Delhi University - PHYSICS-C II: MECHANICS - Inertial Frames

 

Delhi University

PHYSICS-C II: MECHANICS

(Credits: Theory-04, Practicals-02)

Syllabus :

Fundamentals of Dynamics: Inertial frames; Review of Newton’s Laws of Motion. Momentum of variable mass system: motion of rocket. Dynamics of a system of particles. Principle of conservation of momentum. Impulse. Determination of Centre of Mass of discrete and continuous objects having cylindrical and spherical symmetry (1-D, 2-D & 3-D).

Inertial frames:

In physics, an inertial frame of reference, often referred to as an "inertial frame," is a specific coordinate system in which Newton's first law of motion holds true. Newton's first law states that an object at rest will remain at rest, and an object in motion will continue to move with a constant velocity, unless acted upon by a net external force.

 

For an observer within an inertial frame, it seems as though there are no forces acting on an object when it is at rest or moving at a constant velocity. In other words, objects in an inertial frame do not experience any acceleration in the absence of external forces.

 

Key characteristics of inertial frames include:

1.   Constant Velocity: Objects in an inertial frame move with a constant velocity unless acted upon by a force.

2.   Newton's First Law: Newton's first law is satisfied in inertial frames. This law provides the foundation for defining inertial frames.

3.   No Net Forces: In the absence of external forces, the sum of forces acting on an object in an inertial frame is zero.

 

It's important to note that not all coordinate systems are inertial frames. Accelerated frames or frames experiencing non-zero net forces are non-inertial. Understanding inertial frames is crucial for accurately describing and predicting the motion of objects, as Newtonian mechanics is most directly applicable in inertial frames. The concept of inertial frames is a fundamental building block in classical mechanics and lays the groundwork for more advanced topics in physics, such as relativity.

1.    What is an inertial frame of reference?

• An inertial frame of reference is a specific coordinate system in which an observer experiences Newton's first law of motion. In simpler terms, it is a frame in which an object either remains at rest or moves at a constant velocity unless acted upon by a net external force.
1. Explain the key characteristics that define an inertial frame.
• The key characteristics of an inertial frame include:
• Objects in the frame move with a constant velocity in the absence of external forces.
• Newton's first law is satisfied, meaning objects at rest remain at rest, and objects in motion continue at a constant velocity unless acted upon by a net force.
• The sum of forces acting on an object is zero in the absence of external forces.
2. How does Newton's first law of motion relate to inertial frames?
• Newton's first law states that an object at rest will stay at rest, and an object in motion will continue to move with a constant velocity unless acted upon by a net external force. In inertial frames, this law holds true, meaning that objects in these frames do not experience any acceleration in the absence of external forces.
3. Provide examples of situations that can be considered inertial frames.
• Examples of inertial frames include a car moving at a constant speed on a straight highway, a spaceship drifting through deep space without any thrusters firing, or a laboratory on Earth's surface when considering motion over short time intervals.

 

5. Can a car accelerating on a highway be considered an inertial frame? Why or why not?
• No, a car accelerating on a highway cannot be considered an inertial frame. Acceleration implies the presence of a net force, and inertial frames are characterized by the absence of net forces. In this scenario, the passengers in the accelerating car would feel a force pushing them backward (in the direction opposite to acceleration), indicating that the frame is non-inertial.

 

6. Explain why the surface of the Earth is approximately an inertial frame.
• The surface of the Earth is approximately an inertial frame over short time intervals because the Earth's rotation and orbital motion do not cause noticeable effects on objects' motion within the frame over such brief periods. The gravitational force is the primary force acting, and it is treated as a constant force on the Earth's surface.

 

7. How does the concept of inertial frames relate to Newton's laws of motion?
• Newton's laws of motion are most directly applicable in inertial frames. The first law establishes the concept of inertial frames, and the second law (F = ma) is formulated with respect to inertial frames. In these frames, the equations describing motion are simpler and more straightforward.