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This text is meant to accompany class discussions. It is not everything there is to know about uniform circular motion. It is meant as a  prep for class. More detailed notes and examples are given in the class notes, presentations, and demonstrations (click here.)

Click for the questions that go with this reading
2nd Law


Newton's 2nd law says:




  • F = force; measured in Newtons, [N]. Newtons are abbreviated with a capital "N." Not a lower case. Note too that the force is a capital "F." A lowercase "f" means frequency -not force.
  • m = mass; measured in kilograms [kg]
  • a = acceleration [m/s2].
  • This means the force is directly proportional to the acceleration. It is also directly proportional to the mass.

In other words, an UNBALANCED force ,F, gives you an acceleration. Whenever you have a change in speed or direction, it is because of an unbalanced for and Newton's 2nd law.


A note about units ...for all of science

When mass and acceleration are multiplied together, the units become . This make the the unit of force. However, it is not uncommon to simplify a unit and honor a scientist at the same time by naming the unit after the scientist.

The became the "Newton." Abbreviated with a capital, "N." Any time a unit is named after a person, a capital letter is used.


When watching a video, if a body changes its velocity, then this is due to Newton's seconds law. In the video below. The brain's velocity changes because the skull applies an outside force to the brain. This changes the brain's velocity from left to right. Recall that an acceleration is how quickly the velocity changes.


Typically physicists and engineers do not use the term unbalanced force, Instead they use the phrase "net force." The net force is the resultant force when all the forces are added together. This acceleration is called the net acceleration. It is the same acceleration that is used in the kinematics chapter.


Example #1

A 1250 kg car decelerates from 12.0 m/s to 8.00 m/s in 25.5 m by air resistance. What was magnitude of the net force slowing the car down?


Note: In the real world, resistive forces often oppose the motion of objects. Forces like friction and air resistance slow down moving bodies. Even though this particular problem does not say "neglect resistive forces," they are nearly always ignored unless otherwise stated. (Frictional forces will be examined later.)


F = ma is the only equation with force in it. The problem gives the mass, but not the acceleration. However, you can use kinematics to calculate the acceleration. The acceleration in the kinematics equation is the same acceleration is all other equations. So this acceleration can be used in Newton's second law.


Since the question asks for the MAGNITUDE of the net force, the negative sign on the acceleration is ignored.

Example #2

Describe how the 2nd law is demonstrated in the animation below.

Describe how the 2nd law is demonstrated in the animation above.

An acceleration look like a change in speed OR a change in direction.

When the car hits the back of the truck, it changes direction. This means that an unbalanced force, (called the net force,) was applied to the car and truck. Because the truck is so much more massive than the car, it does not show the same change in velocity.


A Special Application of the 2nd Law


Every force is measured in Newtons. When you are near the surface of the Earth the force of gravity is written as

w = mg


  • w = weight (Pull of the gravity) measured in Newtons, [ N ] (lower case "w.")
  • m = mass of the object measured in kilograms [kg]
  • g = acceleration due to gravity measured as 9.80 m/s2.

You only feel your weight when you are standing on something solid, like the ground. This is because the ground is pushing up on you.

Weight depends on the pull of gravity. If you traveled to different places in the solar system, the acceleration due to gravity would change. This means your weight would change. But your mass would remain unchanged.

Example #3

An 8,550 N car has an engine that propels it forward by a 1750 N force. The car travels from 5 m/s to 15 m/s. How much time did this maneuver take? (Ignore frictional forces opposing the car’s motion.)

This video can be found on YouTube at





If you were to jump off a high platform into a pool of water while holding a scale on your feet,the scale would read a weight of zero in the air. To be weightless means to make "g" equal to zero because w = mg. This only happens very far away from the Earth. ...Somewhere in outer space.


If you jumped off a tall platform or building, you are not truely weightless as you accelerate down at a rate of "g." You may FEEL weightless, but you are not weightless. The pull of gravity is still pulling you down to the center of the Earth. Since nothing is opposing the pull of gravity on your feet, you don't FEEL the typical effects of gravity you feel on the ground. If the scale was placed on the ground, the surface of the Earth would push up while gravity pulls you down. This squeeze is how the scale gets its reading. (This discussion ignores air resistance.)


Choose the best answer. It does not matter how many questions you miss. What matters is that you learn from any mistakes.




by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)

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