In this explainer, we will learn how to define Newton’s first law of motion and analyze systems of forces that produce no net acceleration.

There are three very familiar intuitive ideas about the motion of objects and the forces acting on those objects:

- If an object is at rest, it must be the case that no forces act on it.
- If an object is moving, it must be the case that forces act on it.
- If no forces act on a moving object, the object will come to rest.

These intuitive ideas are all incorrect, and Newton’s first law of motion contradicts them.

Newton’s first law of motion tells us that an object can remain at rest while forces act on it, provided that these forces are balanced.

What exactly is meant by balanced forces?

We can recall that force is a vector quantity, so it has a direction as well as a magnitude. If we consider forces that act along the same line, we can consider forces that act in one direction along the line to be positive and forces that act in the opposite direction to be negative, as shown in the following figure.

The forces shown have the same magnitude but act in opposite directions. The force shown by the red arrow is positive and the force shown by the blue arrow is negative.

These forces can be summed, as the following figure shows.

We can see that the sum of the forces is zero. When the sum of a set of forces is zero, these forces are balanced. If the sum of the forces is nonzero, the forces are unbalanced.

The following figure shows an object acted on by two sets of forces, both of which are balanced. The magnitudes of the two forces acting on the object are equal for both sets of forces.

The sum of the forces in either set is zero, so the forces do not act to change the velocity of the object.

The following figure shows an object that is acted on by two sets of forces, both of which are unbalanced.

The object acted on by either of these sets of forces cannot remain at rest, and the velocity of the object must increase in the direction of the net force acting on it.

It is worth noting that if only one force acts on an object, it is necessarily unbalanced.

Let us look at an example about balanced forces.

### Example 1: Identifying the Conditions for the Equilibrium of an Object That Two Forces Act on

Fill in the blanks: An object that is initially at rest and has two forces acting on it will remain at rest if the forces acting on it have and act in .

- the same magnitude, opposite directions
- the same magnitude, the same direction
- different magnitudes, opposite directions
- different magnitudes, the same direction

### Answer

The object is initially at rest. For the object to remain at rest with forces acting on it, the velocity of the object must not change. This means that the forces acting on the object must be balanced.

We can draw a diagram for each of these possibilities, showing the forces acting in each case.

The following figure shows the case where the forces have the same magnitude and act in the same direction.

The following figure shows the case where the forces have different magnitudes and act in the same direction.

In both these cases, the sum of the forces is equivalent to a force acting in the same direction as either of the forces. This is then equivalent to a single force acting on the object, and any single force acting on an object cannot be balanced. We see then that the forces must act in opposite directions.

The following figure shows the case where the forces have different magnitudes and act in opposite directions.

The following figure shows the case where the forces have the same magnitude and act in opposite directions.

We can see that the only case where the forces sum to zero is when the forces have the same magnitude and act in opposite directions. If we use and to represent the forces, we can express this as

The sum will only be zero if the magnitudes of the forces are equal.

We have just shown that a balanced set of forces does not change the velocity of an object. Newton’s first law of motion tells us that the velocity of an object is independent of the forces acting on it.

To see how the velocity of an object is independent of the forces acting on it, let us consider a ball that accelerates as it rolls down a slope, continues to roll along a horizontal surface at constant speed, and then again accelerates as it rolls down a second slope. The position of the ball at equal time intervals is shown in the following figure.

Let us recall one of the familiar intuitive but incorrect ideas about the motion of objects and the forces acting on those objects, remembering that this idea is incorrect. The idea is that if an object is moving, it must be the case that forces act on it.

According to this incorrect idea, a force acts on the ball in the direction of its motion at all times, as shown in the following figure.

This model of the motion of and forces on the ball cannot be correct, as the ball does not change velocity while moving on the horizontal surface, so the net force on the ball is zero while it is on the horizontal surface.

A common incorrect assumption that is made when Newton’s first law of motion is not understood is that when the ball rolls at constant speed along the horizontal surface, no forces act on the ball. This incorrect model of the motion of and forces on the ball is shown in the following figure.

One of the reasons why this model is incorrect is that it cannot explain why the force that acts on the ball while it is on the slope stops acting when the ball moves on the horizontal surface and then starts to act again when the ball reaches the second slope.

According to Newton’s first law of motion, when the ball is on the slope, its speed increases, meaning that the velocity of the ball changes, and so unbalanced forces must act on the ball. It will be helpful to consider what the forces that act on the ball are.

We know that the weight of the ball is a force that acts on the ball. We know two important facts about the weight of the ball:

- The weight of the ball acts at all times.
- The weight of the ball acts vertically downward.

