How does the radius vary with the velocity^2, directly or indirectly? What leads

Question

How does the radius vary with the velocity^2, directly or indirectly? What leads you to this conclusion? How does the centripetal force vary with the velocity^2, directly or indirectly? What leads you to this conclusion? How does the mass vary with the velocity^2, directly or indirectly? What leads you to this conclusion? What is the given equation for F_c? Do your results verify this relationship? What leads you to this conclusion? The Earth's radius is roughly 6371 km. What is the centripetal acceleration experienced by a person standing on the equator due to the Earth's rotation? (Answer in SI units)

Explanation / Answer

here,

Centripital force,
Fc = m*v^2/r --------------------(1)
Fc = m*a -------------------------(2)

Where,
a = Centripital Acceleration
m = mass
v = Velocity
r = Radius of Path

Part 1:
Velocity, V^2 is directly proportional to radius of path.
From Eqn 1
V^2 = F*r/m ----------------(3)

Part 2:
From eqn 1 Fc is directly proportional to v^2.

Part 3:
from eqn 3, v^2 is indirectly proportional to m.

Part 4:
Fc = mv^2/r

Fc = m*a

Part 5 :

Angular velocity of earth, w = 7.292*10^-5 rad/s

Since Linear Velocity, v = w*r

so, a = v^2/r
a = w^2*r^2/r
a = w^2*r
a = (7.292*10^-5)^2 * (6371*10^3)
a = 0.034 m/s^2

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