A reference frame attached to the earth

Step 1: Define the motion of the Earth.

The Earth undergoes both rotation about its own axis and revolution around the Sun.

$$\omega_{\text{rot}} = \text{angular velocity of rotation}$$ $$\omega_{\text{rev}} = \text{angular velocity of revolution}$$

Step 2: State the condition for an inertial frame.

An inertial frame must have zero acceleration.

$$\vec{a}_{\text{frame}} = 0$$

Step 3: Determine the acceleration due to rotation.

The rotation of the Earth about its axis produces a centripetal acceleration at its surface.

$$a_{\text{rot}} = \omega_{\text{rot}}^2 R$$

This acceleration causes a pseudo force to appear in the Earth's reference frame.

$$\vec{F}_{\text{cf}} = m \omega_{\text{rot}}^2 R$$

Step 4: Compare the effects of rotation and revolution.

The acceleration due to rotation is the dominant factor making the Earth a non-inertial frame.

$$a_{\text{rev}} \approx 0.006 \text{ m/s}^2$$ $$a_{\text{rot}} \gg a_{\text{rev}}$$

Answer: (4) It cannot be an inertial frame because the earth rotates about its own axis.