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Line 38: − + − + − + − − Newton originally wrote this as − :<math>\Sigma \vec F = \frac{d \vec p}{dt}</math> − where <math>\vec p</math> is the [[momentum]] of the object. Momentum is defined as mass times velocity, <math> \vec p = m \vec{v}</math> This formulation is more general. It reduces to <math>\vec F = m \vec{a}</math> when the object has a constant mass. − − +
Classical mechanics (view source)
Revision as of 15:22, December 17, 2016
, 15:22, December 17, 2016removed repetition caused by my earlier edit
:<math>\vec{p}</math> is the [[momentum (physics)|momentum]] of the object
:<math>\vec{p}</math> is the [[momentum (physics)|momentum]] of the object
If the mass of the object in question is constant, Newton's second law may be rewritten in the more familiar form of:
Momentum is defined as the product of mass and velocity, <math> \vec{p} = m \vec{v}</math>. If the mass of the object in question is constant, then substituting if for the momentum we find Newton's second law may be rewritten in the more familiar form of:
<math>\Sigma \vec F = m \vec a</math>
<math>\Sigma \vec F = m \vec a</math>
where
where
:<math>m</math> is the mass of the object
:<math>m</math> is the [[mass (science)|mass]] of the object
:<math>\vec a</math> is the acceleration of the object
:<math>\vec a</math> is the [[acceleration]] of the object
This law also applies to a system of objects.
This law also applies to a system of objects.
At first sight it seems that Newton’s first law is redundant, in the sense that it is a special case of the second law: If the force is zero, acceleration is zero, and hence the object moves at a constant velocity. However, the two laws are not redundant. The purpose of Newton’s first law is to define what an inertial reference frame is. Once defined, we can formulate Newton’s second law which is only valid on inertial reference frame.
At first sight it seems that Newton’s first law is redundant, in the sense that it is a special case of the second law: If the force is zero, acceleration is zero, and hence the object moves at a constant velocity. However, the two laws are not redundant. The purpose of Newton’s first law is to define what an inertial reference frame is. Once defined, we can formulate Newton’s second law which is only valid on inertial reference frame.
'''3. For every action, there is an equal and opposite reaction.'''
'''3. For every action, there is an equal and opposite reaction.'''
If object A exerts a force on object B, object B will exert a force equal in magnitude and opposite in direction on object A. For example, if the earth pulls you down with a force of 1500 Newtons, you pull up on the earth with a force of 1500 Newtons. (Of course, since <math>\vec F = m \vec{a}</math>, and the earth's mass is much greater than yours, the earth accelerates much less than you do.)
If object A exerts a force on object B, object B will exert a force equal in magnitude and opposite in direction on object A. For example, if the earth pulls you down with a force of 1500 Newtons, you pull up on the earth with a force of 1500 Newtons. (Of course, since <math>\vec F = m \vec{a}</math>, and the earth's mass is much greater than yours, the earth accelerates much less than you do.)
== Angular Kinematics ==
== Angular Kinematics ==