Dynamics is the branch of physics that addresses the motion of material objects with regards to the factors that affect them  (momentum, force, mass, energy).

Dynamics is a very essential unit to the study of physics, as it makes up the foundation of Newtonian physics.  Newton’s three laws are tendencies of nature that Sir Isaac Newton discovered that begin to describe and explain basic physical principles.  

Law #1: An object at rest or in motion will remain at rest or in motion unless acted upon by a net external force.  This may seem a little confusing at first because if you (for example) roll a tennis ball on a floor, it will eventually stop.  While it may seem like no net external force is acting on it, there is actually friction, air resistance, etc. acting on the ball, making it come to a stop despite the lack of any obvious “net external forces”.

Law #2: Force is equal to the mass of an object times the object’s acceleration (Fnet = ma).  This formula is extremely essential to the study of physics, as it is used in many different instances to solve a large variety of problems.

Law #3: Every reaction has an equal and opposite reaction.  In order for two forces to be an action-reaction pair, they must exert the forces on each other; for example, the force of you on earth (Fye) = the force of earth on you (Fey).  Two forces that would NOT be an action-reaction pair would not act on each other.

Example Problem #1

Which of Newton's three laws explains why, when you're cruising in an airplane, you don't feel any forces acting on you?

Answer: 2nd law

Explanation: Because you are travelling at a constant velocity in the airplane, a = 0m/s^2.  If a = 0, then, according to Fnet = ma, Fnet must equal zero.  This is why you don't feel like you're moving when you really are (except for instances of acceleration, where a does have a value and Fnet does not equal zero).

Solving More Complex Dynamics Problems

Free body diagrams are a very helpful tool in visualizing complex problems.  A free body diagram features a dot (the object being analyzed) and arrows either pointing to or from the object that represent the forces acting on the objects.

Friction will often find its way into tricky physics problems.  The two types of friction essential to a basic understanding of physics are static friction (FS) and kinetic friction (FK).  Static friction is the friction an object experiences while it is stationary, whereas kinetic friction is the friction that an object experiences while it is moving.  The formula for calculating the force of friction (FF) is that Ff = μ(FN).  The letter mu (μ) is a ratio that we use to help us solve for the force of friction or the normal force.

Inclined planes are another way that dynamics problems can get more complicated.  In order to work with inclined planes, you must find the components of forces to help you solve the problem.  For example, with a force like gravity, you’d have to break the force into its x-component (working parallel to the ramp) and its y-component (working normal (perpendicular) to the ramp).  So, Fgy = Fgcosθ = mgcosθ and Fgx = Fgsinθ = mgsinθ.  Remember, on an inclined plane, the normal (perpendicular) force is going to be the force perpendicular to the plane the object is on, NOT necessarily vertical.  Similarly, for forces that are being applied at an angle, you would use trigonometry to find the components of the force, which you can then use to solve the problem.

This image shows how gravity can be broken up into its components

This image shows how gravity can be broken up into its components

Example Problem #2

If you have a block (5kg) on a plane inclined at an angle of 45 degrees with a coefficient of kinetic friction of .35 and you release it, what will the block’s acceleration be?

Answer: 4.60m/s^2

Explanation: First, solve for a using Newton’s 2nd Law: Fnet = ma.  Once you have done this, you should have a = Fnet/m.  Since we know m is 5kg, we just need to solve for Fnet.  The net force will be Fgx (mgsinθ or 5 x 10 x sin45 = 35.36N) - Ff (μk(FN) = .35(35.36) = 12.37N) = 22.99.  22.99/5 = 4.60 m/s^2.