**Inertial and Noninertial Frames of Reference**

**Inertial Frame of Reference:**
An inertial frame of reference is a coordinate system in which Newton's laws of motion hold true without the influence of any external forces. In other words, an inertial frame is a frame that is at rest or moving with a constant velocity relative to the absolute space.

**Examples:**
1. A car moving on a straight road with constant speed: Consider a car moving along a straight road at a constant speed. From the perspective of an observer inside the car, the car appears to be at rest. This is because the observer is also moving with the same velocity as the car. In this case, the car's frame of reference is inertial.

2. A ball rolling on a frictionless surface: Imagine a ball rolling on a perfectly smooth and frictionless surface. In the absence of any external forces, the ball will continue to roll at a constant velocity in a straight line. From the perspective of an observer watching the ball, the ball's frame of reference is inertial.

3. A satellite orbiting the Earth: Consider a satellite orbiting the Earth in space. In the absence of any external forces, the satellite will continue to move in a circular path around the Earth at a constant speed. From the perspective of an observer on the satellite, the satellite's frame of reference is inertial.

**Noninertial Frame of Reference:**
A noninertial frame of reference is a coordinate system that is accelerating or rotating relative to an inertial frame. In a noninertial frame, Newton's laws of motion do not hold true, and additional pseudo or fictitious forces need to be introduced to explain the observed motion.

**Examples:**
1. An elevator accelerating upward: Imagine standing in an elevator that is accelerating upward. From the perspective of an observer inside the elevator, they will feel a force pushing them downwards. This is known as the pseudo or fictitious force, which is introduced to explain the apparent weight of objects in the elevator. In this case, the elevator's frame of reference is noninertial.

2. A car taking a sharp turn: Consider a car taking a sharp turn to the right. From the perspective of an observer inside the car, they will feel a force pushing them towards the left. This is the centrifugal force, which is introduced to explain the apparent outward force experienced in the turning car. In this case, the car's frame of reference is noninertial.

3. A merry-go-round rotating: Imagine a person sitting on a rotating merry-go-round. From the perspective of the person, they will feel a centrifugal force pushing them outward, away from the center of rotation. This force is introduced to explain the apparent outward force experienced by the person on the rotating merry-go-round. In this case, the merry-go-round's frame of reference is noninertial.

In summary, inertial frames of reference are those in which Newton's laws of motion hold true without any external forces, whereas noninertial frames of reference are accelerating or rotating frames where additional pseudo or fictitious forces need to be considered to explain the observed motion.

An inertial frame of reference in classical physics and special relativity is a frame of reference in which a body with zero net force acting upon it is not accelerating; that is, such a body is at rest or it is moving at a constant speed in a straight line. ex-train moving with constant velocity.
A non-inertial reference frame is a frame of reference that is undergoing acceleration with respect to an inertial frame. ... The laws of motion in non-inertial frames do not take the simple form they do in inertial frames, and the laws vary from frame to frame depending on the acceleration.ex- A rotating merry-go-round,A turning car with constant speed, The rotating Earth