Table of Contents

Physics is about trying to find the simple laws that describe all natural phenomena using a vast range of mass, length, and time scales. These scales are defined by systems of units that are built up from a small number of base units, which are set by accurate and precise measurements of conventionally chosen base quantities. Accuracy refers to how close a measured value is to an accepted reference value while precision refers to how close the agreement is between repeated measurements.

The theory of relativity led to a profound change in the way we perceive space and time. The “common sense” rules that we use to relate space and time measurements in the Newtonian worldview differ seriously from the correct rules at speeds near the speed of light. Unlike Newtonian mechanics, which describes the motion of particles, or Maxwell's equations, which specify how the electromagnetic field behaves, special relativity is not restricted to a particular type of phenomenon.

Vectors are essential to physics and engineering. Many fundamental physical quantities are vectors, including displacement, velocity, force, and electric and magnetic vector fields. Scalar products of vectors define other fundamental scalar physical quantities, such as energy. Vector products of vectors define still other fundamental vector physical quantities, such as torque and angular momentum.

When you drive across a bridge, you expect it to remain stable. You also expect to speed up or slow your car in response to traffic changes. In both cases, you deal with forces. The forces on the bridge are in equilibrium, so it stays in place. In contrast, the force produced by your car engine causes a change in motion. Isaac Newton discovered the laws of motion using forces to describe these situations.

One-dimensional kinematics describes motion along a straight line using functions such as velocity and acceleration. These functions calculate the object's rate of change in properties like time and position. Relationships between the functions are determined using derivatives and integral calculus. Vectors geometrically indicate the object's motion at any given instant with respect to a given function.

A complete description of kinematics explores motion in two and three dimensions given most objects in the universe move along curved paths. This description heavily uses vectors to represent the functions investigated in the previous section in three-dimensional space. Projectile motion and uniform circular motion are the two most common types of motion along curved paths. In the real world, the reference frames of the kinematic functions must be defined in order to analyze motion properly.

Newton's laws of motion can be applied in numerous situations to solve motion problems. Some scenarios contain multiple force vectors acting in different directions on an object while others contain several physical quantities such as forces, acceleration, and position. All of these problems can be solved using concepts from kinematics and dynamics. But additional forces to consider in these situations are drag force, friction, and centripetal force.

Work, kinetic energy, and power are basic physical concepts that are involved in every physical motion in the universe. An exploration of how these quantities are related to one another will lead to the discovery of the work-energy theorem. The usefulness of such a theorem lies in the modest amount of calculations required to solve problems applying Newton's laws that relate the forces acting on an object to the accelerations that they produce.

Potential energy is a significant concept that allows for the formulation of the law of conservation of mechanical energy which can be applied to simple systems to make solving problems easier. Conservation is a physical property of a given quantity stating that it stays constant regardless of the path taken to get to the quantity's final state. The law of conservation of energy will be applied in increasingly more detail through situations involving more complex and varied systems.

Linear momentum is a conserved quantity that describes how the motion of an object depends on its mass and velocity. The impulse-momentum theorem is another relationship that puts an additional constraint on how a system evolves in time. Conservation of momentum is useful for understanding collisions in which it is just as powerful, just as important, and just as useful as conservation of energy and the work-energy theorem.

We begin to address rotational motion in this chapter, starting with fixed-axis rotation. Fixed-axis rotation describes the rotation around a fixed axis of a rigid body; that is, an object that does not deform as it moves. We will show how to apply all the ideas we’ve developed up to this point about translational motion to an object rotating around a fixed axis. In the next chapter, we extend these ideas to more complex rotational motion.

Quantum mechanics is a powerful framework for understanding the motions and interactions of particles at small scales, such as atoms and molecules. The ideas behind quantum mechanics often appear quite strange. In many ways, our everyday experience with the macroscopic physical world does not prepare us for the microscopic world of quantum mechanics. The purpose of this chapter is to introduce you to this exciting world.