Newton’s Second Law states that when a net force acts on an object, the change in the object’s state of motion will be inversely proportional to the mass of the object and directly proportional to the net force acting on the object.

**Newton’s second law of motion** is closely related to Newton’s first law of motion. It mathematically states the cause and effect relationship between force and changes in motion. Newton’s second law of motion is more quantitative and is used extensively to calculate what happens in situations involving a **force.** It states that when a net force acts on an object, the change in the object’s state of motion will be inversely proportional to the mass (*m*) of the object and directly proportional to the net force (*F _{net}*) acting on the object. It can be written as:

*F _{net} = ma*

The equation illustrates that the acceleration of a **system** is directly proportional to and in the same direction as the **net external force** acting on the system, and inversely proportional to its mass. The effect of the force, **acceleration**, is a change in the object’s velocity (in magnitude, direction, or both). The smaller the mass experiences a given force, the greater its acceleration. The greater a mass experiences a given force, the smaller its resulting acceleration or effect of that force. The direct proportionality between *F *and *a* demonstrates that for a given mass, the greater the force, the greater the acceleration.

**F**_{net }= *m***a** is used to define the units of force in terms of the three basic units for mass, length, and time. The SI unit of force is called the **newton** (abbreviated N) and is the force needed to accelerate a 1-kg system at the rate of 1 m/s^{2}. That is, since **F**_{net }= *m***a**, 1 N = 1 kg ⋅ m/s^{2}.

While almost the entire world uses the newton for the unit of force, in the United States the most familiar unit of force is the pound (lb), where 1 N = 0.225 lb.

When an object is dropped, it accelerates toward the center of Earth. Newton’s second law states that a net force on an object is responsible for its acceleration. If air resistance is negligible, the net force on a falling object is the gravitational force, commonly called its *weight* w. Weight can be denoted as a vector w because it has a direction; *down* is, by definition, the direction of gravity, and hence weight is a downward force. The magnitude of weight is denoted as *w**. *In the absence of air resistance, all objects fall with the same acceleration *g*.

The equation for *weight*—the gravitational force on a mass m:

*w = mg
*g = 9.80 m/s

^{2}(on Earth)

When the net external force on an object is its weight, we say that it is in **free-fall**. That is, the only force acting on the object is the **force of gravity**. In the real world, when objects fall downward toward Earth, they are never truly in free-fall because there is always some upward force from the air acting on the object.

Remember, it is important to be aware that **weight** and **mass** are very different physical quantities. Mass is a scalar measurement, the quantity of matter (how much “stuff”,) and does not vary in classical physics. Meanwhile, weight is a vector measurement, the gravitational force, and varies depending on gravity.

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**Practice Questions**

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**Key Points**

• Acceleration (*a*) is defined as a change in velocity, meaning a change in its magnitude or direction, or both.

• An external force is one acting on a system from outside the system, as opposed to internal forces, which act between components within the system.

• Newton’s second law of motion states that the acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass.

• In equation form, Newton’s second law of motion is: a= Fnet/m

• This is often written in the more familiar form: **F**_{net }= *m***a**.

• The weight **w** of an object is defined as the force of gravity acting on an object of mass *m*. The object experiences an acceleration due to gravity** g**: **w** = *m***g**.

• If the only force acting on an object is due to gravity, the object is in free fall.

• Friction is a force that opposes the motion past each other of objects that are touching.

Key Terms

**Newton’s second law of motion**: States when a net force acts on an object, the change in that object’s state of motion will be inversely proportional to the mass (*m*) of the object and directly proportional to the net force (*F*) acting on the object. It can be written as *F = ma*.

**Force**: A force is any interaction that, when unopposed, will change the motion of an object. A force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate.

**System**: A portion of the physical universe chosen for analysis. Everything outside the system is known as the environment. The environment is ignored except for its effects on the system.

**Net external force**: The vector sum of all external forces acting on an object or system; causes a mass to accelerate.

**Acceleration**: The rate at which an object’s velocity changes over a period of time.

**Newton**: A newton (N) is the international unit of measure for force. One newton is equal to 1 kg*m/s^2

**Free-fall**: A situation in which the only force acting on an object is the force due to gravity friction: a force past each other of objects that are touching; examples include rough surfaces and air resistance.

**Gravity: **The natural force that causes things to fall toward the earth; is written as *g *in equations (g = 9.8 m/s^{2}).

**Mass: **The measure of the amount of matter in a substance or an object.

**Weight:** The weight of an object is related to the force acting on the object, either due to gravity or to a reaction force that holds it in place.