define the laws of motion
Answers
Definition of law of motion
1: a statement in dynamics: a body at rest remains at rest and a body in motion remains in uniform motion in a straight line unless acted upon by an external force
— called also Newton's first law of motion
2: a statement in dynamics: the acceleration of a body is directly proportional to the applied force and is in the direction of the straight line in which the force acts
— called also Newton's second law of motion
3: a statement in dynamics: for every force there is an equal and opposite force or reaction
— called also Newton's third law of motion
Explanation:
Newton's first law
See also: Inertia
The first law states that an object at rest will stay at rest, and an object in motion will stay in motion unless acted on by a net external force. Mathematically, this is equivalent to saying that if the net force on an object is zero, then the velocity of the object is constant.
{\displaystyle \sum \mathbf {F} =0\;\Leftrightarrow \;{\frac {\mathrm {d} \mathbf {v} }{\mathrm {d} t}}=0}{\displaystyle \sum \mathbf {F} =0\;\Leftrightarrow \;{\frac {\mathrm {d} \mathbf {v} }{\mathrm {d} t}}=0}
where:
{\displaystyle \mathbf {F} }\mathbf {F} is the net force being applied ({\textstyle \sum }{\textstyle \sum } is notation for summation),
{\displaystyle \mathbf {v} }\mathbf {v} is the velocity, and
{\textstyle {\frac {\mathrm {d} \mathbf {v} }{\mathrm {d} t}}}{\textstyle {\frac {\mathrm {d} \mathbf {v} }{\mathrm {d} t}}} is the derivative of {\displaystyle \mathbf {v} }\mathbf {v} with respect to time {\displaystyle t}t (also described as the acceleration.)
Newton's first law is often referred to as the principle of inertia.
Newton's first (and second) law is valid only in an inertial reference frame.[4]
Newton's second law
The second law states that the rate of change of momentum of a body over time is directly proportional to the force applied, and occurs in the same direction as the applied force.
{\displaystyle \mathbf {F} ={\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}}}{\displaystyle \mathbf {F} ={\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}}}
where {\displaystyle \mathbf {p} }\mathbf {p} is the momentum of the body.
Some textbooks use Newton's second law as a definition of force,[5][6][7] but this has been disparaged in other textbooks.[8]:12–1[9]:59
Constant Mass
For objects and systems with constant mass,[10][11][12] the second law can be re-stated in terms of an object's acceleration.
{\ of the body, and a is the body's acceleration. Thus, the net force applied to a body produces a proportional acceleration.
Variable-mass systems
Main article: Variable-mass system
Variable-mass systems, like a rocket burning fuel and ejecting spent gases, are not closed and cannot be directly treated by making mass a function of time in the second law;[11][12] The equation of motion for a body whose mass m varies with time by either ejecting or accreting mass is obtained by applying the second law to the entire, constant-mass system consisting of the body and its ejected or accreted mass; the result is[10 {d} t}
where u is the exhaust velocity of the escaping or incoming mass relative to the body. From this equation one can derive the equation of motion for a varying mass system, for example, the Tsiolkovsky rocket equation.
Under some conventions, the quantity on the left-hand side, which represents the advection of momentum, is defined as a force (the force exerted on the body by the changing mass, such as rocket exhaust) and is included in the quantity F. Then, by substituting the definition of acceleration, the equation becomes F = ma.
Newton's third law
An illustration of Newton's third law in which two skaters push against each other. The first skater on the left exerts a normal force N12 on the second skater directed towards the right, and the second skater exerts a normal force N21 on the first skater directed towards the left.
The magnitudes of both forces are equal, but they have opposite directions, as dictated by Newton's third law.
The third law states that all forces between two objects exist in equal magnitude and opposite direction: if one object A exerts a force FA on a second object B, then B simultaneously exerts a force FB on A, and the two forces are equal in magnitude and opposite in direction: FA = −FB.[13] The third law means that all forces are interactions between different bodies,[14][15] or different regions within one body, and thus that there is no such thing as a force that is not accompanied by an equal and opposite force. In some situations, the magnitude and direction of the forces are determined entirely by one of the two bodies, say Body A; the force exerted by Body A on Body B is called the "action", and the force exerted by Body B on Body A is called the "reaction". This law is sometimes referred to as the action-reaction law, with FA called the "action" and FB the "reaction". In other situations the magnitude and directions of the forces are determined jointly by both bodies and it isn't necessary to identify one force as the "action" and the other as the "reaction". The action and the reaction are simultaneous, and it does not matter which is called the action and which is called reaction; both forces are part of a single interaction, and neither force exists without the other.[13]