Aristotle’s fallacy

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NCERT Class 11 Physics Chapter 4 Section 4.2

Quick answer

Aristotle’s fallacy is the old belief that an external force is needed to keep a body moving. It is wrong: a body moving along the ground slows down because friction or air resistance acts against its motion, not because the push runs out. In uniform straight-line motion in an inertial frame, a steady push can balance resistance, leaving zero net force (F_net = 0).

With your textbook

NCERT Physics Part I (Class 11), Chapter 4 “Laws of Motion”, Section 4.2 “Aristotle’s fallacy”, page 50.

Open the official NCERT chapter (PDF, 2.1 MB, ncert.nic.in) (opens in a new tab)

Checked against the 2026-27 reprint on 19 Oct 2026.

What is Aristotle’s fallacy?

Aristotle’s law of motion, as NCERT phrases it

For our purpose here, the Aristotelian law of motion may be phrased thus: An external force is required to keep a body in motion.

NCERT Physics Part I (Class 11), Section 4.2, page 50

In plain words: Aristotle believed that a moving body keeps moving only while something keeps pushing or pulling it, and that it stops as soon as the push stops. This belief is wrong, and the mistake is called Aristotle’s fallacy.

In the Newtonian model, stated in an inertial frame, no net force is needed to keep a body moving at constant velocity. Galileo’s investigations helped establish this idea, which Newton expressed as his first law. A net force is needed only to change the velocity, that is, to start, stop, speed up, slow down or turn a body. When you push a box along the ground at a steady speed, your push does not drive the motion: it only cancels friction, so the net force on the box is zero.

Why the idea seems right

Aristotle’s view is not foolish. It is exactly what everyday life seems to show:

A toy car on a string. A child has to keep pulling the string to keep the car going. Let the string go, and the car soon stops.
A football on grass. A kicked ball rolls for a while and then comes to rest by itself.
An arrow in flight. Aristotle explained that an arrow keeps flying because the air behind it keeps pushing it.

Many objects sliding or rolling on ordinary terrestrial surfaces slow down and come to rest because resistive forces act on them. So it is natural to conclude that motion needs a force. The flaw is in why the bodies stop.

Where the argument goes wrong

NCERT answers the question directly:

What is the flaw in Aristotle’s argument? The answer is: a moving toy car comes to rest because the external force of friction on the car by the floor opposes its motion.

NCERT Physics Part I (Class 11), Section 4.2, page 50

So the body does not stop because the push has run out. It stops because another force, friction, acts against its motion. The child’s pull has a different job: it cancels friction.

When the toy car moves at a steady speed in a straight line, two horizontal forces act on it: the pull F of the string forward and the friction f of the floor backward. They are equal in size, so the net force is zero:

Uniform motion on a rough floor

F - f = 0

F_{\text{net}} = 0

This leads to the key corollary: if friction and drag were absent and the remaining forces balanced, no horizontal driving force would be needed to keep the car in uniform motion. The car would simply keep going.

When the pull is removed, friction is the only horizontal force left, so the car slows down with

a = -\frac{f}{m}

where m is the mass of the car and the minus sign means the acceleration is opposite to the motion.

Friction between solids, and viscous drag in liquids and air, are present almost everywhere around us. That is why a force is needed in practice to keep things moving, and why the fallacy lasted so long. To find the true law, Galileo imagined a world without friction, where a moving body never slows down. That idea became the law of inertia, which Newton stated as Newton’s first law of motion.

Question	Aristotle’s answer	The correct answer
Is a force needed to keep a body moving?	Yes, always	No net force; a push only cancels friction. A net force is needed only to change velocity
Why does a rolling ball stop?	The push runs out	Friction acts against its motion
Net force on a body in uniform motion	Forward, along the motion	Zero
What keeps an arrow flying?	The air behind it pushes it	Nothing is needed; gravity bends its path and air drag slows it

Seeing it in daily life

Cycling on a straight, level road. You keep pedalling at a steady speed only to balance air drag and rolling friction. Stop pedalling and these forces slow you down.
Pushing a loaded trolley. Once the trolley is moving, a steady push keeps it at a steady speed, because the push just matches friction. A harder push makes it speed up.
A puck on ice. Ice has very little friction, so a puck slides a long way after a single hit. The less the friction, the longer a body keeps moving without help.
A spaceship far from stars and planets. With its engines off, it keeps moving at constant velocity, because no net external force acts on it.

