Newton's 1st Law
Law of Inertia
Object will continue to move at a constant velocity unless acted on by external force
When force is applied, acceleration is created
Newton's 2nd Law
The more mass an object has, the harder it is to move
Newton's 3rd Law
If A exerts a force on B, then B exerts a force of equal magnitude in the opposite direction of A.
For ever action(force) there is an equal and opposite reaction(force).
Tension [if connected by a string/rope]
Why use the vector sum?
To find vector F Use all of the forces acting on the mass in a vector sum of the direction x and direction y.
Solving Force Problems
Use Newton's second law F=ma to find the force
First find the components in the x and y direction because acceleration has x and y components(vector)
Once components are obtained(usually from a diagram), put them in a vector sum and set them equal to "ma". Because you are usually given mass, this makes life easy to find acceleration or even a missing force.
Pay attention to the signs of everything.
Acceleration in the y direction
If an object is not going up or down on a frictionless surface, it has an acceleration of 0 in the y direction. This also means that the Normal force and weight are equal to 0 (cancel each other out). If a problem does not indicate the mass is being taken off the floor, assume Ay to be O
Usually, when a problem asks for a Normal Force, it's asking for the sum of the forces in the y direction
Angles and Components
Any vector with an angle that is not at an axis has components.
As theta increases, the y component of F becomes larger and the normal force becomes smaller, Eventually, the normal force is equal to zero when the weight and y component of F are equal. At that point, the object leaves the surface.= IF THERE IS NO NORMAL FORCE THEN THE OBJECT IS NOT ON A SURFACE; DEFINITION OF NORMAL FORCE IS THE FORCE OF THE SURFACE ON AN OBJECT!!!
Object is not moving
It's acceleration is 0 in both x and y directions.
When looking for a particular variable in a vector sum, and you have 2 different vector sums at hand with the a variable in common, you can think of it like basic algebra if one of the equations has 2 "things" inside of it... you can set the "things" equal to each other and substitute it in the other equation :D
In an incline, the axes are rotated so that what ever was positive x in the 90 plane will be in the negative x direction, while the positive y remains positive. this creates components for the weight. Theta for weight is always equal to that of the incline. Remember that acceleration of y is still 0 because it never leaves the ramp and the rotation of the axes is different.
The components of weight will also be unconventional:
w(x) will be wsin(theta)
w(y) will be -wcos(theta)
What is the acceleration?
Sum of components in the x direction because (1)there is no acceleration in the y direction and (2) Newton's Second Law F=ma
When you use the absvl of a number for the inverse tangent, you will always get the INTERIOR ANGLE. This means you must draw out the problem to know what angle to add or subtract from to get the right angle.
Normal Force and Inclines
The normal force depends on the angle of an incline so if Fn is given, it can be used to find theta :D