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If Newton II is defined as ##\sum F = \dot{p}## and ##p = mv##, why do we consider Newton I as a separate law for cases where ##\sum F = 0##? Is Newton I really independent of Newton II?
Newton's first law is spelt out to repudiate the Aristotelian position that objects will naturally come to rest. With that out the way, Newton's 2nd law explains how they actually behave.vco said:If Newton II is defined as ##\sum F = \dot{p}## and ##p = mv##, why do we consider Newton I as a separate law for cases where ##\sum F = 0##? Is Newton I really independent of Newton II?
So there is no strict reason we couldn't state that there are only 2 laws of motion instead of 3?Michael Price said:Newton's first law is spelt out to repudiate the Aristotelian position that objects will naturally come to rest. With that out the way, Newton's 2nd law explains how they actually behave.
Often the first law is considered a definition of inertial reference frames and the second law is considered a definition of forces.vco said:If Newton II is defined as ##\sum F = \dot{p}## and ##p = mv##, why do we consider Newton I as a separate law for cases where ##\sum F = 0##? Is Newton I really independent of Newton II?
That makes sense, but I don't see why we couldn't attribute both of these definitions to the second law.Dale said:Often the first law is considered a definition of inertial reference frames and the second law is considered a definition of forces.
The second law only holds in a reference frame where the first law holds.vco said:That makes sense, but I don't see why we couldn't attribute both of these definitions to the second law.
Hmm, maybe it is possible, but I don’t see an obvious way (and I haven’t seen anyone do something like that). You need to define an inertial frame (so that acceleration is defined) and force.vco said:That makes sense, but I don't see why we couldn't attribute both of these definitions to the second law.
I don’t know how without an independent definition of either an inertial frame (needed to define acceleration) or force.kent davidge said:I think the second law implies the first, but the converse is not true.
Yes, Newton's first law and second law are two independent principles of classical mechanics that describe the motion of objects. They are not dependent on each other and can be applied separately to different situations.
Newton's first law states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. This is also known as the law of inertia.
Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This can be written as the formula F=ma, where F is force, m is mass, and a is acceleration.
While they are two separate laws, they are related in that Newton's first law can be seen as a special case of his second law. When there is no net force acting on an object (F=0), the acceleration will also be 0, meaning the object will remain at rest or in uniform motion.
Yes, Newton's laws of motion are still valid and widely used in modern physics and engineering. They are considered fundamental principles of classical mechanics and have been extensively tested and supported by evidence.