GM"_e/("R"_e +"h"))` ...(1)
This is the velocity with which satellite revolves around the earth.
The satellite covers distance = `2pi("R"_e +"h")` with velocity v.
`"T"=(2pi("R"_e + "h"))/"v"`
h << `"R"_e` (satellite is very near to the surface of the earth)
`"T" = 2pisqrt("R"_e/"g")`
Shaalaa.com | motion of satellites
Consider earth satellites in circular orbits. A geostationary satellite must be at a height of about 36000 km from the earth's surface. Will any satellite moving at this height be a geostationary satellite? Will any satellite moving at this height have a time period of 24 hours?
Two satellites A and B move round the earth in the same orbit. The mass of B is twice the mass of A.
A satellite is orbiting the earth close to its surface. A particle is to be projected from the satellite to just escape from the earth. The escape speed from the earth is ve. Its speed with respect to the satellite
A pendulum having a bob of mass m is hanging in a ship sailing along the equator from east to west. When the ship is stationary with respect to water the tension in the string is T0. (a) Find the speed of the ship due to rotation of the earth about its axis. (b) Find the difference between T0 and the earth's attraction on the bob. (c) If the ship sails at speed v, what is the tension in the string? Angular speed of earth's rotation is ω and radius of the earth is R.
A body stretches a spring by a particular length at the earth's surface at the equator. At what height above the south pole will it stretch the same spring by the same length? Assume the earth to be spherical.
At what rate should the earth rotate so that the apparent g at the equator becomes zero? What will be the length of the day in this situation?