Newton's Laws of Motion by Owen Borville November 19, 2025
Dynamics is the study the causes of motion and of how forces affect the motion of objects in relation to the mass of the object. Kinematics only describes the motion of objects.
Force is a push or pull on an object and is a vector with magnitude and direction. External forces are any outside forces that act on an object or body. A free-body diagram is a drawing of all external forces acting on a body (object). The SI unit of force is the newton (N).
Isaac Newton's (1643-1727) Laws of Motion: 1st Law of Motion: states that a body at rest remains at rest, or if in motion, remains in motion at a constant velocity unless acted on by a net external force (a cause). (1st Law of Motion is also the law of inertia).
Inertia is the tendency of an object to remain at rest or remain in motion. Inertia is related to an object's mass. Mass is the quantity of matter in a substance. If the object's velocity is constant relative to a given frame, the frame is inertial. Newton's first law is valid for an inertial reference frame.
Equilibrium is achieved when the forces on a system are balanced.
A net force of zero means that an object is either at rest or moving with a constant velocity (not accelerating).
Acceleration, (a), is the change in velocity, its magnitude, direction, or both. An external force is a force acting on a system from outside the system. Internal forces act between components within the system.
Newton's second law of motion states that the acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass.
2nd Law of Motion equation: a = Fnet/m, or Fnet = ma (mass times the acceleration).
Newton's second law can also describe net force as the instantaneous rate of change of momentum and therefore, a net external force causes nonzero acceleration.
Fnet (vector) = dp/dt, p = momentum.
The weight (w) of an object is defined as the force of gravity or net force acting on an object of mass m. The object experiences an acceleration due to gravity (g): w = mg (vector).
If gravity is the only force acting on an object, the object is in free fall. Some upward resistance force from the air acts on all falling objects on Earth, so objects in free fall can never truly be in free fall.
Friction is a force that opposes the motion past each other of objects that are touching and causes an object to slow down. Friction forces are experienced by objects moving (or tendency to move) parallel to the interface opposing the motion.
The force in a spring obeys Hooke's law, so that its magnitude is proportional to the displacement and has a sense in the opposite direction of the displacement.
F (vector)= -kx
Real forces have a physical origin, whereas fictitious forces occur because the observer is in an accelerating or non-inertial frame of reference.
Newton's Third Law of Motion is the basic symmetry in nature and states that whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction to the force that the first body exerts.
F(AB) (vector) = -F(BA)
Two equal and opposite forces do not cancel because they act on different systems.
A thrust is a rection force that pushes a body forward in response to a backward force. Rockets, airplanes, cars, and thrust faults of rock are pushed forward by a thrust reaction force. Action-reaction pairs include swimmers pushing off a wall, helicopters creating lift by pushing air down, large scale atmospheric circulation patterns like a Hadley cell (warm air rising while cool air is pushed downward), and an octopus propelling itself forward by ejecting water from its body.
Normal force (N) is the force applied by a surface to an object in contact with the surface or resting on it; the force perpendicular to and away from the surface. When objects rest on a non-accelerating horizontal surface, the magnitude of the normal force is equal to the weight of the object. N = mg(vector)
When objects rest on an inclined plane that makes an angle (θ) with the horizontal surface, the weight of the object can be resolved into components that act perpendicular and parallel to the surface of the plane. These components can be calculated using:
w∥ = wsin(θ) = mgsin (θ)
w⟂ = wcos(θ) = mgcos (θ)
Tension (T) is the pulling force that acts along a stretched flexible connector, such as a rope or cable. When a rope supports the weight of an object that is at rest, the tension in the rope is equal to the weight of the object: T (vector)= w = mg If the object is accelerating, tension is greater than weight. If the object is accelerating opposite to the motion, tension is less than weight.
Application of Newton's Laws: Some applications of Newton's laws have multiple force vectors in different directions on an object. Fnet = ma or Fnet = 0.
Fnet (vector) = ∑F = F1 + F2 +.....
The normal force is not always equal in magnitude to the weight of the object. If the object is accelerating, the normal force will be less or greater than the weight of the object. An object on an inclined plane has a normal force that is always less than the full weight of the object.
