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Laws of Motion
Newton’s first law of motion: An object continues to remain at rest or in a state of uniform
motion along a straight line unless an external unbalanced force acts on it.
Newton’s second law of motion : The rate of change of momentum is proportional to the
applied force and the change of momentum occurs in the direction of the force.
Newton’s third law of motion: Every action force has an equal and opposite reaction force
which acts simultaneously. [ Equal in magnitude and opposite in direction. ]
Centripetal force : In uniform circular motion of a body, the force acting on the body is
directed towards the centre of the circle. This force is called centripetal force.
Thus, 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. ‘Centripetal’ means centre seeking, i.e., the
object tries to go towards the centre of the circle because of this force.
Example : The moon revolves around the earth due to the gravitational force exerted on it by
the earth. This force is directed towards the centre of the earth and is thus a centripetal force.
Kepler's laws of planetary motion –
First Law: The orbit of a planet is an ellipse with the Sun at one of the foci.
Figure shows the elliptical orbit of a planet revolving around the Sun. S denotes the position of
the Sun.
Second Law: The line joining the planet and the Sun sweeps equal areas in equal intervals of
time.
AB, CD and EF are distances covered by the planet in equal intervals of time.
The straight lines AS, CS and ES sweep equal areas in equal intervals of time.
Area ASB = Area CSD = Area ESF.
Amjad Sir………………..9511794292
, Third Law: The square of the period of revolution of a planet around the Sun is directly
proportional to the cube of the mean distance of the planet from the Sun.
T2 ∝ r3,
i.e., T2/ r3 = constant = K.
Newton's universal law of gravitation : Every object in the Universe attracts every other
object with a definite force. This force is directly proportional to the product of the masses of
the two objects and inversely proportional to the square of the distance between them.
As the law of gravitation given by Newton is applicable throughout the universe and to all
particles. Hence it is called universal law.
Mathematical form of Newton's universal law of gravitation
Consider two objects of masses m1 and m2. We assume that the objects are very small
spheres of uniform density and the distance r between their centres is very large compared to
the radii of the spheres (Fig.).
The magnitude (F) of the gravitational force of attraction between the objects is directly
proportional to m1m2 and inversely proportional to r2
∴ F∝(m1m2)/r2
∴ F=(Gm1m2)/r2
Where G is the constant of proportionality, called the universal gravitational constant.
The above law means that if the mass of one object is doubled, the force between the two
objects also doubles. Also, if the distance is doubled, the force decreases by ¼ .
Note:_ in SI units, the unit of G is Nm2 kg-2.
The value of G was first experimentally measured by Henry Cavendish.
In SI units its value is 6.673 x 10-11 Nm2/ kg2
Uniform circular motion / Magnitude of centripetal force
If a planet is revolving around the Sun in a circular orbit in uniform circular motion, then the
centripetal force acting on the planet towards the Sun must be
F = mv2/r,
The speed of the planet can be expressed in terms of the period of revolution T as follows,
The distance travelled by the planet in one revolution =perimeter of the orbit=2 𝜋 r
Speed=Distance/Time
Amjad Sir………………..9511794292
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