How to deduce the centripetal acceleration formula?

First draw (a sector)
In DT time, the magnitude of V remains unchanged, and its direction change angle = displacement radian D θ
DV = V-V '(vector subtraction) = VD θ (D θ is infinitesimal, arc length is about chord length)
a=dv/dt
=vdθ/dt
=wv
=w^2*r=v^2/rv

Is there something wrong with the centripetal acceleration formula
I know how to deduce the centripetal acceleration formula, but after learning trigonometric function, the problem comes out. It is obtained by using the ratio of arc length and velocity difference equal to the ratio of velocity and radius, and by using the differential method, the arc length is approximately equal to the chord length. However, we can use trigonometric function a ^ 2 = B ^ 2 + C ^ 2-2bccosa to get chord length directly and work out another formula. Why use differential method to work out inaccurate value?

No problem. This is based on calculus. If you want to study physics in the future, it will be mentioned in mechanics
The amount of knowledge is not the same

Expression of centripetal acceleration
an= = = = =

The expression of centripetal acceleration an = V ^ 2 / r = ω ^ 2R = (2 π / T) ^ 2R = V ω = (2 π f) ^ 2R

How many formulas are there for centripetal acceleration?

From Newton's second law
A (direction) = f (direction) / M
A (direction) = V ^ 2 / r = ω ^ 2R = ω v = (2 π / T) ^ 2 * r = (2 π f) ^ 2 * r

Which formula is better for two questions
1. It is known that the temperature of the air in the container is 40 ℃ and the pressure is 8000pa. At this time, the volume of compressed air in the container is one-fifth of the original volume, and the pressure is 425000pa
Find the temperature of the air at this time
2. The limit positive space is 1.00 * 10 to the power of - 18. Let the temperature be 20 ℃
Find the average number of molecules in 1cm and 179; air under this vacuum

1. PV = NRT (n is the amount of gas substance, which remains unchanged in the question; R is the gas constant, 8.314j / (mol * k))
2. PV = NRT (n is the amount of gas substance, converted to the number of molecules, 1mol = 6.02 * (10 ^ 23))

It's not hard. I just forgot the formula,
In a 100 meter deep mine, the accumulated water is 9 cubic meters per minute. In order not to let the water stay in the mine, how much power pump should be used to pump water?
A pump, with a flow rate of 300 cubic meters per hour, can pump water to a maximum height of 18m, a speed of 1500r / min, an efficiency of 80%, and a weight of 12kg
What kind of motor can drive it to work normally

1：P=FS F=pvg=1000*(9/60)*10=1500N s=100m
P = 150 kw
In fact, the work needed to deliver 0.15 cubic meters of water to 100 meters per second is power
2: I don't quite understand this. What do you want to do with speed and weight? If not, it's the same as the above question, but it needs to be divided by 80%

What are the formulas for efficiency and power

Efficiency and power are two different concepts
Efficiency = output power / input power x 100%
Power refers to the ability to do work per unit time. DC power = uxi, AC power = UXIX power factor

Physical formula, ratio formula, definition formula and determination formula are different and meaningful

The ratio formula is the ratio of two physical quantities. It is a big concept. The definition formula is the formula that defines the physical quantity. The determination formula is the formula that determines the physical quantity. There is no obvious boundary between the two. Just like Ohm's law, it is the definition formula of resistance and the determination formula of current. They are all ratio formulas

How many formulas are there in terms of physical free fall?

h=1/2gt^2
There is only one formula
The rest is moving in a straight line with constant velocity. Change the displacement x to h; change the acceleration a to G; and remember that the exit velocity of the free falling body is 0
All the formulas come out
The free falling body is only a uniformly accelerated linear motion with initial velocity of 0 and acceleration of G

What is the meaning of free falling motion formula?
What is the general value of G

g=9.8
Acceleration of a 1 kg object falling

How to deduce the centripetal acceleration formula?