(16) Newton and His Laws

Lesson Plan for Newton and His Laws

 Isaac Newton

Isaac Newton was born in 1642, the year Galileo died. Almost all his creative years were spent at the University of Cambridge, England, first as a student, later as a greatly honored professor. He never married, and his personality continues to intrigue scholars to this day: secretive, at times cryptic, embroiled in personal quarrels with scholars, bestowing his attention not just on physics and mathematics, but also religion and alchemy.

The one thing everyone agrees on is his brilliant talent. Three problems intrigued scientists in Newton's time: the laws of motion, the laws of planetary orbits, and the mathematics of continuously varying quantities--a field nowadays known as [differential and integral] calculus. It may be fairly stated that Newton was the first to solve all three.

Newton's laws of motion

The laws of motion are of special concern here, because both orbital motion and the principle of rocket motion are based on them.

Newton proposed that all motions conform to three principles, formulated in mathematical terms and involving concepts which he was the first to define rigorously. One such concept was force, the cause of motion, another was mass, a measure of the amount of matter set in motion; the two are usually denoted by the letters F and m. "Newton's three laws of motion" are stated below, in modern terms: as will be seen, they all need quite a bit of explanation.

(1) In the absence of forces, an object ("body") at rest will stay at rest, and a body moving at a constant velocity in a straight line continues doing so indefinitely.

(2) When a force is applied to an object, it accelerates. The acceleration a is in the direction of the force and proportional to its strength, and is also inversely proportional to the mass being moved:

a = k(F/m)

where k is some number, depending on the units in which F, m and a are measured. With proper units (we will come back to that), k = 1 giving

a = F/m

or in the form usually found in textbooks

F = m a

More accurately, one should write

F = ma

with both F and a vectors in the same direction (denoted here in bold face, though this convention is not always followed on this web site). However, when only a single direction is understood, the simpler form can also be used.

(3) "The law of reaction," sometimes stated as "to every action there exists an equal and opposite reaction." In more explicit terms:

"Forces are always produced in pairs, with opposite directions and equal magnitudes. If body #1 acts with a force F on body #2, then body #2 acts o n body #1 with a force of equal strength and opposite direction."

The First Law

The prime example of motion, and probably the only kind which before Newton's time could be mathematically described, is that of falling objects. However, other motions also exist--especially, horizontal motions in which gravity does not play the leading role. Newton addressed those as well.

Consider a hockey puck sliding on a sheet of ice. It can travel great distances, and the smoother the ice, the further it goes. Newton realized that what ultimately stopped such motions was the friction of the surface. If an ideally smooth ice could be produced, with no friction at all, the puck would continue indefinitely, in the same direction and with the same velocity.

That is the gist of the first law: "straight motion at a constant velocity does not require any forces." Adding such a motion to any other motion does not bring any new forces into play, everything stays the same: in the cabin of a jetliner moving in a straight line at a constant velocity of 600 miles per hour, nothing is changed--coffee pours the same way, and a spoon still falls straight down.

The Third Law

The third law, the law of reaction, states that forces never occur singly, but always in equal and opposite pairs. Whenever a gun fires a bullet, it itself recoils backwards. Firefighters aiming the nozzle of a big hose at a fire must grasp it firmly, because as the jet of water shoots out of it, the hose itself is forcibly pushed back (rotating garden sprinklers work by the same principle). In a similar way, the forward motion of a rocket comes from the reaction of the fast jet of hot gas shooting out from its rear.

Those familiar with small boats know that before jumping from a boat to the dock, it is wise to tie the boat to the dock first, and to grab a handhold on the dock before jumping. Otherwise, even as you jump, the boat "magically" moves away from the dock, possibly making you miss your leap or pushing the boat out of reach. It is all in Newton's third law: as your legs propel your body towards the dock, they also apply to the boat an equal force in the opposite direction, which pushes it away from the dock.

The Bicycle

A more subtle example is afforded by the bicycle. It is well known that balancing a bicycle standing still is almost impossible, while on a rolling bike it is quite easy. Why?

Different principles are at work in each case. Suppose you sit on a bike that stands still, and find it is leaning to the left. What do you do? The natural tendency is to lean to the right, to counterbalance the lean with your weight. But in moving the top of your body to the right, by Newton's 3rd law you are actually pushing the bike to lean more to the left. Maybe you should lean to the left and push the bike back? It might work for a fraction of a second, but now you are really out of balance. No way!

On a rolling bike, balance is kept by a completely different mechanism. By slightly turning the handlebars right or left, you impart some of the rotation of the front wheel (angular momentum) to rotate the bike around its long axis, the direction in which it rolls. That way the rider can counteract any tendency of the bike to topple to one side or the other, without getting into the vicious circle of action and reaction.

To discourage thieves, some bikes contain a lock which clamps the handlebars in a fixed position. When such a bike is locked in the forward-facing direction, it can be rolled by a walking person, but it cannot be ridden because it cannot be balanced.

Next Stop: #17 Mass

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Author and curator: David P. Stern