In physics, you will often decide to make assumptions or idealizations. When you do, you should always consider the three questions below.
Figure2.5.1.Questions to ask when you make an assumption.Figure2.5.2.Introducing the particle model, an example of an assumption in physics.
The motion of real objects is often extremely complicated. For example, when you toss a coin, it will likely rotate so that different parts of the coin move at different speeds, and in different directions.
To begin to investigate motion, you will make a simplifying assumption that an object in motion can be treated as a particle. When you make this assumption, you are using the particle model because you are modeling the motion of an object as if it were a particle.
Assumption2.5.3.The Particle Model.
When you assume that a system can be treated as a point particle, you treat it as only undergoing translational motion (motion without rotation). Under this assumption, you treat all the mass of the system as existing at the object’s center of mass 1 .
When you encounter a new assumption, you might want to consider not just when it is good to make the assumption, but instead when the assumption might fail. As an assumption, the particle model tends to fail when there is (important) rotational motion or when your system has multiple pieces that are moving differently. For example, sliding a spinning top may not be a good example for the particle model, as the translational motion is deeply tied with both the top’s shape and rotation.
The particle model is almost always useful because it is extremely simple (like many of the assumptions you will make). However, by assuming an object is a particle, you are neglecting information about its size, extent, and rotation. The particle model is most reasonable when these properties do not have a substantial impact on its translational motion. Once you have a firm understanding of translational motion, you can amend your model to include other kinds of motion. Within the particle model, you sometimes make a further assumption to consider motion only along a straight-line path (one-dimensional translational motion) rather than motion in two- or even three-dimensions.
ExercisesActivities: Applying the Particle Model
For each of the following contexts, do you think it is reasonable to use the particle model? Why or why not? What object or system are you treating as a particle?
1.
You drive your car from Corvallis to Portland.
2.
You throw a softball from one base to another.
3.
You slowly open a heavy door.
4.
An Olympic athlete does a flip while snowboarding.
5.
Two snowballs break into pieces as they collide in midair.
center of mass is a property you will not need until you begin studying rotational motion
