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How much of classical physics can be purely derived from Newton's 3 Laws of motion?

Can Newton's laws derive conservation of momentum? Or any other conservation laws?

Consider this example

Let there be no external forces.

When standing in a stationary bus and the bus accelerates forwards, the person thrusts in the direction opposite the acceleration of the bus.

How do you explain this?

1. Newton’s third law, every action has an equal and opposite reaction. A 10N force exerted by the bus to the right means a 10N force on the person to the left. The person weighs less than the bus so accelerates more to the left than the bus to the right.

2. Conservation of linear momentum. The centre of mass of the initial system is stationary so centre of mass will stay in the one place as long as no external forces act. When the bus moves to the right, the person must move to the left in order to maintain the original position of the centre of mass. However the bus is much heavier so the person has to move faster to the left in order to maintain the position of the centre of mass. Hence the person accelerates quicker to the left.

Both explanations match observation although using different principles. So I wonder whether the two principles are linked, if not derivable from each other?

OR is it the case that classical physics is usually explanined from conservation laws plus Newton's Laws? So the conservation laws and Newton's laws are separate?

Can Newton's laws derive conservation of momentum? Or any other conservation laws?

Consider this example

Let there be no external forces.

When standing in a stationary bus and the bus accelerates forwards, the person thrusts in the direction opposite the acceleration of the bus.

How do you explain this?

1. Newton’s third law, every action has an equal and opposite reaction. A 10N force exerted by the bus to the right means a 10N force on the person to the left. The person weighs less than the bus so accelerates more to the left than the bus to the right.

2. Conservation of linear momentum. The centre of mass of the initial system is stationary so centre of mass will stay in the one place as long as no external forces act. When the bus moves to the right, the person must move to the left in order to maintain the original position of the centre of mass. However the bus is much heavier so the person has to move faster to the left in order to maintain the position of the centre of mass. Hence the person accelerates quicker to the left.

Both explanations match observation although using different principles. So I wonder whether the two principles are linked, if not derivable from each other?

OR is it the case that classical physics is usually explanined from conservation laws plus Newton's Laws? So the conservation laws and Newton's laws are separate?

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