How to derive the expression of centripetal acceleration an = V ^ 2 / R

How to derive the expression of centripetal acceleration an = V ^ 2 / R

Let's use the knowledge of acceleration first. Acceleration is a physical quantity that represents the speed of change, 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

What are the formulas of high school physics optics~

The relationship between refractive index and light speed in the same medium sinc = 1 / n the critical angle of total reflection
c=λf
Wavelength measurement by double slit interference with λ = D Δ X / L
E = hv-w maximum initial kinetic energy of photoelectric effect
That's all

Summary of junior high school physics formula

1. Velocity: v = s / T 2, gravity: g = mg 3, density: ρ = m / V 4, pressure: P = f / S 5, liquid pressure: P = ρ GH 6, buoyancy: (1), f floating = f '- f (pressure difference) (2), f floating = G-F (apparent gravity) (3), f floating = g (floating, suspension) (4), Archimedes principle: F floating = g row =

If four lines intersect on the plane, at most several pairs of vertex angles can be formed
I wrote 10, but I was wrong

Intersection of two straight lines
One focus, two pairs of vertex angles
N=2*C(4,2)=12
12

If A1, A2, A3 and A4 are used to represent the number of triangles in figure 1.2.3.4, then A1 = 3, A2 = 8, A3 = 15, and the relationship between A10 and A9

a1=3 a2=8,a3=15,a4=24
5 7 9 bn=5+(n-1)*2=2n+3
a(n+1)-an=bn=2n+3
a(n+1)-(n+1)^2+y(n+1)=an-n^2+y*n
y=-2
an=n^2+2n
a10=120
a9=81+18=99
a10-a9=21

If the vectors A1, A2,..., am are linearly independent, we prove that a1-a2, a2-a3.am-1-am, am al are linearly related

The sum of these vectors is equal to 0, which has nothing to do with whether A1, A2,..., am are linear or not

As shown in the figure, how many pairs of vertex angles are there when three straight lines intersect each other? How many pairs of complements? How many pairs of apposition angles? How many pairs of wrong angles? How many pairs of inner corners on the same side?

There are 6 pairs of vertex angle, 12 pairs of complementary angle, 12 pairs of apposition angle, 6 pairs of internal stagger angle and 6 pairs of internal angle

What are antiparietal angle, appositive angle, internal stagger angle and internal angle of the same side?

Opposite vertex angle: two sides of an angle are opposite extension lines of the other angle. These two angles are opposite vertex angle. After two lines intersect, there is only one common vertex and two sides of the two angles are opposite extension lines. Such two angles are called opposite vertex angle. Two lines intersect to form two opposite vertex angles

What is opposite vertex angle? What kind of angle does it refer to? What is apposition angle? Internal angle of the same side? Internal stagger angle?
What is opposite vertex angle? What kind of angle does it refer to? What is apposition angle? Internal angle of the same side? Internal stagger angle. Please explain!
There's a reward of 900. There's a lot more

Don't you know if you can see clearly? 1 & nbsp; 2 as long as it's two intersecting straight lines, then the two nonadjacent corners of the four corners must be intersecting straight lines. 2 & nbsp; 4 is a & nbsp; stagger angle & nbsp; 2 & nbsp; 3 is the same angle & nbsp; 2 and the right corner of 4 is

The radius of the inscribed sphere of the frustum is r, and the ratio of the total area of the frustum to the sphere area is 21 / 8?

The longitudinal section of the frustum is first drawn as pi = R1 + R2, the height of frustum 2R is (r2-r1) ^ 2 + (2R) ^ 2 = (R1 + R2) ^ 2 ← (R ^ 2 = R1 * R2), the total area of frustum = pi (R1 + R2) ^ 2, the spherical area = 4Pi * R ^ 2, the ratio of the total area to the spherical area of frustum 2R is 21 / 8, so 2 (R1 + R2) ^ 2 = 21R ^ 2 ← solving the above two equations can get a little