Sample Answers

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Questions on Newton's Principia.

[Note: these are questions from p. 36 of our textbook. The questions you are supposed to answer are posted at the website, not in the textbook.]

1. How does Newton define quantity of matter' and quantity of motion'?

The quantity of matter is the combination of its density and volume. The quantity of motion is its velocity plus the quantity of matter.

2. How does Newton distinguish absolute and relative space?

Absolute space is the immovable context in which all else is understood to move. Relative space is the space in which any thing is understood to move relative to anything else.

3. What is the difference between absolute and relative motion?

Absolute motion is the change of position of a body from one absolute place to another; relative motion is the change of position of a body from one relative place to another.

4. How could one distinguish between the two in practice?

Only by referring to the motion of bodies relative to some body, place, or space we regard as immovable.

5. What was the point of the example of the bucket filled with water?

That bodies have absolute motions independent of their relative (apparent) motion.

6. State and explain each of Newton's three laws of motion.

(1) A body maintains straight-line motion unless affected by an external force: only air resistance and gravity restricts the motion of bodies. (2) Change is motion is proportional to and in the direction of external forces: when a body changes motion, it results from external forces. (3) For any action there is an equal and opposite reaction: motion in one direction with a certain force is balanced by a comparable opposite motion.

7. What are the four rules for the study of natural philosophy?

(1) The fewest number of causes should be used to explain nature. (2) Similar causes should be used to explain similar effects. (3) If certain qualities of bodies cannot be changed and are always found experimentally in bodies, they should be understood as characteristic of bodies universally. (4) Inductive generalizations of experiences should be assumed as true even if it is possible to explain phenomena with contrary hypotheses.

8. What purpose do these rules serve?

To provide a foundation for science ("natural philosophy") by presuming the uniformity and testability of nature and the transferability of knowledge in one area to another.