Week 1 - Newton's law and vectors

What does Newton’s first law state?

An object remains at rest or moves at a constant velocity unless acted upon by an unbalanced force.

What does Newton’s second law state?

The net force acting on an object is proportional to the product of the mass of the object and it’s rate of change in momentum hence acceleration

What does Newtons third law states?

For every action, there is an equal and opposite reaction; if one object exerts a force on a second, the second exerts an equal and opposite force on the first.

Provide the Sine rule for resultant force

\frac{\left\vert\overrightarrow{c}\right\vert}{\sin\beta}=\frac{\left\vert\overrightarrow{a}\right\vert}{\sin\delta}=\frac{\left\vert\overrightarrow{b}\right\vert}{\sin\alpha} , aka the angle opposite to the line

Provide the cosine rule for the resultant force

\left\vert c\right\vert^2=\left\vert a\right\vert^2+\left\vert b\right\vert^2-2\left\vert\overrightarrow{a}\right\vert\left\vert\overrightarrow{b}\right\vert\cos\beta

Provide the formula for finding scalar projections

F_x= F cos (theta x) or F sin (theta y)

F_y= F cos (theta y) or F sin (theta x)

What is the formula for calculating the force using components in 2d and 3d

2D: F (vector) = F_x (i-hat) + F_y (j-hat)

3D: F(vector) = \left\vert\overrightarrow{F}\right\vert\overrightarrow{e}

What is the formula using the sum for the unit vector

cos²(theta x) + cos²(theta y) + cos²(theta y) = e

How do you calcualute the magnitude of the force F, when the vector is not at the origin?

What does the length of a vector represnet?

It’s magnitude

How would find the unit vector of A?

By dividing it’s components by the magnitude of A