Dynamics is the study the causes of motion and of how forces affect the motion of objects in relation to the mass of the object. Kinematics only describes the motion of objects.
Force is a push or pull on an object and is a vector with magnitude and direction. External forces are any outside forces that act on an object or body. A free-body diagram is a drawing of all external forces acting on a body (object). The SI unit of force is the newton (N).
Isaac Newton's (1643-1727) Laws of Motion: 1st Law of Motion: states that a body at rest remains at rest, or if in motion, remains in motion at a constant velocity unless acted on by a net external force (a cause). (1st Law of Motion is also the law of inertia).
Inertia is the tendency of an object to remain at rest or remain in motion. Inertia is related to an object's mass. Mass is the quantity of matter in a substance. If the object's velocity is constant relative to a given frame, the frame is inertial. Newton's first law is valid for an inertial reference frame.
Equilibrium is achieved when the forces on a system are balanced.
A net force of zero means that an object is either at rest or moving with a constant velocity (not accelerating).
Acceleration, (a), is the change in velocity, its magnitude, direction, or both. An external force is a force acting on a system from outside the system. Internal forces act between components within the system.
Newton's second law of motion states that the acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass.
2nd Law of Motion equation: a = Fnet/m, or Fnet = ma (mass times the acceleration).
Newton's second law can also describe net force as the instantaneous rate of change of momentum and therefore, a net external force causes nonzero acceleration.
Fnet (vector) = dp/dt, p = momentum.
The weight (w) of an object is defined as the force of gravity or net force acting on an object of mass m. The object experiences an acceleration due to gravity (g): w = mg (vector).
If gravity is the only force acting on an object, the object is in free fall. Some upward resistance force from the air acts on all falling objects on Earth, so objects in free fall can never truly be in free fall.
Friction is a force that opposes the motion past each other of objects that are touching and causes an object to slow down. Friction forces are experienced by objects moving (or tendency to move) parallel to the interface opposing the motion.
The force in a spring obeys Hooke's law, so that its magnitude is proportional to the displacement and has a sense in the opposite direction of the displacement.
F (vector)= -kx
Real forces have a physical origin, whereas fictitious forces occur because the observer is in an accelerating or non-inertial frame of reference.
Newton's Third Law of Motion is the basic symmetry in nature and states that whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction to the force that the first body exerts.
F(AB) (vector) = -F(BA)
Two equal and opposite forces do not cancel because they act on different systems.
A thrust is a rection force that pushes a body forward in response to a backward force. Rockets, airplanes, cars, and thrust faults of rock are pushed forward by a thrust reaction force. Action-reaction pairs include swimmers pushing off a wall, helicopters creating lift by pushing air down, large scale atmospheric circulation patterns like a Hadley cell (warm air rising while cool air is pushed downward), and an octopus propelling itself forward by ejecting water from its body.
Normal force (N) is the force applied by a surface to an object in contact with the surface or resting on it; the force perpendicular to and away from the surface. When objects rest on a non-accelerating horizontal surface, the magnitude of the normal force is equal to the weight of the object. N = mg(vector)
When objects rest on an inclined plane that makes an angle (θ) with the horizontal surface, the weight of the object can be resolved into components that act perpendicular and parallel to the surface of the plane. These components can be calculated using:
w∥ = wsin(θ) = mgsin (θ)
w⟂ = wcos(θ) = mgcos (θ)
Tension (T) is the pulling force that acts along a stretched flexible connector, such as a rope or cable. When a rope supports the weight of an object that is at rest, the tension in the rope is equal to the weight of the object: T (vector)= w = mg If the object is accelerating, tension is greater than weight. If the object is accelerating opposite to the motion, tension is less than weight.
Application of Newton's Laws: Some applications of Newton's laws have multiple force vectors in different directions on an object. Fnet = ma or Fnet = 0.
Fnet (vector) = ∑F = F1 + F2 +.....
The normal force is not always equal in magnitude to the weight of the object. If the object is accelerating, the normal force will be less or greater than the weight of the object. An object on an inclined plane has a normal force that is always less than the full weight of the object.
