How is the expression of centripetal acceleration derived

Many students are puzzled by this problem (which is worth praising), and I have answered it countless times. If we understand and hope to help more students to solve the historical questions, we might as well try to use the knowledge of acceleration to explain that acceleration is a physical quantity that represents the speed change, because speed is a vector, Therefore, it not only includes the special case caused by the change of velocity: linear motion a = (v0-vt) / T, but also includes the special case caused by the change of velocity direction: uniform circular motion a = ω · v Among them, Δ θ, Δ L, t and R respectively represent the change of velocity direction (angle), the arc length corresponding to the change of velocity direction (angle), the time required for the change of direction, and the radius of uniform circular motion. I hope it is helpful to summarize the knowledge of acceleration, and I don't know if I can fully understand it

Derivation of centripetal acceleration formula an = V ^ 2 / R

As can be seen from the diagram on page 21, OA / VA = AB / △ V R / v = △ s / △ V (for uniform circular motion, VA = VB, expressed by the same letter V; when Θ is very small, there is no difference between arc length and chord length, ab = △ s) R / v = V △ T / △ V multiply V and △ V △ v r = V ^ 2 △ T, so △ V / △ t = an = V ^ 2 / R

The mathematics problem of the first grade of junior high school is known that angle 1 and angle 2 are complementary to each other. Angle 1 is 30 larger than angle 2. How much is angle 2?

Angle 1 + angle 2 = 180
(angle 2 + 30) + angle 2 = 180
Angle 2 = 75

What is adjacent complement? It's best to give a picture to see
I can't tell a complement from a neighbor

2004 lines intersect at a point, there are several pairs of vertex angle
1. How many pairs of vertex angles are there when two lines intersect at one point?
How many pairs of vertex angles are there when three straight lines intersect at one point?
3. How many pairs of vertex angles are there when four straight lines intersect at one point?
If n lines intersect at one point, how many pairs of vertex angles are there?
5. If 2004 straight lines intersect at one point, several pairs of vertex angles can be formed

Group 1.2
Group 2.6
Group 3.12
4.n*(n-1)
5. 2004 * (2004-1) (calculate by yourself)
It must be right. If you don't believe it, you can check it

When two lines intersect, there are two pairs of vertex angles. How many pairs of vertex angles are there when n lines intersect?

The intersection of N lines is
1 + 2 +... + (n-1) = n (n-1) / 2
So there are n (n-1) / 2 pairs of vertex angles, i.e
N (n-1)

How many pairs of vertex angles do n lines intersect at a point

N straight lines are n × (n-1) opposite vertex angles

Two lines intersect,

Wrong answer on the first floor!
Because 2 times ∠ 3 = 3 times ∠ 1,
Therefore, 3 = 3 / 2 times 1, and because 3 + 1 = 180 degrees,
So we can substitute 3 / 2 times ∠ 1 + 1 = 180 ° and get ∠ 1 = 72 °,
Because ∠ 1 and ∠ 4 are opposite vertex angles,
Therefore, 4 = 1 = 72 degree

In the graph composed of N lines, how many pairs of vertex angles can there be at most?

That's n straight lines at one point
In this way, each line will form two pairs of vertex angles with another n-1 line
So n × (n-1)
But the pairwise combination will be repeated once, so the above result is divided by 2
n×﹙n－1﹚/2＝﹙n²－n﹚/2
So there can be at most (n & # 178; - n) / 2 pairs of opposite vertex angles

If n lines intersect with different points, how many pairs of vertex angles? How many pairs of apposition angles? How many pairs of internal stagger angles? How many pairs of internal angles on the same side?

n(n-1)

How is the expression of centripetal acceleration derived