Solved examples

Example 1: Toy car on a string

A child pulls a toy car of mass 0.5 kg with a horizontal string. The car moves at a steady 0.6 m s^⁻¹ while the pull is 0.25 N. (a) What is the friction on the car? (b) The child lets go of the string. Assuming friction stays the same, find the car’s deceleration, the time it takes to stop and the distance it covers before stopping.

Given: m = 0.5 kg, F = 0.25 N, and the speed when the string is released is u = 0.6 m s⁻¹.

(a) The velocity is constant, so the net force is zero and friction balances the pull:

f = F = 0.25\ \text{N}

(b) After the release, friction is the only horizontal force. The magnitude of the deceleration is

\begin{aligned} a &= \frac{f}{m} = \frac{0.25\ \text{N}}{0.5\ \text{kg}} \\ &= 0.5\ \text{m s}^{-2} \end{aligned}

Taking a as this magnitude, the car stops (final speed v = 0) after

t = \frac{u}{a} = \frac{0.6}{0.5} = 1.2\ \text{s}

and from v² = u² − 2as with v = 0:

\begin{aligned} s &= \frac{u^{2}}{2a} = \frac{(0.6)^{2}}{2 \times 0.5} \\ &= 0.36\ \text{m} \end{aligned}

Answer: Friction is 0.25 N. After the release the car decelerates at 0.5 m s⁻², and stops after 1.2 s and 0.36 m. The car stops because of friction, not because the pull has “run out”.

Example 2: Pushing a box at a steady speed

A worker pushes a 20 kg box across a floor at a steady 0.5 m s^⁻¹ with a horizontal push of 60 N. (a) What is the friction on the box? (b) What push would make the box speed up at 0.2 m s^⁻², if friction does not change?

(a) Steady speed in a straight line means zero net force, so friction is f = 60 N, opposite to the push.

(b) Now the net force must produce the acceleration. By Newton’s second law of motion:

\begin{aligned} F - f &= ma \\ F &= f + ma \\ &= 60 + 20 \times 0.2 \\ &= 64\ \text{N} \end{aligned}

Answer: Friction is 60 N. A push of 64 N speeds the box up at 0.2 m s⁻². Only the extra 4 N changes the motion; the other 60 N just cancels friction, which is exactly the part Aristotle mistook for the cause of motion.

Example 3: Less friction, longer motion

A puck slides on ice at 4 m s^⁻¹ and slows down uniformly at 0.05 m s^⁻². (a) How far does it slide, and for how long? (b) Repeat for a smoother surface on which the deceleration is 0.025 m s^⁻².

(a) Take a as the magnitude of the deceleration. With final speed zero, v² = u² − 2as gives

\begin{aligned} s &= \frac{u^{2}}{2a} = \frac{4^{2}}{2 \times 0.05} \\ &= 160\ \text{m} \end{aligned}

t = \frac{u}{a} = \frac{4}{0.05} = 80\ \text{s}

(b) Halving the deceleration doubles both:

s = \frac{4^{2}}{2 \times 0.025} = 320\ \text{m}

t = \frac{4}{0.025} = 160\ \text{s}

Answer: 160 m in 80 s, then 320 m in 160 s. As friction gets smaller, the puck goes farther. With no friction at all, the deceleration would be zero and the puck would never stop. This is the idealisation Galileo made: imagine friction removed altogether.

Common mistakes to avoid

Common mistake

Drawing a force along the motion

For a ball thrown upward, students often draw a “force of the throw” pointing up while the ball rises. Once the ball leaves the hand, the only forces on it are its weight and air drag, both acting downward while it rises. The ball keeps rising because of its velocity, not because of a force.

Common mistake

Thinking a push is stored in the body

A kicked ball does not carry the kick with it. The kick acts only while the foot touches the ball; after that, its motion is governed by the forces still acting, including gravity, friction while in contact with the ground, and air resistance. Gravity slows a rising ball even without friction.

Common mistake

Thinking that uniform motion means no forces at all

A car moving at a steady speed in a straight line on a level road has several forces on it: the forward friction of the road on the driving wheels, air drag and rolling friction backward, its weight and the normal force. They balance, so the net force is zero.

