## Sunday, August 31, 2008

### Newton’s Laws of Motion - Study Plan - Session - 1

5.1 First law of motion (From HC Verma Part 1)

Study Plan

Day 1

5.1 First law of motion
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Points to be remembered

First law of motion

If the (vector) sum of all the forces acting on a particle is zero then and only then the particle remains unaccelerated (i.e., remains at rest or moves with constant velocity).

We can say in vector notation
a = 0 if and only if resultant force F = 0

A frame of reference in which Newton's first law is valid is called an inertial frame of reference.

A frame of reference in which Newton's first law is not valid is called a noninertial frame of reference. (Example: lamp in an elevator cabin whose cable had broken)

Example of lamp in an elevator whose cable had broken:

In the cabin when one measures with reference to the cabin, the lamp hanging from the ceiling has no acceleration. Hence the forces acting on the lamp, its weight (W) and the tension in the string supporting it are balancing each other. We can infer that W = T.

But for an observer on the ground, lamp is accelerating with acceleration g, when he considers the forces acting on the lamp as W and T once again, W is not equal to T as lamp is acceleating. Both cannot be right at the same time, and it means in one of the frames Newton's first law is not applicable.

Inertial frame: Hence inertial frame is a frame of reference in which Newton's first law is valid.

Is earth an inertial frame of reference?
Strictly it is not. But as a good approximation, earth can be taken as an inertial frame of reference.

All frames moving uniformly with respect to an inertial frame are themselves inertial.

This relation was derived from the relation that converts acceleration with respect to one frame into acceleration with respect to another frame. When the other frame is moving with uniform velocity it acceleration with respect to the frame in reference is zero.

Examples: A train moving with uniform velocity with respect to ground, a plane flying with uniform velocity with respect to a high etc. The sum of forces acting on a suit case kept on the shelves of them with turnout to be zero.

Concepts covered in the session

First law of motion
Frames of reference (concept from Chapter 3)
Inertial frame of reference
noninertial frame of reference
Inertial frames other than earth (frames moving with uniform velocity w.r.t earth)

Example 5.1 deals with forces acting on heavy particle hanging from a string fixed with the roof. the particle is stationery. The forces acting are pull of the earth downward due to gravity and pull of the string vertically upward.

Go through examples in worked out examples

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2.

Attempt questions in Objective questions (OBJ I)

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5.

Attempt questions in Objective questions (OBJ II)

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2.
3.