**Please show procedure** You are standing on the ground on the Earth at point o

Question

**Please show procedure**

You are standing on the ground on the Earth at point on the Equator. As the Earth turns you undergo uniform circular motion, the radius of the circle is RE=6370km. There are two forces acting on you, the normal force of the ground and the gravitational force.

a. Write the equation for Newton's second law that describes your motion. Be sure to include both forces stated above.

b. Write the equaion in terms of the angular speed of the Earth (w)

c. How fasr does the Earth need to turn for your apparent weight to vanish? (Hint: solve the equation for the condition where the normal force goes to zero.) Express answer in revolutions/day.

Explanation / Answer

here,

Re = 6.37 * 10^6 m

let the angular speed of the earth be w

and normal force be N

(a)

using newton's seccond equation

m*a = m*g - N

where a is the accelration

(b)

centripital accelration , ac= w^2*r

then the equation is

m*w^2*r = m*g - N

(c)

for apparanet wight to vanish

N = 0

m*w^2*r = m*g

w^2 * 6.37 * 10^6 = 9.8

w = 1.24 * 10^-3 rad/s

w = 17.05 rad/s

the angular speed is 17.05 rad/s

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