Problem : Magnetic forces are often at least as powerful as gravitational forces. Consider a 5 kg piece of iron suspended in mid-air by a powerful magnet above the piece of iron. How much force does the magnet exert on the iron?

The iron does not move, implying a constant velocity (v = 0). Thus, by Newton's First Law, the sum of the forces on the iron must be zero. In this case, there are two forces acting upon the iron: the gravitational force of the earth, and the magnetic force of the magnet. Thus FG + GM = 0. We can calculate the gravitational force using the fact that the gravitational acceleration on earth is 9.8 m/s2: FG = ma = (5 kg)(9.8 m/s2) = 49 N, directed downward. the magnet must exert a force of 49 N in the upward direction.

Problem :

The earth rotates around the sun with a constant speed. Is the earth an inertial reference frame?

At first glance, the earth seems to be an inertial reference frame, as it retains constant speed. However, it does not retain constant velocity. Recall that velocity is a vector while speed is a scalar. Though the magnitude of the velocity remains constant, the direction changes. In fact, when we calculate the change in velocity through vector addition we see that Δv points in the exact direction of the gravitational force exerted on the earth by the sun, as expected by Newton's Second Law:

Solution 2
Since the earth has a constantly changing velocity, it experiences constant acceleration, and is not an inertial reference frame.