Newton’s Laws of Motion - UNLV Faculty

Newton's Laws of Motion

1. Law of Uniform Motion Every object continues in its state of rest or of uniform motion in a straight line unless a force changes the motion.

2. Law of Acceleration The rate of change of motion of an object is proportional to the force applied "on" the object and in the direction of the line of application of the force.

3. Law of Action-Reaction For every force applied "on" an object, there is an equal and opposite force applied "by" the object.

These laws of motion are used to describe the forces (kinetics) causing motion (kinematics).

Kinetics is the branch of mechanics that is focused on understanding the forces causing motion.

Law of Uniform Motion

Of course, you already know all about the Law of Uniform Motion since this is really just stating an observation. Consider, for example, a block placed on a table. Clearly you know that the block won't move unless someone (or something) pushes on the ball. This is (in essence) Newton's 1st Law: The object won't have a change in motion unless something pushes or pulls on the object. Something that is helpful is to replace the word `motion' with the kinematic parameter `velocity.' In this example, the velocity of the block is zero and it will remain zero until something pushes or pulls on it to give it some velocity.

Now, consider that the object is pushed and has some velocity. What happens then? In reality, the object slows down and stops. Before Newton (well, really, before Galileo), the understanding of physics was that all objects eventually came to rest (i.e., the natural state is zero velocity). That made sense because that is what we see happen. However, Newton looked at things a bit different and thought, what would happen to that block if it was given some velocity while placed on a really, really slippery surface? In that case, the block would continue to move with a constant velocity. The point Newton was making was that the block would only have a change in motion if a force was applied to it (in the first example, that force slowing the block down is known as Friction force).

Ok, so Newton's 1st Law is rather obvious and is just a statement relating the observation of kinematics and kinetics. Since the law mentions force, the purpose of the next law was to define what a force is.

Law of Acceleration

Our first definition of a force is a `push or a pull that tends to cause motion.' The force does not need to cause motion (e.g., I can push on a wall but not move it). To understand this law, we need to always identify the forces acting "on" the object. In other words, we need to identify any pushing or pulling `on' the object.

A force is a vector quantity and therefore is described by magnitude and direction. When drawing forces, we will use arrows with the magnitude of the force represented by the length of the arrow and the direction represented by the direction of the arrow. Additionally, other parameters used to understand the effect of a force are line of application and point of application of the force. The line of application of a force is the straight line projection of a force in both directions while the point of application is where the force is acting on the object.

Let's consider that a force does act on a ball (below) in such a way as to change its motion. What effect does a force have on motion? Let's consider two balls of identical size but of different weights resting on the table:

A

B

16 lb

1 lb

Consider identical forces (i.e., same magnitude and direction) applied to each ball, what will happen? Will ball A have the same change in motion as ball B? Hopefully you said "No, Ball B will have a greater change in motion." Why? First, consider that the 16 lb and 1 lb weights are forces, and during this course, we will typically use the SI units of Newtons to represent force. Clearly the heavier the object, the less effect a given force will have on changing motion. OK, good observation. However, it is not `weight' that determines the effect of the force; rather it is the object's inertia.

Inertia: The measure of an object's resistance to change motion (Note that the word `CHANGE' is very important to the definition of inertia).

Inertia is quantified by the measure of an object's mass. You may remember that an object's weight is the product of an object's mass and the acceleration due to the force of gravity. Or, W = mg

In SI units, the units of mass are kilograms (kg), and the acceleration due to gravity is 9.8 m/s2. Now, consider the Ball A and B above have weights of 71.3 N and 4.4 N, respectively. Rearranging the weight equation, m =W/g. Therefore, Ball A has a mass of 7.3 kg and Ball B has a mass of 0.4 kg.

Newton's 2nd Law of Motion, Law of Acceleration, states that the acceleration of an object is proportional to the magnitude of the force exerted upon it and inversely proportional to the mass of the object. Mathematically, this law of motion is defined as:

Fon = ma

units: kgm/s2 = N

Where Fon are the forces acting "on" the object, `m' is the mass of the object and `a' is the acceleration of the object.

Or, rearranging, a = Fon/m

Therefore, the ball with the greater mass (Ball A) undergoes less acceleration than Ball B for a given force because of the difference in inertia. In other words, Ball A has a greater resistance to change motion (i.e., inertia) than Ball B.

Remembering that a = v/t, we can rewrite Newton's 2nd law of motion as:

F = mv/t

We can rewrite the equation as:

F = (mv)/t

Now, we can restate Newton's 2nd Law of Motion: An object's rate of change of momentum is proportional to the force applied to the object.

Momentum is an object's quantity of motion and is calculated as:

p = mv

units: kgm/s

Finally, we can rearrange F = (mv)/t as:

Ft=(mv)

This is known as the Impulse-Momentum relationship.

Impulse is defined as the length of time a force is applied to an object (Ft). Technically, an impulse causes a change in motion. This relationship is a very important relationship to understand when investigating human performance.

Consider landing from a jump. Can you land `softly' and `stiffly'? Is there a difference in kinematics in how you do these different landing strategies? Considering that your change in momentum is identical regardless of landing style, can you explain the mechanical differences between strategies?

Law of Action-Reaction

So Newton's 1st Law of Motion is really just stating an observation while Newton's 2nd Law of Motion is defining what a force does. The key to using Newton's 2nd Law is to identify all the forces acting "on" the object. That is, if we know all the pushing/pulling on the object, we can understand that object's acceleration.

Newton's 3rd Law of Motion is key to the laws of motion and states that for every force acting "on" and object there is an equal and opposite reaction force caused "by" the object. For example, if I push on the wall, the wall pushes back on me. If I push on a ball, the ball pushes back on me.

The key to using Newton's Laws of Motion is to identify the forces acting "on" an object to understand that object's motion. However, sometimes we are interested in the forces caused "by" an object. In that case, often what we do is measure the reaction force and then conceptually understand that the force is in reaction to the one we are interested in.

For example, when running and walking, we push down on the Earth. In the Biomechanics Lab, we use a force platform to measure the reaction force to the amount of pushing the person exerts on the ground. Therefore, we refer to these forces as Ground Reaction Forces (GRF). That is, we do not actually measure the force of the person pushing ... instead, we measure the reaction to that pushing.

The important aspect of Newton's 3rd Law of Motion is that for every force, there is an equal (magnitude) and opposite (direction) force. The key to using Newton's 2nd Law of Motion is to identify only the forces acting "on" an object ? when we do that, we can understand the change in motion (F=ma) of the object. That being said, sometimes, we will discuss the forces caused "by" the object ... but when we do that, we still need to identify the forces acting "on" the object to use Newton's 2nd Law.

Exercise Can you construct a PVA relationship illustrating the COM vertical motion during running? Remembering that F=ma, the acceleration is the acceleration of person's Center of Mass (COM). Start vi=-1 m/s and ai = -9.8 m/s2. Next, construct a Vertical Force vs. time plot considering F = ma, where m = mass of runner. Compare your theoretical plot to actual data collected in the laboratory.

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