Gravitational acceleration

Gravitational acceleration, written as g, is the acceleration an object gains from gravity alone, equal to about 9.81 m/s² near Earth's surface. It's the same for every freely falling object regardless of mass.

What is gravitational acceleration?

Gravitational acceleration is how fast an object's velocity changes when gravity is the only force acting on it. Near Earth's surface that value is about $g = 9.81 \text{ m/s}^2$, which means a falling object gains 9.81 m/s of speed every second it falls. We use the symbol $g$ for it everywhere in this course.

The surprising part is that $g$ doesn't depend on the object's mass. A bowling ball and a feather would fall with the same acceleration if you removed air resistance, because heavier objects feel more gravitational force but also have more inertia to overcome. Those two effects cancel exactly. The value of $g$ does shift slightly with location, getting a bit weaker at high altitude and at the equator compared to the poles, but for problems in Principles of Physics I you'll usually treat it as a constant 9.81 m/s² (or 9.8) pointing straight down.

Why gravitational acceleration matters in Principles of Physics I

Gravitational acceleration shows up the moment you start applying Newton's Laws of Motion (Topic 4.2). When you write a free-body diagram for a falling or thrown object, the gravitational force is $F_g = mg$, and dividing that by mass gives you the acceleration $g$. It's the connection between force and motion for anything near Earth.

It also drives gravitational potential energy (Topic 12.2), where the stored energy $U = mgh$ uses the same $g$. Whenever you track energy in free fall, a swinging pendulum, or a projectile, $g$ is the bridge between height and energy. Getting comfortable with it early makes kinematics, dynamics, and energy conservation problems much smoother.

How gravitational acceleration connects across the course

Free Fall (Unit 4)

Free fall is the situation where gravity is the only force acting, so the object's acceleration is exactly g. Every free-fall kinematics problem plugs g into equations like v = v₀ + gt.

Weight and f_g = mg (Unit 4)

An object's weight is the gravitational force on it, found by multiplying its mass by g. Same g, but weight changes with mass while the acceleration stays constant.

Gravitational Potential Energy (Unit 12)

GPE uses U = mgh, the same g you use for falling objects. This lets you swap between energy stored at a height and speed gained on the way down.

Newton's Law of Universal Gravitation (Unit 4)

Setting the universal gravitation force equal to mg shows where the 9.81 m/s² value actually comes from: it depends on Earth's mass and radius.

Is gravitational acceleration on the Principles of Physics I exam?

Expect to use g constantly. On problem sets and quizzes you'll plug it into kinematics equations for objects thrown or dropped, into $F_g = mg$ for free-body diagrams, and into $U = mgh$ for energy problems. A common task is solving for fall time or final speed given a height, or finding a mass's weight from its mass. Watch for sign conventions: g points downward, so whether you write it as +9.81 or -9.81 depends on which direction you called positive. You may also be asked conceptual questions, like why two objects of different mass hit the ground at the same time in free fall.

Gravitational acceleration vs Weight

Gravitational acceleration (g) is a rate of velocity change measured in m/s² and is the same for all objects. Weight is a force measured in newtons, found by multiplying mass by g, so it changes with mass. Two objects can share the same g while having very different weights.

Key things to remember about gravitational acceleration

• Gravitational acceleration g is about 9.81 m/s² near Earth's surface and points straight down.

• Every freely falling object accelerates at g regardless of its mass, because more gravitational force is balanced by more inertia.

• The gravitational force on an object is its weight, calculated as F_g = mg.

• The same g that appears in free-fall kinematics also appears in gravitational potential energy, U = mgh.

• g varies slightly with altitude and latitude, but you'll usually treat it as a constant 9.81 m/s² in this course.

Frequently asked questions about gravitational acceleration

What is gravitational acceleration in physics?

It's the acceleration an object gains from gravity alone, written as g and equal to about 9.81 m/s² near Earth's surface. That means a freely falling object speeds up by 9.81 m/s every second.

Do heavier objects fall faster than lighter ones?

No. Ignoring air resistance, all objects fall with the same acceleration g, so a heavy and a light object dropped together hit the ground at the same time. Heavier objects feel more force but also have more inertia, and the two effects cancel.

How is gravitational acceleration different from weight?

Gravitational acceleration g is a rate measured in m/s² and is the same for every object. Weight is the gravitational force on an object, measured in newtons and found by F_g = mg, so it depends on the object's mass.

Why is g 9.81 m/s² on Earth?

It comes from Newton's law of universal gravitation applied at Earth's surface, where the force depends on Earth's mass and radius. Dividing that force by an object's mass gives an acceleration of about 9.81 m/s².

Does gravitational acceleration change with location?

Slightly. It's weaker at higher altitudes and a bit smaller at the equator than at the poles, but in most Principles of Physics I problems you treat g as a constant 9.81 m/s² (sometimes rounded to 9.8).