"Every particle of matter in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The direction of the force is along the line joining the particles."
or
The force by which the Earth attracts objects towards its centre is called gravitational force.
Centripetal force is the force acting on a body moving in a circular path, in a direction towards the centre of the circular path.
OR
A force acts on any object moving along a circle and it is directed towards the centre of the circle. This is called the Centripetal force.
Define Centripetal force.
At each of circular path, the particle, instead of moving straight continuously, turn towards the centre. Therefore, the motion in the circular path is under the action of a force called the centripetal force.
"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."
Define Uniform circular motion.
When a particle moves with a constant speed in a circular path, its motion is said to be the uniform circular motion.
Define angular velocity.
Angular velocity of a particle is the rate of change of angular displacement.
When a particle moves with a constant speed in a circular path, its motion is said to be uniform circular motion.
The gravitational force due to the earth on a body results in its acceleration. This is called acceleration due to gravity and is denoted by ‘g’. Acceleration is a vector.
The weight of an object is defined as the force with which the earth attracts the object.
Mass is the amount of matter present in the object. The SI unit of mass is kg.
Define acceleration due to gravity.
The acceleration produced in a body under the influence of the force of gravity alone is called acceleration due to gravity.
"Potential energy is the work done against conservative force (or forces) in achieving a certain position or configuration of a given system."
OR
The energy stored in an object because of its position or state is called potential energy.
"The minimum velocity with which a body should be thrown vertically upwards from the surface of the Earth so that it escapes the Earth’s gravitational field, is called the escape velocity (ve) of the body."
Newton’s Universal Law of Gravitation:
F = \[G\frac{m_1m_2}{r^2}\]
where:
Kepler’s Third Law relates the time period T of a planet’s revolution to the semi-major axis a of its elliptical orbit:
T2 ∝ a3
where,
The area swept by the planet of mass m in a given interval Δt is:
\[\Delta\vec{A}=\frac{1}{2}(\vec{r}\times\vec{v}\Delta t)\]
The gravitational force of attraction (F) between two bodies of mass m1 and m2 separated by a distance r is:
F: Gravitational Force of attraction (in Newtons, N).
\[m_1, m_2\]: Masses of the two objects (in kilograms, kg).
r (or d in the first part): Distance between the two objects (in meters, m).
G: The constant of proportionality, called the Universal gravitational constant.
Value in SI units: \[G=6.67\times10^{-11}\mathrm{N}\cdot\mathrm{m}^2/\mathrm{kg}^2\]
Dimensions: \[[G]=[\mathrm{L}^3\mathrm{M}^{-1}\mathrm{T}^{-2}]\]
Based on the relationship between work and energy, the change in potential energy is given by:
\[\vec F\] · d\[\vec x\] = dU
\[v_e=\sqrt{\frac{2GM}{R}}\]
