Unit 1 - Vectors & Static Equilibrium
Lesson 1 - Vector Addition and Subtraction
Vector Addition
Triangle Method
Vector Addition
The Parallelogram Method
Properties of Vector Addition
a + b = b + a.
(u + v) + w = u + (v + w).
Subtraction of Vectors
Switch the direction of the vector that is being subtracted.
Adding Vectors Algebraically
Use trigonometry.
Lesson 2 - Relative Velocities
Velocities in the same direction (vector addition)
Velocities in the different direction (vector subtraction)
Different reference
Question with mult-velocities
The same object can have different relative velocities.
Lesson 3 - Components Vectors
Vectors can be broken down into several components.
Use trigonometry.
Addition of Component Vectors
Pythagoream Theorem
Model Procedures in Problem Solving
Draw a free body diagram.
Identify the unknown force and determine if Newton’s law of motion applies to this problem.
Calculate the x-component of each force vector
Calculate the y-component of each force vector
Lesson 4 - Equilibrium of Forces
Force are balanced.
Force are unbalanced.
rest (v = 0 & a = 0)
Acceleration
Friction
Reaults from relative motion between objects.
Types
Stactic friction
Sliding friction
Rolling friction
Air friction
Viscous friciton
Ff = μ Fn
Working with Common Force
frictional forces
gravitational forces
normal force
Incline ramp
Equilibrium
Acceleartion
Parallel applied force
Lesson 5 - Static Equilibrium and Torque
Torque
Produced by the force is proportional to the magnitude of the force and the line of action of the force and the distance between the point where the object tends to rotate
Force couple
Pair of external forces acting in equal but opposite directions
The resultant of the two factors of a force couple is 0.
Produced by a force directly proportional to the size of the force.
Moment arm - Perpendicular distance between the force and rotation.
T=Fr
Mathematical Definition
Counterclockwise torques (+)
Clockwise torques (—)
Torque can be added or subtracted.
Static Equilibrium
∑F = 0
∑t= 0
Lesson 6 - Acceleration
a = ∆v/∆t (a = (vfin – vint)/ (tfin – tint).)
Average acceleration
for the entire duration
Instantaneous acceleration
at a specific instant in time
vector
It can be displayed by the slope on a velocity – time graph.
Lesson 7 - Mathematics and Motion
vf = vi + a∆t
∆d = u∆t +1/2 a∆t2
Acceleration due to Gravity(a = 9.8 m/s)
Jerry Zou