How to calculate the arc length and radius when the chord length and arch height are known

How to calculate the arc length and radius when the chord length and arch height are known

Given the chord length L. arch height h, how to calculate the arc length C. radius R. the center angle of the arc is A.R ^ 2 = (R-H) ^ 2 + (L / 2) ^ 2R ^ 2 = R ^ 2-2 * r * H + H ^ 2 + L ^ 2 / 42 * r * H = H ^ 2 + L ^ 2 / 4R = H / 2 + L ^ 2 / (8 * h) a = 2 * arc sin ((L / 2) / R) degree = 2 * (arc sin ((L / 2) / R)) * pi / 180 arc C = a * r

Known chord length 16 meters, radius and arc length

Given chord length L = 16m, arch height h = 2m, calculate radius R and arc length C?
The central angle of the arc is a
R^2=(R-H)^2+(L/2)^2
R^2=R^2-2*R*H+H^2+L^2/4
2*R*H=H^2+L^2/4
R=H/2+L^2/(8*H)
=2/2+16^2/(8*2)
=17 meters
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((16/2)/17)
=145 degrees
=56.145*PI/180
=0.979915 radians
C = R * a = 17 * 0.979915 = 16.659m

Given chord length 1600, arch height 354, calculate radius and arc length

Given chord length L = 1600 and arch height h = 354, calculate radius R and arc length C?
The central angle of the arc is a
R^2=(R-H)^2+(L/2)^2
R^2=R^2-2*R*H+H^2+L^2/4
2*R*H=H^2+L^2/4
R=H/2+L^2/(8*H)
=354/2+1600^2/(8*354)
=1080.95
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((1600/2)/1080.95)
=478 degrees
=95.478*PI/180
=1.6664 radians
C=A*R
=1.6664*1080.95
=18041.3
Radius r = 1080.95, arc length C = 18041.3

When two satellites A and B move around the earth in a circle, and the ratio of the period is ta: TB = 1:8, the ratio of the orbit radius to the velocity is ()
A. RA：RB=4：1     VA：VB=1：2B. RA：RB=4：1      VA：VB=2：1C. RA：RB=1：4     VA：VB=1：2D. RA：RB=1：4      VA：VB=2：1

According to the meaning of the topic, gravity provides the centripetal force of circular motion, gmmr2 = MR4 π 2t2 = mv2r, so we can know the radius of circular motion r = 3gmt24 π 2, so we can get the linear velocity v = GMR of RARB = 3 (TATB) 2 = 14 satellite, we can know the linear velocity vavb = rbra = 21, so ABC is wrong and D is correct

Is the acceleration of circular motion V ^ 2 △ r

The acceleration of uniform circular motion is
But if it's not uniform circular motion, it's not. You're talking about normal acceleration and tangential acceleration

Circular motion a
A is not = V / T
Why is it in circular motion
v^2/r

The definition of acceleration is a = LIM (△ V / △ T), △ t → 0, where a and △ V are vectors. Because the change of velocity is not necessarily consistent with the direction of velocity (such as circular motion), the direction of acceleration is not necessarily along the direction of velocity

To find the periodic formula of uniform circular motion
Forget, sweat

1. V (linear velocity) = L / T = 2 π R / T (L represents arc length, T represents time, R represents radius) 2, ω (angular velocity) = θ / T = 2 π / T (θ represents angle or radian) 3, t (period) = 2 π R / V = 2 π / ω 4, n (frequency) = 1 / t 5, ω = 2 π n 6, v = R ω 7, f (centripetal force) = Mr ω ^ 2 = MV ^ 2

An object moves in a circle of radius r at a uniform speed. The arc length of a circle t is 2 μ R (w = 2 μ g / T in the formula of angular velocity)
When an object moves in a circle with radius r at a uniform speed, the length of the arc that it turns in a cycle T is 2 μ R, (w = 2 μ g / T in the formula of angular velocity), why is the angle of rotation 2 μ? Is it not 360 degrees?
I'm talking about why the angle of turning is "two schools"

W = 2 Wu / T, the result is not angle, but angular velocity
Angle θ = L / (1 / 180 * π R)

Correlation formula of uniform circular motion
I don't understand the meaning of each symbol,

1. V (linear velocity) = L / T = 2 π R / T
2. ω (angular velocity) = θ (rotation angle) / T = 2 π / T
3、T=2πr/v=2π/ω
4、n=1/T
5、ω=2πn
6、v=rω
7. F centripetal force = Mr ω ^ 2 = MV ^ 2 / r = MR4 π ^ 2 / T ^ 2
8. A centripetal acceleration = R ω ^ 2 = V ^ 2 / r = R4 π ^ 2 / T ^ 2 = R4 π ^ 2n ^ 2
X ^ 2 is the square of X
You'd better look at the textbook. It's all on it

How to deduce the formula of uniform circular motion
A how?

First write the expression of centripetal force F = MV ^ 2 / R
From Newton's second law f = ma
By combining the above two formulas, we can get Ma = MV ^ 2 / R and eliminate m, thus we can get a = V ^ 2 / R
It's much simpler than the book