Sorry for the messy handwriting but this is what I got
Answer:
.a = 849.05 m / s²
Explanation
The centripetal acceleration is
a = v² / r
Linear and angular velocity are related
v = w r
Angular velocity and frequency are related by
w = 2π f
Let's replace
a = w² r
a = 4π² f² r
Let's reduce to the SI system
f = 2.30 rev / s (2π rad / 1 rev) = 14.45 rad / s
.r = 10.3 cm = 0.103 m
Let's calculate
a = 4π² 14.45² 0.103
.a = 849.05 m / s²
Answer:
The Milky Way is about 1,000,000,000,000,000,000 km (about 100,000 light years or about 30 kpc) across. The Sun does not lie near the center of our Galaxy. It lies about 8 kpc from the center on what is known as the Orion Arm of the Milky Way