Quick revision summary

Aristotle’s law of motion said that an external force is needed to keep a body moving. This is wrong, and is called Aristotle’s fallacy.
Bodies around us stop because friction and viscous drag act against their motion, not because the push runs out.
A push on a moving body cancels friction. In uniform motion the forces balance and the net force is zero.
With zero net force in an inertial frame, a moving body keeps a constant velocity: the law of inertia. On a level frictionless floor, weight and normal force can still act and balance.
A net force is needed only to change velocity: to start, stop, speed up, slow down or turn a body.

Formula sheet

F_net = 0 in uniform motion
F = f (steady pull against friction)
a = −f/m (slowing down once the pull stops)

Questions students ask

What is Aristotle’s law of motion?

Aristotle’s law of motion, as NCERT phrases it, says that an external force is required to keep a body in motion. It seems to match everyday experience, since things left to themselves slow down and stop. But it is wrong: a moving body slows down because friction or air resistance acts on it, and with zero net force it would keep moving at constant velocity in an inertial frame.

Who proved Aristotle’s fallacy wrong?

Galileo Galilei showed in the seventeenth century that Aristotle’s fallacy is wrong. From experiments with balls on smooth inclined planes, he argued that without friction a moving body would never slow down: the law of inertia. Newton then made it his first law of motion: no net force is needed to keep a body moving at constant velocity.

What is the difference between Aristotle’s and Galileo’s views of motion?

Aristotle held that motion needs a continuing force and that rest is the natural state of a body. Galileo showed that rest and uniform motion in a straight line are equivalent states, and that a net force is needed only to change the velocity. Galileo’s view is the one Newton’s laws are built on.

Is a force needed to keep a body moving at constant velocity?

No net force is needed to keep a body moving at constant velocity. A body moving at constant velocity has zero acceleration, so by Newton’s second law the net force on it is zero. On the ground a push is still needed in practice, but only to cancel friction and air resistance; with no horizontal resistance and balanced vertical forces, no driving force is needed.

Practice questions

Try each question first, then open the answer to check your working.

Q1. A cyclist rides at a steady 5 m s^⁻¹ along a straight, level road. The forward force of the road on the cycle is 20 N. What is the total backward force of air drag and rolling friction, and what is the net force on the cycle?

Show answerHide answer

The velocity is constant, so the net force is zero. The backward forces therefore add up to 20 N, balancing the forward 20 N.
Q2. An arrow keeps flying after it leaves the bow. How did Aristotle explain this, and what is the correct explanation?

Show answerHide answer

Aristotle said that the air behind the arrow keeps pushing it. In fact no forward force is needed: the arrow keeps moving because nothing has to act on a body to keep its velocity. The forces that do act on it, gravity and air drag, only change its velocity: gravity bends its path downward and air drag slows it.
Q3. A 2 kg block slides on a horizontal floor and slows down uniformly from 6 m s^⁻¹ to rest in 3 s. Find the friction on the block. What horizontal force would keep it moving at a steady 6 m s^⁻¹?

Show answerHide answer

The deceleration is 6/3 = 2 m s⁻², so friction is f = ma = 2 × 2, which is 4 N. To keep a steady 6 m s^⁻¹, the push must just cancel friction: 4 N in the direction of motion.
Q4. A trolley rolls along a straight track at a constant velocity. A student says, “There must be a net forward force on it, otherwise it would stop.” What is wrong with this statement?

Show answerHide answer

Constant velocity means zero acceleration, so the net force on the trolley is zero. A forward force may act on it, but only to balance friction; if there were no friction, no forward force would be needed at all. A net force would change its velocity.

Aristotle’s fallacy

What is Aristotle’s fallacy?

Why the idea seems right

Where the argument goes wrong

Seeing it in daily life

Solved examples

Example 1: Toy car on a string

Example 2: Pushing a box at a steady speed

Example 3: Less friction, longer motion

Common mistakes to avoid

Quick revision summary

Questions students ask

What is Aristotle’s law of motion?

Who proved Aristotle’s fallacy wrong?

What is the difference between Aristotle’s and Galileo’s views of motion?

Is a force needed to keep a body moving at constant velocity?

Practice questions

Sources and review

Topics in Laws of Motion