Question

We can show why we don’t have observable radial acceleration effects even though the Earth is

spinning and we can com

ment quickly on the tangential acceleration we experience.

a)

Specifically, show that Cleveland’s centripetal (i.e., radial) acceleration due to the earth’s

rotation is negligible in comparison with the acceleration we feel due to gravity.

Put your

answe

r in “gees” for a direct comparison.

b)

By the way, what is our angular acceleration in Cleveland? (Hoohah!) And therefore what

is our tangential acceleration?

Answer 1

Let the object be at lattitude , Then the tangential acceleration of the object is given by,

( is angular acceleration) (Here R_e is radius of the earth, is the angular velocity of rotation for earth).

And, the radial acceleration of the object is given by, (it is caused due to centripetal force)

In case of rotation the angular acceleration of earth is 0 since angular velocity of earth is constant, due to this the magnitude of tangential acceleration is 0 and negligible.

(a) For Cleveland the lattitude is 41.5 degrees. Therefore, the centripetal acceleration experienced is,

(The data for Radius and angular velocity is taken online)

As compared to the 9.81 m/s^2 ie. acceleration due to gravity you can see that how small the radial acceleration is.

(b) The angular acceleration at cleaveland is 0, there is no angular acceleration since earth is rotating at constant angular velocity, therefore there is no tangential acceleration component.