Lesson 2: Newton's First Law and Inertia

2.1 Observation and the old belief

• Imagine returning home after a long trip: everything is as you left it.
• This simple fact, "things stay as they are unless something changes them", is the basis of Newton's first law.

• Everyday experience seems to contradict it: if you push a box on the floor, it slides some distance, slows down and stops.
• Ancient thinkers concluded that rest is the natural state of matter and that every motion dies away.
• Experiments showed that this is wrong: the box stops because of friction, a force opposing its sliding.
• If friction did not exist (as on very smooth ice, or in space) the box would go on moving for ever without stopping.

2.2 Statement of the law

Newton's first law of motion: An object remains at rest, or moves with constant velocity in a straight line, unless a resultant force acts on it and changes this state.

Mathematical form: ΣF = 0 (the object keeps its state)

where ΣF is the resultant of all forces acting on it. Several forces may act, but if they cancel each other the resultant is zero.

2.3 Consequences of the first law

• If ΣF = 0, then a = 0: the velocity does not change, whether the object is at rest or moving.
• A force is needed to start a stationary object moving or to stop a moving one (that is, to change its velocity).
• No force is needed to keep an object moving at constant velocity (only to cancel friction/air resistance). A car moving steadily on a straight road has an engine force that exactly balances the resistances: ΣF = 0.

Example 1. A car moves at a steady 25 m/s along a straight road. The engine force is 900 N forward. What is the resistance to motion? Since the velocity is constant, ΣF = 0, so the resistance is 900 N backward.

Example 2. A book rests on a table: its weight (downward) is balanced by the table's upward force; ΣF = 0, so it remains at rest.

2.4 Inertia

Newton's first law is also called the law of inertia.

Inertia is the tendency of a stationary object to remain at rest, and of a moving object to continue moving with the same velocity in a straight line; that is, objects resist any change in their state of rest or motion.

Everyday examples of inertia

• A passenger standing in a bus is thrown forward when the bus brakes suddenly: his body tends to keep moving forward.
• When a train suddenly moves forward, a small bag lying under a seat appears to slide backward relative to the train, because it tends to stay at rest while the train moves forward under it.
• A card under a coin on a glass: flick the card away quickly and the coin drops into the glass, since it tends to remain at rest.

Measure of inertia. Observation shows that the difficulty of stopping a moving body depends on its mass and its velocity:

• A large truck is hard to stop, a small bicycle is easy, if they move at the same velocity.
• A car moving fast is hard to stop; the same car moving slowly is easy to stop. The two factors together define a new quantity, the momentum.