# Physics Unit 4 The Newtonian World

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Newton’s Laws of Motion

Newton’s First Law

·        An object either remains at rest or keeps travelling at constant velocity provided no resultant force acts.

Newton’s Second Law

·        The net force acting on an object is equal to the rate of change of the linear momentum of an object. (F=ma is just a special case where m is constant)

Linear Momentum () = mass of an object (m) x velocity (v)

Net Force on a body is the rate of change of momentum

(N or kgms-2) - Net Force

- Change in Momentum

- Change in Time

Newton’s Third Law

·        When two objects interact, the forces they exert on each other are equal in magnitude and opposite in direction.

Impulse (Ns or kgms-1) = force x change in time = Change in Momentum

In a force against time graph, the area underneath in the impulse

Collisions

Principle of Conservation of Momentum

·        The total momentum before a collision = the momentum after a collision, provided no external forces act

Elastic and Inelastic Collisions

·        In an elastic collision, the total kinetic energy of the system remains constant. Momentum and total energy are conserved.

·        In an inelastic collision, the total kinetic energy in not conserved. Some of the KE is transformed into heat, sound, etc. Momentum and total energy is conserved.

·        A total inelastic collision is when the two bodies stick together and they move off with the same velocity

Circular Motion

Period (T) is the time it takes for an object to make a complete orbit around its circular path.

Circumference of a Circle is  radians

The Angular Displacement  of a body is the angle in radians through which a point has been rotated.

s - Arc length

One Radian is when the Arc Length is equal to the radius

Conversions

Tangential Velocity

t is for time

Angular Velocity

·        Is the rate at which the object’s angular displacement changes (the rate at which it is going around the circle)

Centripetal

Definition – Moving or trending towards a centre.

Centripetal Acceleration (a)

An object moving along a circular path has a changing velocity, even if its speed is constant. It is being accelerated towards the centre of the circle.

Centripetal Force

A force that acts on a body moving in a circular path and is directed toward the centre around which the body is moving

Using the equation   we get:

Gravitational Fields

Newton’s Law of Gravitation

·        This law states that any two bodies attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them

Gravitational Force

F - The force due to the gravitational attraction between the two objects (N)

G – The Gravitational Constant

M – Mass of the