Newton’s Laws Study Guide
Key Physics Terms
Vector: A quantity that represents magnitude (size) and direction. It is usually represented with an arrow to indicate the appropriate direction. They may or may not be drawn to scale.
Resultant: the result of adding two or more vectors; vector sum.
Vector Component: the parts into which a vector can be separated and that act in different directions from the vector.
Vector Addition: The process of combining vectors; added tip to tail.
Static Equilibrium: A motionless state where all the forces acting on an object yield a net force of zero.
Dynamic Equilibrium: A condition of constant motion/zero acceleration where all the forces acting on an object yield a net force of zero.
Friction Force: A force that acts to resist motion of objects that are in contact.
Normal Force: Support force that acts perpendicular to a surface. If the surface is horizontal, this force balances the weight of the object.
Force: A vector quantity that tends to accelerate an object; a push or a pull.
Net Force, Fnet: : A combination of all the forces that act on an object
Key Formulas
v=d/t
a = Δv/Δt=(v_{f}v_{i})/t
d=v_{i}t+at^{2}/2
v_{f}^{2}=v_{i}^{2}+2ad
acceleration due to gravity = 9.8 m/s^{2}
Pythagorean Theorem: c^{2}=a^{2}+b^{2}
Sin θ = opp/hyp
Cos θ = adj/hyp
Tan θ = opp/adj
Fnet=ma
μ=Ff/FN
F_{net}=ΣF = the sum of all forces
Variables Used
v= velocity (usually average velocity or constant velocity)
a=acceleration
F= force
F_{f}=frictional force
F_{N}=normal force
Δ= change in
θ= angle
m=mass
μ=coefficient of friction
Vector Diagram
Static vs. Dynamic Equilibrium
 In static equilibrium, the net force on an object is zero; the object is also stationary. The forces balance out to leave the object motionless.
 In dynamic equilibrium, the net force on an object is zero; however, the object is still moving at a constant velocity. The forces balance out to leave the object in its current state of motion with no accelerations or changes.
Typical Key Metric Units
 Acceleration: m/s^{2}, m/s/s
 Time: seconds, s
 Force: Newtons, N
 Mass: kilograms, kg
 Coefficient of friction: no units
Newton’s Laws
 Newton’s 1st law : An object at rest wants to stay at rest, an object in motion tends to stay in motion; inertia.
 Newton’s 2nd law : F_{net}= ma.
 Newton’s 3rd law: For every force that is an equal and opposite force; action and reaction.
Newton’s Laws Problem Solving Tips
 These tips will make it easier to solve any force related physics problems.
 Thoroughly read the entire problem.
 Draw a diagram if needed. Include a diagram to show all forces acting on a particular body.
 Identify all given information.
 Identify the quantity to be found.
 Select appropriate formula(s) that incorporate what you know and what you want to find.
 Convert units if needed. Use units throughout your calculations.
 Do any mathematical calculations carefully.
Typical Dynamics Problem
Example: A model rocket of mass 3 kg has an engine that produces 100N of upward thrust/force. What is the resulting acceleration of the model rocket when it is fired. Assume its mass is constant throughout its motion. Ignore any frictional forces.
Given information:
Mass = 3 kg
Upward force = 100N
Unknown:
acceleration= ?
F_{net}= ?
First, find the weight of the rocket:
Although the mass is known, that isn’t the same as its weight.
Using F=ma Weight = 3kg (9.8m/s^{2})=29.4N
Second, find the net force on the rocket:
Our upward force is considered positive, the weight negative.
F_{net}=ΣF =100N29.4N=70.6N
Lastly, solve for the acceleration:
Use F_{net}=ma 70.6N=3kg(a) a=23.5m/s^{2}
