 # Newton's Laws of Motion Isaac Newton, English physicist and mathematician, 1642-1727

### Isaac Newton

Without a doubt, Isaac Newton is the most prolific and influential scientist in history. His application of empirical principles and his mathematical inventions revolutionised science, producing the laws which explain the phenomena of the universe: motion, gravity and optics.

He was the first to explain and quantify force, as an action at a distance. This means that gravity is the same for an apple and for the Moon, revealing the gravitational field. Later, the same principles were applied successfully to electrical fields.

Nature and nature's laws lay hid in night;
God said "Let Newton be" and all was light.

Alexander Pope, an epitaph for Newton.

##### Newton's First Law of Motion
An object at rest will remain at rest, and an object in motion will continue to move at constant velocity, unless a net force is applied.

Consequences:
• Equilibrium: a system in equilibrium is one in which the net force on the system is zero
• Conservation of Momentum in both elastic and inelastic collisions
• Conservation of kinetic energy in elastic collisions but not inelastic.
• Conservation of angular momentum.
Examples to help visualise the concept:
Newton's First Law of Motion in action: A hammer head will keep moving when the handle stops because of inertia.
• Striking a hammer handle vertically on a table, so that the hammerhead is driven on to the handle more firmly: the handle is caused to decelerate rapidly due to the reaction force of the table. The hammer head will continue to move relative to the handle, due to its inertia. The only force resisting its motion is the friction of the head's socket against the shaft of the handle, which is lower than the reaction force of the table against the handle, causing the head to slip down the handle shaft until firmly wedged into place.

### Equations

ρ = mv

where ρ is the momentum, and m is the mass of an object moving at constant velocity v.

##### Newton's Second Law of Motion
When a net force is applied to an object it changes its motion according to: F = ma, where F is the net force, m is the mass, and a is the resultant acceleration in the same direction as the net force.

#### Grand Unified Theory

Newton's F = ma is probably the most famous equation in science, matched only by Einstein's \$E = mc^2\$ for recognisability by the general public.

Both of these equations express an assumption, certainly believed by both Newton and Einstein, that the fundamental rules of nature will be simple. Both geniuses searched for the grand unified theory of everything - a simple explanation which explains all natural phenomena. The search continues, primarily through research into particle physics and string theory, and discoveries like the Higg's boson take us a small step closer to realising this ambitious dream.

Consequences:
• A force must be applied to cause work to be done upon a mass, or to change its energy or position in a gravitational field.
• There is a difference between mass (kg) and weight (N). Gravitational acceleration is the same for all masses in the same gravitational field, but the gravitational force (weight) is proportional to the mass being accelerated.
• Planetary motion can be explained as acceleration towards the focus of the orbit (centre of a large mass, such as the Earth for the Moon and satellites, and the Sun for all other members of the solar system family of objects), even though speed is largely constant. The force in this case is centripetal.
##### Equations

Fnet = ma

where \$F_{net}\$ is ∑F, the sum of all applied forces, which include friction and air resistance, and m is the mass of an object experiencing constant acceleration a

The unit of force is newton, N. In base units 1 N = 1 kg.m/s2

ρ = mv

where ρ is the momentum, and m is the mass of an object moving at constant velocity v

The unit of momentum is kg.m/s, or N.s

The Second Law of Motion may also be expressed in terms of the impulse on an object: the net force applied to an object will cause a change in the momentum. The impulse is the rate of change of linear momentum Fnet = δρ/δt, where Fnet is the sum of all forces acting on the mass, and δρ is the change in momentum ρ.

##### Newton's Third Law of Motion
When a net force is applied to a body, that body experiences an equal and opposite reaction force. Newton's Third Law of Motion is experienced by every application of force

Newton's Third Law of Motion means that any force will experience a force which acts equally in the opposite direction. It is why we 'feel' a wall push back at us, or when a skater pushes another, she will be pushed back in the opposite direction.

Consequences:
• Impacts result in force of equal magnitude being applied to both participants.
• Work is a measure of the energy used to change the condition of an object. When a billiard ball strikes another ball of equal mass in an ideal elastic collision, the second ball is accelerated to the velocity of the first ball, which stops. There is work done on both objects in order to exchange the kinetic energy.
• Momentum is conserved: Projectiles, such as bullets and rockets, cause an equal force of recoil in the opposite direction of their acceleration. This is also the reason that we risk injury stepping off skateboards too quickly, and that small boats are hard to step out of.
• In an accelerating frame, such as a lift, we experience a reaction force from the floor of the lift, which adds or subtracts from our apparent weight, depending on the direction of the lift's acceleration.
• The centripetal force of circular motion results in an equal and opposite centrifugal 'force'. More strictly an 'effect' than a true force, centrifugal force creates artificial gravity in rotating spaceships.
##### Action-Reaction Force Pairs Since Newton's Third Law states that every force will experience an equal and opposite reaction force. This is known as an action-reaction pair of forces. e.g. A man's weight is a reaction force upwards, equal and opposite to the gravitational attraction force downwards.

In the diagram, forces C and D are an action-reaction pair of forces, but A and B are. The friction force is not always equal to the applied force, since it is equal to the mass of the object times the coefficient of friction of the surface. A reaction force is produced by the applied force and is always equal in magnitude and opposite in direction.

##### Equations

Fapplied = Freaction

Apparent weight = Fg + ma

where Fg is the force of gravity on a mass (normal weight), m is the mass of the object, and a is the acceleration in the axis of the gravitational field (up or down).

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