If the weight of the ball was the only force acting on the ball, the ball would increase in velocity whether it was on a slope or on a horizontal surface, as the weight acts at all times. The weight always acts vertically downward, so the direction of increase of the velocity of the ball would be vertically downward. This would result in the ball moving like a ball falling freely. Clearly this is not how the ball is actually observed to move.

The observed motion of the ball can be correctly explained by Newton’s first law of motion by recognizing that two forces act on the ball at all times, one of which is the weight of the ball.

When the ball is on the horizontal surface, the two forces are balanced, and when the ball is on a slope, the forces are unbalanced. The forces acting on the ball are shown in the following figure.

The force shown in red is the weight of the ball, and the force shown in blue is the normal reaction force on the ball due to its contact with the surface supporting it.

We can see that the velocity of the ball on the horizontal surface is independent of the forces acting on the ball while it is on the surface. The velocity of the ball when it is on the horizontal surface is the result of the increase of its velocity as it rolled down the first slope. The velocity gained by the ball due to rolling down the first slope merely remains unchanged while the ball rolls along the horizontal surface.

Let us look at an example involving balanced weight and reaction forces.

### Example 2: Determining the Reaction Force on an Object in Equilibrium

A book at rest on a table has a weight of 8 N.

- At what rate is the book accelerating?
- What is the net force acting on the book?
- What magnitude force does the table apply to the book?

### Answer

The book is at rest on a table. As the book is at rest, its velocity is zero and does not change from zero; otherwise, the book would not remain at rest.

The fact that the velocity of the book does not change means that the book has zero acceleration, and this means that the forces on the book must be balanced.

The weight of the book acts vertically downward and has a magnitude of 8 N. To balance the weight of the book, the table must exert a vertically upward force on the book with the same magnitude as the weight of the book.

In summary, the acceleration of the book is zero, the net force on the book is zero, and the magnitude of the force that the table applies to the book is 8 N.

The ball rolling at constant speed along a horizontal surface and the book from the preceding example that is at rest on a table both have balanced forces acting on them, and the velocities of both the ball and the book are constant. A velocity of zero that remains zero is a constant velocity. We see from this that being at rest is just a special case of having a constant velocity, where the value of the constant velocity is zero for an object at rest.

Newton’s first law of motion has an important implication, which is that if an object is not acted on by unbalanced forces, not only will the velocity of the object not increase, but also it will not decrease. An object that has a constant velocity will continue to move with this velocity unless a force acts on it.

An object moving in a straight line and that has no unbalanced forces act on it will continue to move in a straight line without changing speed. A motion of this type is not usually observed on Earth, as moving objects experience friction from surfaces they are in contact with as well as resistance from the air. Objects moving along very low-friction surfaces like ice are observed to travel a greater distance before coming to rest than over surfaces with greater friction. An object moving in a straight line along a surface with zero friction, inside a container from which all air had been removed, would move without slowing until it reached the edge of the container anyway.

Let us now look at an example in which the motion of an object that is not acted on by any frictional force is considered.

### Example 3: Identifying the Directions of the Forces Acting on a Satellite

A satellite orbits Earth at a constant speed, traveling in a circle around Earth. Which of the following diagrams correctly shows the forces acting on the satellite, where the forces are shown by black arrows? The satellite is completely outside Earth’s atmosphere and has no engine.

### Answer

The question states that the satellite is completely outside Earth’s atmosphere. Obviously, the satellite is also not in contact with Earth. Together, these facts mean that no frictional forces act on the satellite.

The satellite has a mass, and so it must be acted on by a weight force. It is a misconception that if a satellite is beyond Earth’s atmosphere then no weight force acts on it. It is worth noting that malfunctioning satellites sometimes fall to Earth, which would be impossible if no weight force acted on satellites.

The weight of the satellite acts toward Earth. Diagrams (a) and (c) do not show a weight force so they must be incorrect and can be eliminated.

The satellite is stated to have no engine, so it has no way of producing the force shown in diagram (e) that acts in the direction of the satellite’s velocity. Diagram (e) must be incorrect and can be eliminated.

We are left then with diagrams (b) and (d). In diagram (d), the forces on the satellite are balanced. With no unbalanced forces acting on it, the satellite would necessarily move in the direction of its current velocity. The direction of the current velocity shown in diagram (d) is away from Earth, so the satellite would have to move away from Earth in a straight line. The question states, however, that the satellite orbits Earth, moving along a circular path. This alone makes diagram (d) incorrect, but it is also worth noting that diagram (d) shows a force acting on the satellite in the opposite direction to its weight, and no such force could be acting on the satellite.

By eliminating all the other diagrams, we see that diagram (b) is correct. We can see independently of the other diagrams that diagram (b) is correct, as the only force acting on the satellite is its weight. This is correct as the satellite has no engine and no friction acts on it. Having a single force acting means that the forces on the satellite are necessarily unbalanced and so the satellite does not continue to move in the direction of its current velocity, as it would if the forces on it were balanced. Instead, the satellite moves on a circular path around Earth, traveling at a constant speed.

