"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."
The rate of change of angular velocity of a body is called angular acceleration.
The component of acceleration directed towards the centre of the circular path is called centripetal acceleration (or radial acceleration).
The force directed towards the centre along the radius, required to keep a body moving along a circular path at constant speed, is called centripetal force.
When a particle moves with a constant speed in a circular path, its motion is said to be uniform circular motion.
OR
The motion of a body moving with constant speed along a circular path is called uniform circular motion.
OR
The motion of a body moving with constant speed along a circular path, where the velocity is always tangential to the circular path and remains constant in magnitude, is called uniform circular motion.
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.
The angle traced out by the radius vector at the centre of the circular path in a given time, expressed as Δθ = θ2 − θ1, is called angular displacement.
The rate of change of angular displacement of a body undergoing circular motion is called angular velocity.
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.
OR
The amount of work done against conservative forces which causes a change in P.E. is called potential energy.
The gravitational potential energy per unit mass at a point is called gravitational potential.
The amount of work done in bringing a given body from infinity to that point against the gravitational force is called gravitational 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
\[v_e=\sqrt{\frac{2GM}{R}}\]
Statement:
The law which states that every particle of matter attracts every other particle in the universe with a force whose magnitude is directly proportional to the product of masses and inversely proportional to the square of distance between them is called Newton's Law of Gravitation.
Derivation:
Newton's Universal Law of Gravitation states that every particle of matter attracts every other particle of matter with a force which is:
Combining both, the gravitational force is expressed as:
F = G\[\frac{m_1m_2}{r^2}\]
where G is the Universal Gravitational Constant, measured by Henry Cavendish using the Cavendish balance, with the value:
G = 6.67 × 10−11Nm2/kg2
