Newton's Laws

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Dynamics is a branch of mechanics focused on the causes of motion.

While kinematics analyzes motion itself, dynamics explores the forces behind it—specifically incorporating the concepts of force, momentum, and energy.

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​Before we examine the Laws in detail, this video gives an overview of what dynamics is, and is useful as an intro to its study, or as a review.

​Short on time?
Just need a review?
A summary of the three laws 
Otherwise keep going

Understanding Newton's Laws

One of the fundamental principles of dynamics is the concept of force. In the late 17th century, Isaac Newton introduced this concept in his landmark work, Principia, where he formulated what are now known as Newton’s Three Laws of Motion.


(Note: Although momentum and energy are closely related to force, those concepts are explored in detailed dedicated sections.)


Simply put newton's laws of motion can be divided up into three laws
 1st Law
An object at rest, or constant velocity, or stay, addressed, or constant velocity, unless acted on by an external force.

2nd Law
The acceleration of an object is directly proportional to the net force acting, and indirectly to the mass of the object*

3rd Law
If object A applies a force on object B , then object B always applies an equal but opposite force back on A

The first two laws describe how forces act on a single object, whereas the third law addresses the interaction between two separate objects.

Why learn them in reverse order?

  • Start with the 3rd Law: It is often the most intuitive and easiest to visualize with real-world examples.
  • Move to the 2nd Law: Once you understand how objects exert forces on each other, exploring how force affects acceleration follows naturally.
  • Finish with the 1st Law: Newton’s First Law then becomes a simple logical extension—it is simply what happens under the 2nd Law when the net force is zero (a = 0).

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Theory
Lets' now move on to the video when using the animation at pHET, I explain the three laws, starting at the 3rd, then the second and finally the first.
Test your understanding

Interactive Activity

Take an opportunity to explore the PhET simulation yourself. (Tip: Click the three dots in the bottom-right corner to enter full-screen mode.)

  1. Demonstrate the 1st Law: Go to the Net Force tab. Start a tug-of-war game with unbalanced forces so the cart accelerates. While it is moving, quickly balance the forces on both sides. What do you observe?
  2. Demonstrate the 2nd Law: Explore the remaining tabs (Motion, Friction, and Acceleration). Observe how changing the applied force and total mass affects the resulting acceleration.


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Problems to try
1. A bicyclist and his bicycle have a total mass of 105 kg. What force is necessary to bring the bicycle to rest from a speed of 25 m/s over a distance of 4 m to avoid a tree?

Given: m = 105 kg, vi = 25 m/s, vf = 0 m/s, s = 4 m

Step 1 (Calculate Acceleration): Using vf2 = vi2 + 2as

02 = 252 + 2(a)(4)

0 = 625 + 8a → a = -78.125 m/s2

Step 2 (Calculate Force): Using F = ma

F = 105 kg × 78.125 m/s2 = 8203.125 N

Answer: 8,200 N (or 8.2 kN opposing motion)
2. It takes an upward force of 109 N to lift a stone straight up, producing an upward acceleration of 12 m/s2. Calculate the mass of the stone.

Given: Fapplied = 109 N, a = 12 m/s2, g = 9.8 m/s2

Step 1 (Set up Net Force Equation): Net upward force = Applied force - Gravity

Fnet = Fapplied - mg = ma

109 - m(9.8) = m(12)

109 = 21.8m → m = 5 kg

Answer: 5 kg
3. A 1000 kg car accelerates uniformly from rest, covering 100 m in 10 s. If resistive forces total a constant 200 N, what forward force must the engine provide?

Given: m = 1000 kg, s = 100 m, t = 10 s, vi = 0 m/s, Fresistance = 200 N

Step 1 (Calculate Acceleration): Using s = vit + ½at2

100 = 0 + ½a(10)2 → 100 = 50a → a = 2 m/s2

Step 2 (Calculate Engine Force): Fnet = Fengine - Fresistance = ma

Fengine - 200 = 1000 × 2

Fengine = 2000 + 200 = 2200 N

Answer: 2,200 N
4. A person with a mass of 80 kg stands on a scale inside an elevator. The scale displays a reading of 75 kg. Describe the possible motion of the elevator.

Analysis: The scale reading (75 kg) is lower than the actual mass (80 kg), which means the scale's normal force is less than the gravitational force (FN < mg).

Acceleration: a = (75 - 80)g / 80 = -0.0625g ≈ -0.61 m/s2 (downward net force).

Answer: The elevator is accelerating downward at 0.61 m/s2. This means it is either speeding up while moving downward, or slowing down while moving upward.
Extra videos
I produced this video in order to demonstrate newtons first law and in particular the concept of inertia.
You can perform this party trick yourself, it's not magic it's physics!

You can establish students understanding of newtons third law by giving them a well known scenario.
​Newton's third law, often described as an action and reaction force, has often confused students. This video uses a horse and a cart to hopefully clarify understanding.
Picture

How well do you know forces?


​Test your understanding of Newton's Laws. So do the quiz and try to get full marks

Then check your understanding if necessary with the video
 
* This is not how Newton described it, where he expressed it as the net force is proportional to the rate of change of momentum. But considering that many students have yet to coner momentum when learning the laws, it is expressed in this form.
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