Question

Difference between d alemberts principle and newtons 2nd law

Answer 1

Newtons second law of motion is basically applicable when the frame of reference is an inertial frame. Inertial frame is the frame of reference which is either is at rest or move with constant velocity. eg. of application of Newton’s second law is :- Suppose you are observing the bus moving in front of you while you are at rest or you are moving at a constant velocity.

D’Alembert principle is basically similar to the newtons second law but it differs at its application. it is applied when the frame of reference is not inertial, ie. frame of reference is accelerating.

for eg:- observing the bus when you are sitting in the bus and bus is accelerating.

So in short both the principle say same things but the difference is in their place of application, one is applied in inertial frame of reference and other is applicable in non inertial frame of reference.

Answer 2

The difference between D'Alembert's principle and Newton's 2nd law is that in Newton's 2nd law, force is given as $F=ma$ while in D'Alembert's principle, force is given as $F-ma=0$.

Explanation:

• The differences between D'Alembert's principle and Newton's 2nd law are given as:

   Newton's Second law:

• According to Newton's second law of motion, force is expressed as the product of mass and acceleration.
• It is represented mathematically by the formula:

        $F=ma$

• It is applied to dynamic problems.
• Acceleration is not zero in this case.

   D'Almebert's principle:

• According to D'Alembert's principle, the force plus the negative of the product of mass and acceleration is equal to zero.
• It is represented mathematically by the formula:

        $F-ma=0$

• Here, $-ma$ is called inertial pressure which given as $\[F* = - ma\]$. Therefore, $\[{F_{total}} = F + F* = 0\]$.
• It is used to convert dynamic problems into static ones.
• There are no accelerations in static problems.

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