# Inertial and Uniformly Accelerated Frames of Reference

## Problems from IIT JEE

Problem (IIT JEE 1986): A reference frame attached to the earth,

1. is an inertial frame by definition.
2. cannot be inertial frame because the earth is revolving around the sun.
3. is an inertial frame because Newton's laws are applicable in this frame.
4. cannot be an inertial frame because the earth is rotating about its own axis.

Solution: The inertial frame is defined by Newton's first law of motion. Suppose there is a particle with no physical force (gravitational, electromagnetic, weak, or nuclear) acting on it. By Newton's first law, this particle is at 'rest' or in 'uniform motion'. But 'rest' or 'uniform motion' are defined w.r.t. a reference frame. The reference frame in which this particle is at 'rest' or in 'uniform motion' is called an inertial frame.

A frame having uniform motion w.r.t. another inertial frame is also inertial. An accelerating or rotating frame is non-inertial. Thus, the frame attached to the earth is non-inertial because this frame is rotating due to spinning of the earth about its axis as well as due to revolution of the earth around the sun. The readers are encouraged to find the angular velocity of this frame due to spinning and revolution of the earth. Hint: $\omega_\text{spin}=15\;\mathrm{deg/hr}$, $\omega_\text{revolution}=0.04\;\mathrm{deg/hr}$.