Anyone who has ever instinctively braced her hands on a car's dashboard in anticipation of the vehicle coming to a sudden stop understands the concept of inertia, even if she has never devoted any specific thoughts to the laws of physics.
It may not occur to this alert passenger that the same physical principle explains why she consciously tilts her head back against her seat's head rest whenever the driver is about to depress the gas pedal: She knows from experience that a "lead-footed" driver is apt to put her at risk for whiplash and subject her to a rearward-directed force when the car takes off.
Moving down the urgency scale, trying to get the last bit of salad dressing or ketchup out of a bottle by shaking it, getting a running start in athletic events like the long jump and the continued oscillation of a rocking chair after you stop trying to rock it all represent examples of the law of inertia, Newton's first law of motion, in everyday life.
On an everyday level, you might hear a friend joke that "inertia" kept him or her from getting out of bed and doing a 5-mile run that morning. While such forgivable indolence is not technically a formal example of inertia in the world of physics, this kind of lighthearted chatter about one's own supposed resemblance to a sloth is nevertheless illustrative of one of the most important concepts in all of applied physics.
What Is Inertia in Physics?
The principle of inertia describes the tendency of an object to remain in a state of rest or remain in motion at a constant velocity. It is thus a measure of an object's resistance to changing its state, be it a moving body or something sitting on a table. If an object has more inertia, it requires more work to change its state, be it rest or a constant velocity. Correspondingly, objects with less inertia are in easier-to-change states.
One reason the "constant velocity" aspect may not be intuitive is the existence of friction. When you kick a ball down a field, it bounces and eventually rolls to a stop because of the friction of the turf. But if the playing field could be rendered frictionless, the ball would keep going forever at a constant velocity unless stopped by an outside force. (Needless to say, this state of things would also certainly affect the rules of play of ball games – and everything else – on Earth.)
- Sometimes, you'll see the law of inertia mentioned with the term "constant speed" instead of "constant velocity." While true, this is not descriptive enough; speed is only a magnitude (number value), whereas velocity is a vector quantity and therefore includes direction (x, y, z) as well.
Newton's Laws of Motion
Isaac Newton (1642-1726) remains the possessor of one of the most remarkable intellects in human history, having in effect assembled the mathematical discipline of calculus from scratch and contributing knowledge about the motion of bodies that inspired Galileo Galilei, a great architect of astrophysics ideas in his own right, and countless others.
Newton's first law is sometimes called the law of inertia because it describes this tendency of an object as dependent on the presence or absence of an external force. With no net force on a object, its motion will not change. As such, this law is not a contributor to the equations of motions also developed by Newton, perhaps helping to explain why some students are unfamiliar with it.
Newton's second law proposes that forces act to accelerate masses, or mathematically,
This law relates net force in a system, including the direction, to the mass and motion of its particles. To calculate net force, you simply take the vector sum of all forces acting on the object. Finally, Newton's third law asserts that for every force there exists an equal and opposite force in nature – the "equal and opposite reaction" also sometimes applied jokingly but tellingly in everyday language.
Why Inertia Is Important
The basic project of all of physics is understanding the motion of objects, including many the human eye cannot see and particles whose existence may be little more than a playful idea. Real-world applications of the law of inertia include the design of safety devices for vehicles, including but not limited to seat belts, that can provide an external force to stop a body's motion in the event of a sudden change in the physics of the immediate environment.
The inertia of an object also has interesting uses in space travel. For example, once a device escapes Earth's gravity, it will continue on its given trajectory until it encounters another gravitational field or object. Space probes can be sent great distances without any additional fuel required other than that needed to "escape" Earth, enact minor navigational changes or land on another object.
As discussed earlier, objects set in motion on Earth do not immediately appear to be "intent" on continuing at a constant velocity because of the external force of friction. Because friction is virtually everywhere (even air imposes a great deal of it at higher velocities) and is constantly slowing objects down unless additional forces are continually added to combat it, the sheer breadth of the law of inertia is not intuitive.
Moment of Inertia
Sometimes called rotational inertia, the moment of inertia is the angular analogue of inertia. It is a property of a body that depends on the body's mass, radius and axis of rotation. Inertia I is to rotational motion what mass is to linear motion, but although inertia and mass are analogues, inertia has units of mass times the square of distance (e.g., kg⋅m2).
This quantity describes how hard or easy it is to change an object's rotation, including getting it started rotating or stopping it when it is already rotating.
Also, whereas linear kinetic energy is expressed as
rotational kinetic energy is given by
where ω represents angular velocity in radians per second.
Rotational Inertia: Further Discussion
It is important to recognize that the concept of inertia would make no sense without recourse to reference frames, or inertial frames. An inertial frame is one that can be treated as stationary so that other objects in the frame can be assigned meaningful values for v, a, r and so on. It is a frame in which Newton's laws therefore apply. A grid coordinate system is usually superimposed on part of this frame, which is often Earth itself.
While the Earth, for all practical purposes, is "fixed" in relation to most everyday human endeavors, careful experiments can show that physical data collected in a lab in a given location differs slightly over time thanks to the rotation of the Earth along with its revolution around the sun, translational motion through the Milky Way Galaxy itself and so on.
Personal experience also seems to present violations of the law of inertia. In almost all cases, this misunderstanding arises from unknowingly treating a reference frame as inertial when it is not. For example, if you are on a moving merry-go-round, especially one with a high angular velocity, you feel as if you are being accelerated sideways at all times, rather than feeling like your body "wants" to keep moving in a straight line tangent to the edge of the merry-go-round.
- Stanford University: Newton's Three Laws of Motion
- BC Open Textbooks: Newton’s First Law of Motion: Inertia
- Physics LibreTexts: Newton’s First Law of Motion: Inertia
- Georgia State University: HyperPhysics: Moment of Inertia
- University of New South Wales: Inertial Frames, Newtonian Mechanics and Why the Laws Are the Same in the Train and on the Platform