There is no force acting on the satellite in the opposite direction to its velocity, so no force acts to slow the satellite. This explains why the satellite orbits Earth at a constant speed, not slowing down. As long as no force acts on the satellite other than its weight, it will continue to orbit Earth for an unlimited time.

Let us now look at an example involving testing the understanding of Newton’s first law of motion.

### Example 4: Defining Newton’s First Law of Motion

Which of the following statements most correctly describes Newton’s first law of motion?

- An object will not change its velocity unless a net force acts on the object.
- An object will not move unless a net force acts on the object.
- An object will move until a net force acts on the object.
- An object will change direction if a net force acts on the object.

### Answer

Let us first determine whether it is correct to say that an object will move until a net force acts on it.

This is clearly incorrect as an object can be at rest and have no net force act on it.

Let us next determine whether it is correct to say that an object will not move unless a net force acts on it.

It is correct to say that an object that a net force acts on cannot remain at rest. This does not necessarily mean that an object that no net force acts on cannot be moving. The object could have been moving before the net force on it became zero. If so, the object would continue to move after the net force on it became zero. The velocity of the object would no longer change but would not become zero if it was not already zero.

Let us next determine whether it is correct to say that an object will change direction if a net force acts on it.

If the net force on an object is in a direction that is not the direction of the current velocity of the object, then the object will indeed change direction, as it will accelerate in the direction of the net force. If the net force acts in the opposite direction to that of the current velocity of the object, then, if it acts for enough time, it will reverse the direction of the velocity of the object. A net force can act in the same direction as that of the current velocity of the object, in which case it will not change the direction in which the object moves.

Finally, let us next determine whether it is correct to say that an object will not change its velocity unless a net force acts on it.

We can test the correctness of this statement by asking how an object would move if no net force acted on it. According to Newton’s first law of motion, the object will remain at rest if it was already at rest, and if it was moving at a velocity, it will continue to move at that velocity. In either case, the velocity of the object would not change. It is therefore correct to say that an object will not change its velocity unless a net force acts on it, and so this statement is the closest in meaning to Newton’s first law of motion of the four options.

Let us look at another such example.

### Example 5: Recognizing the Possible Motion of and Forces Acting on an Object That No Net Force Acts on

The net force on an object is zero.

- Which of the following statements about the object must be true?
- The speed of the object is constant.
- The speed of the object is zero.
- A single force with a magnitude greater than zero acts on the object.
- Multiple forces with magnitudes greater than zero act on the object.

- Which of the following statements about the object must be false?
- A single force with a magnitude greater than zero acts on the object.
- Multiple forces with magnitudes greater than zero act on the object.
- The speed of the object is constant.
- The speed of the object is zero.

### Answer

**Part 1**

Let us first consider which of the statements must be true for an object with no net force acting on it.

The object can be at rest or have a constant nonzero velocity, so the speed of the object need not be zero.

The net force on the object due to a single force cannot be zero, so it cannot be true that a single force acts on the object. This does not necessarily mean that multiple forces must be acting on the object, as the object could have no forces acting on it.

The only necessarily true statement is that the speed of the object must be constant, as the velocity of the object must be constant.

**Part 2**

And now, let us consider which of the statements must be false for an object with no net force acting on it.

We have shown that the object could be at rest or moving at a constant speed, so we are incorrect if we say that “the speed of object is zero” must be false or that “the speed of the object must be constant” must be false. A speed of zero is a constant speed, so these two options are equivalent.

Multiple forces could act on the object and balance each other to result in zero net force, so we are incorrect if we say it must be false that multiple forces can act on the object to produce zero net force.

If a single force with a magnitude greater than zero acts on the object, this is necessarily an unbalanced force, so it must be false to say that a single force with a magnitude greater than zero acts on an object on which the net force is zero.

In summary, the answer to the first part of the question is that the speed of the object is constant and the answer to the second part of the question is that a single force with a magnitude greater than zero acts on the object.

Let us now summarize what we have learned in these examples.

### Key Points

- A single force acting on an object necessarily produces a nonzero net force on it.
- Multiple forces acting on an object can balance to produce either zero or nonzero net force.
- The velocity of an object must change if a nonzero net force acts on it.
- The velocity of an object does not change unless a nonzero net force acts on it.
- An object at rest that is acted on by zero net force will remain at rest for an unlimited time as long as the net force acting on it continues to be zero.
- A moving object that is acted on by zero net force will continue to move without any change of direction or speed for an unlimited time as long as the net force acting on it continues to be zero.