the earth has a radius of 6.38×10^16 meter and turns around once on its axis in 24 hour.what is the radial acceleration of perso

Question

3 years ago

12

n at the earth equator

1 answer:

Scrat [10] · Answer 1 · 2021-11-08T22:20:24+03:00

337493603.8m/s²

Explanation:

Radius of the earth = 6.38 x 10¹⁶m

time = 24hr (86400s)

Unknown:

Centripetal acceleration = ?

Solution:

The centripetal acceleration is directed inward to keep the body from falling off the surface of the earth.

centripetal acceleration = $\frac{v^{2} }{r}$

where v is the velocity and r is the radius

also;

v = wr

where w is the angular velocity

substituting in the equation for centripetal acceleration gives;

a = w²r

also w = $\frac{2 x pi}{T}$

therefore;

a = $\frac{4 \pi ^{2} r }{T^{2} }$

a = $\frac{ 4 x 3.142^{2} x 6.38 x 10^{16} }{86400^{2} }$

a = 337493603.8m/s²

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