Newton’s laws of motion -- Does the 1st Law presuppose the 2nd Law?

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Homework Statement
Is Newton‘s first law of motion necessary supposing that we already know that Newton‘s second law of motion is valid?
Relevant Equations
None
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Is this a homework question? If so, tell us what you think before you can receive help.
 
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feesicksman said:
Homework Statement: Is Newton‘s first law of motion necessary supposing that we already know that Newton‘s second law of motion is valid?
Good question!
 
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Consider a mass at the end of a string moving in a circle at constant speed on a horizontal frictionless plane. At some point the string is cut. After the string is cut, the second law says$$0 = 0$$ which is not very useful for describing the motion of the mass.
 
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Related to Newton’s laws of motion -- Does the 1st Law presuppose the 2nd Law?

Does Newton's First Law presuppose the Second Law?

Newton's First Law, often called the Law of Inertia, describes the behavior of objects when no forces are acting upon them. The Second Law provides a quantitative measure of how forces affect motion. While the First Law can be seen as a special case of the Second Law where the net force is zero, it does not presuppose it. Instead, both laws work together to describe different aspects of motion.

What is Newton's First Law of Motion?

Newton's First Law of Motion states that an object at rest will remain at rest, and an object in motion will continue in its motion at a constant velocity, unless acted upon by a net external force. This law is also known as the Law of Inertia.

What is Newton's Second Law of Motion?

Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass. This law is often summarized by the formula F = ma, where F is the net force, m is the mass, and a is the acceleration.

How do Newton's First and Second Laws relate to each other?

Newton's First Law can be considered a special case of the Second Law where the net force is zero. The First Law describes the behavior of objects in the absence of external forces, while the Second Law quantifies the relationship between force, mass, and acceleration. Together, they provide a comprehensive framework for understanding motion.

Can Newton's First Law be derived from the Second Law?

Yes, Newton's First Law can be derived from the Second Law. If we set the net force (F) to zero in the Second Law equation (F = ma), we get a = 0, which means there is no acceleration. Thus, an object will maintain its state of rest or uniform motion, which is exactly what the First Law states.

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