Mechanics is the branch of physics dealing with the motion of objects. Understanding mechanics is critical to any future scientist, engineer or curious human who wants to figure out, say, the best way to hold a wrench when changing a tire.

Common topics in the study of mechanics include Newton's laws, forces, linear and rotational kinematics, momentum, energy and waves.

## Newton's Laws

Among other contributions, Sir Isaac Newton developed three laws of motion that are crucial to understanding mechanics.

- Every object in a state of uniform motion will remain in that state of motion unless an external force acts on it. (This is also known as the
*law of inertia.*) - Net force equals mass times acceleration.
- For every action there is an equal and opposite reaction.

Newton also formulated the universal law of gravitation, which helps describe the attraction between any two objects and the orbits of bodies in space.

Newton's Laws do such a good job predicting the motion of objects that people often refer to his laws and the predictions based on them as Newtonian mechanics or classical mechanics. However, these calculations do not *precisely* describe the physical world under all conditions, including when an object is travelling near the speed of light or working on an incredibly small scale – special relativity and quantum mechanics are fields that allow physicists to study motion in the universe beyond what Newton could investigate.

## Forces

Forces *cause* motion. A force is essentially a push or a pull.

Different types of forces that a high school or introductory college student is sure to encounter include: gravitational, friction, tension, elastic, applied and spring forces. Physicists draw these forces acting on objects in special diagrams called *free-body diagrams* or *force diagrams*. Such diagrams are critical in finding the net force on an object, which in turn determines what happens to its motion.

Newton's laws tell us that a net force will cause an object to change its velocity, which can mean its speed changes *or* its direction changes. No net force means the object stays just how it is: moving at a constant velocity or at rest.

A *net force* is the sum of multiple forces acting on an object, such as two tug-of-war teams pulling on a rope in opposite directions. The team that pulls harder will win, resulting in more force directed their way; that's why the rope and the other team end up accelerating in that direction.

## Linear and Rotational Kinematics

Kinematics is a branch of physics that allows the motion to be described simply by applying a set of equations. Kinematics *does not* refer to the underlying forces, the cause of the motion, at all. This is why kinematics is also considered a branch of mathematics.

There are four main kinematics equations, which are sometimes called the equations of motion.

The quantities that can be expressed in the kinematic equations describe *line__ar motion* (motion in a straight line), but each of these can also be expressed for *rotational motion* (also called circular motion) using analogous values. For instance, a ball rolling along the floor linearly would have a *linear velocity v*, as well as an *angular velocity ω*, which describes its rate of spinning. And whereas a *net force* causes a change in linear motion, a *net torque* causes a change in an object's rotation.

## Momentum and Energy

Two other topics that fall into the mechanics branch of physics are momentum and energy.

Both of these quantities are *conserved,* which means, in a closed system, the total amount of momentum or energy cannot change. We refer to these types of laws as conservation laws. Another common conservation law, usually studied in chemistry, is conservation of mass.

The laws of conservation of energy and conservation of momentum allow physicists to predict the velocity, displacement and other aspects of the motion of various objects that interact with one another, such as a skateboard rolling down a ramp or billiard balls colliding.

## Moment of Inertia

Moment of inertia is a key concept in understanding rotational motion for different objects. It is a quantity based on the mass, radius and axis of rotation of an object that describes how difficult it is to change its angular velocity – in other words, **how hard it is to speed up or slow down its spinning**.

Again, since rotational motion is *analogous* to linear motion, moment of inertia is analogous to the linear concept of inertia, as stated by Newton's first law. More mass and a larger radius give an object a higher moment of inertia, and vice versa. Rolling an extra-large cannonball down a hallway is harder than rolling a volleyball!

## Waves and Simple Harmonic Motion

Waves are a special topic in physics. A mechanical wave refers to a disturbance that **transfers energy through matter** – a water wave or a sound wave are both examples.

Simple harmonic motion is another type of periodic motion in which a particle or object oscillates around a fixed point. Examples include a small-angle pendulum swinging back and forth or a coiled spring bouncing up and down as described by *Hooke's law*.

Typical quantities physicists use to study waves and periodic motion are period, frequency, wave speed and wavelength.

Electromagnetic waves, or light, are another type of wave that can pass through empty space because energy is carried not by matter, but by oscillating fields. (*Oscillation* is another term for *vibration.*) While light does act like a wave and its properties can be measured with the same quantities as a classical wave, it also acts as a particle, requiring some quantum physics to describe. Thus, light doesn't *entirely* fit into the study of classical mechanics.

## Math in Classical Mechanics

Physics is a very mathematical science. Solving mechanics problems requires knowledge of:

- Vectors vs. scalars
- Defining a system
- Setting a reference frame
- Vector addition and vector multiplication
- Algebra, and for some two-dimensional motion, trigonometry
- Velocity vs. speed
- Distance vs. displacement
- Greek letters – these are often used for units and variables in physics equations

## One-Dimensional Motion vs. Motion in Two Dimensions

The scope of a high school or introductory college physics course usually includes two levels of difficulty in analyzing mechanics situations: looking at one-dimensional motion (easier) and two-dimensional motion (harder).

Motion in one dimension means the object is moving along a straight line. These types of physics problems can be solved using algebra.

Motion in two-dimensions describes when an object's motion has both a vertical and a horizontal component. That is, it is moving in **two directions at once***.* These types of problems can be multi-step and may require trigonometry to solve.

Projectile motion is a common example of two-dimensional motion. Projectile motion is any type of motion where the only force acting on the object is gravity. For example: a ball being thrown in the air, a car driving off a cliff or an arrow being shot at a target. In each of these cases, the object's path through the air traces the shape of an arc, moving both horizontally and vertically (either up and then down, or just down).