How many hours will be in a day if the radius of Earth increases by 70 m? I am little confused about the linear momentum and angular momentum, will the linear momentum of earth change due to changing of its radius or it will stay as it was and i know that the moment of inertia will increase and Can i treat with this rotation as Harmonic motion  
 A: Neither the linear momentum or the angular momentum will change (they are conserved quantities), unless you apply a force or a torque respectively.
In this case, the change in radius will likely change the moment of inertia. And as the (constant) angular momentum depends on the product of moment of inertia and angular velocity, then the angular velocity must also change.
If you assume that the radius change is homologous - that is, the whole earth is stretched outwards by a small factor, then the moment of inertia increases as the square of the radius, and the angular velocity decreases by a factor $(R+\Delta R)^2/ R^2$.
i.e
$$ k (R+\Delta R)^2 (\Omega - \Delta \Omega) = k R^2 \Omega,$$
where $k$ is some constant involving the mass of the Earth and both the LHS and RHS are the (constant) angular momentum of the Earth, after and before you make it bigger.
More complicated ways of changing the radius would give different results, as would adding mass to make the new radius.
Unless mass were added, then the linear momentum would be unchanged.
A: If we treat the Earth as an isolated system then both its linear and angular momenta will remain constant.
To answer your question you need only consider the angular momentum. The angular momentum is given by:
$$ L = I\omega $$
Since $L$ is a constant, if the moment of inertia changes from $I_1$ to $I_2$ then we have:
$$ I_1\omega_1 = I_2\omega_2 $$
and therefore:
$$ \omega_2 = \frac{I_1}{I_2}\omega_1 $$
Can you take it from here?
