Physics / Mechanics

# Gravitation and Circular Motion

According to Newton's Universal Law of Gravitation, there will always be an attractive force bewteen one particle and another particle in this universe and the magnitude of this force is directly proportional to the product of the masses of these particles and inversely proportional to the square of the distance that is separating them.

## Newton's Law of Gravitation

• Gravitational force is always attractive and it originates because of the mass of the body. Gravitational force remains constant irrespective of the medium between the two objects.

• The gravitational force of attraction between two bodies with masses 'm1' and 'm2' and which are separated by a distance 'd' is directly proportional to the product of their masses and inversely proportional to square of the distance between them.

Formula wise, Newton's law of gravitation can be expressed as, F α m1m2/d2

• Acceleration due to Gravity :
• Acceleration due to gravity is the acceleration that is gained by an object towards the other object due to its gravitational pull. Acceleration due to gravity of Earth (g) is 6 times more when compared to acceleration due to gravity of Moon. Acceleration due to gravity (g) of earth is 9.806 m/s2

• The value of 'g' depends on, (i) Shape of the Earth (g at Equator is less than g at Poles), (ii) Latitude (g increases from 00 - 900), (iii) Altitude (with height, g decreases) and (iv) Depth (with depth, g decreases).

## Projectile Motion

Any body which is projected with some angle to the horizontal plane is called a Projectile. It traces a two dimensional path called parabolic path. It has two velocities, one along the horizontal direction and other along the vertical direction. The horizontal velocity of a projectile remains constant throughout its motion. Its vertical velocity first decreases while ascending, becomes zero at the topmost point in its path and increases thereafter while descending.

• Orbital Velocity : The velocity with which a body has to be projected horizontally to the ground in order to make it go round the earth in a fixed orbit is called orbital velocity.

Vo = √(gR) = 7.92 km/s (where R is the radius of the earth).

• Escape Velocity : The velocity with which a body has to be projected in order to make it escape the gravitational pull of the earth is called escape velocity.

Ve = √(2gR) = 11.2 km/s.

• Geostationary Orbit : It is the circular orbit which lies in the Equatorial plane of the earth at a height of 36,000km from the surface of the earth.

## Circular Motion

• If an object is tied to a string and rotated circularly, the tension in the string works as Centripetal force for the body moving in the circular path. The force required to make a body to rotate is Centripetal force.

• A body when rotates, experiences an apparent outward force on it, known as Centrifugal force.

The Centrifugal force experienced by the rotating body,

F = mv2/r, where 'm' is the mass of the body, 'r' is the radius of the string and 'v' is the tangential velocity.

Inertia of direction is the cause for the centrifugal force, which is nothing but an outward acting force exerted on rotating particles.

• Centrifugation is nothing but subjecting a body to centrifugal force and Centrifuge is an instrument for applying centrifugal force on particles.

In order to separate different particles of a compound material, they are subjected to centrifugation. As the masses differ from particle to particle, the magnitude of centrifugal force differs for each particle and hence they are thrown out with different forces.