Home » Physics » Forces: Laws of Motion » Newton’s 2nd and 3rd laws of motion

Newton’s 2nd and 3rd laws of motion

Sir Isaac Newton

Isaac Newton animated GIF


Unbalanced forces acting on an object
cause it to accelerate


Mass Resists Acceleration

For a constant force, an increase in mass
will result in a decrease in the acceleration.

Acceleration is inversely proportional to mass.

Mass resists acceleration (because it has inertia)


Push something TWICE as massive,
it accelerates HALF as much

Push something TEN times as massive,
it accelerates ONE-TENTH as much.

mass resists accel

Acceleration is inversely proportional to mass.

Acceleration is directly proportional to the net force

accel proportional to force

accel proportional to the net force

Acceleration is inversely proportional to the mass

accel is inversely proportional to mass

accel = Force / Mass


The gravitational acceleration is constant

Twice the force, exerted on twice the inertia, produces the same acceleration, as half the force exerted on half of the inertia.

Both accelerate equally

Although the total masses in both cases is different, the total forces are also different. The “2”s cancel out, so the resulting acceleration is the same.

Gravitational acceleration g is constant


6.3 Newton’s Second Law of Motion

Force = mass x acceleration
F = m•a
F = ma

Isaac Newton does it all by 26

6.4 Friction

Friction is a force that can affect motion. To push an object across a table at a constant speed requires a force that balances the force of friction. When the object moves at constant speed, your push force = the friction force. See the unit here on Physics of Friction (KaiserScience)


6.5 Pressure is applying force over an area

pressure = force / area

pressure is measured in Newtons/square meter

The honorary unit of pressure is the Pascal, named after the great French scientist Blaise Pascal (1600s) He was a mathematician, physicist, inventor, writer and Christian philosopher.

Common units of pressure.

If you divide a lot of pressure over a large amount of area, then the amount of pressure in any one area is small – hence the amazing bed of nails trick!


Here is an example of the power of air pressure – if a solid steel tank train car is sealed, and then evacuated, the air pressure inside is 0 Pascals. But the external air pressure is over 100,00 Pa, so this is the result!

Air pressure demonstration imploding tanker train

6.7 Falling and Air Resistance

See the unit on https://kaiserscience.wordpress.com/physics/kinematics/penny-drop/

 7.5 Defining systems



7.6 The Horse-Cart Problem

from https://www.lhup.edu/~dsimanek/physics/horsecart.htm

A horse is harnessed to a cart. If the horse tries to pull the cart, then the horse must exert a force on the cart.

By Newton’s 3rd law, the cart exerts an equal & opposite force on the horse.

Newton’s 2nd law : acceleration is equal to the ∑ force divided by the mass.   a = F/m

Since the two forces are equal and opposite, they add to zero.

Thus the acceleration of the system must be zero.

If it doesn’t accelerate, and it started it rest, it must remain at rest.

Therefore no matter how hard the horse pulls, it can never move the cart?!  Nope….we’re obviously missing something here.  

Doctor Who You probably just missed a bit

What could it be? We need to think 🙂 Shh!  Quiet time – use your brain!

Doctor Who Capaldi Shut Up


List all the physical errors and mistakes in the above paragraph and explain why they are wrong. Show a free-body force diagram of the horse and cart, identifying all relevant forces, and then write a short paragraph describing this situation correctly.

How can this sled move, if the forces are all in pairs?



Conversion factors

The gravity of Earth would impart a downward acceleration, g = 9.8 m/s2, to objects on its surface, were those objects not  supported by an upward force, measurable in newtons. This force is felt as the weight of an object. The acceleration is due to gravity, g ≅ 10 m/s2,

1 kg × g = 9.8 N ≅ 10N

Thus these approximate conversions hold:

  • 1 kg is about 10 N of force

  • 1/10 of a kg is about 1 N

  • 100 kg is about a kN


Lessons from The Physics Classroom:

  1. Lesson 1 – Newton’s First Law of Motion
    1. Newton’s First Law
    2. Inertia and Mass
    3. State of Motion
    4. Balanced and Unbalanced Forces
  2. Lesson 2 – Force and Its Representation
    1. The Meaning of Force
    2. Types of Forces
    3. Drawing Free-Body Diagrams
    4. Determining the Net Force
  3. Lesson 3 – Newton’s Second Law of Motion
    1. Newton’s Second Law
    2. The Big Misconception
    3. Finding Acceleration
    4. Finding Individual Forces
    5. Free Fall and Air Resistance
    6. Double Trouble
  4. Lesson 4 – Newton’s Third Law of Motion
    1. Newton’s Third Law
    2. Identifying Action and Reaction Force Pairs


Many students believe that an object cannot be moving unless there is a force on it, or that an object will naturally come to a stop, without any external force acting on it. Reality: when objects seem to come to a stop by themselves, there really are unseen friction forces acting to stop the object.

Learning Standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework
HS-PS2-1. Analyze data to support the claim that Newton’s second law of motion is a
mathematical model describing change in motion (the acceleration) of objects when
acted on by a net force.

HS-PS2-10(MA). Use free-body force diagrams, algebraic expressions, and Newton’s laws of motion to predict changes to velocity and acceleration for an object moving in one dimension in various situations

A FRAMEWORK FOR K-12 SCIENCE EDUCATION: Practices, Crosscutting Concepts, and Core Ideas
How can one predict an object’s continued motion, changes in motion, or stability?

Interactions of an object with another object can be explained and predicted using the concept of forces, which can cause a change in motion of one or both of the interacting objects… At the macroscale, the motion of an object subject to forces is governed by Newton’s second law of motion… An understanding of the forces between objects is important for describing how their motions change, as well as for predicting stability or instability in systems at any scale.

Massachusetts Science and Technology/Engineering Curriculum Framework (2006)

1. Motion and Forces. Central Concept: Newton’s laws of motion and gravitation describe and predict the motion of most objects.

1.4 Interpret and apply Newton’s three laws of motion.
1.5 Use a free-body force diagram to show forces acting on a system consisting of a pair of
interacting objects. For a diagram with only co-linear forces, determine the net force acting on a system and between the objects.
1.6 Distinguish qualitatively between static and kinetic friction, and describe their effects on the motion of objects.
1.7 Describe Newton’s law of universal gravitation in terms of the attraction between two objects, their masses, and the distance between them.
1.8 Describe conceptually the forces involved in circular motion.

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