Section Summary

4.1 Force

• Dynamics is the study of how forces affect the motion of objects and systems.
• Force is a push or pull that can be defined in terms of various standards. It is a vector and so has both magnitude and direction.
• External forces are any forces outside of a body that act on the body. A free-body diagram is a drawing of all external forces acting on a body.

4.2 Newton's First Law of Motion: Inertia

• Newton’s first law states that a body at rest remains at rest or, if moving, remains in motion in a straight line at a constant speed, unless acted on by a net external force. This law is also known as the law of inertia.
• Inertia is the tendency of an object at rest to remain at rest or, if moving, to remain in motion at constant velocity. Inertia is related to an object’s mass.
• Friction is a force that opposes motion and causes an object or system to slow down.
• Mass is the quantity of matter in a substance.

4.3 Newton's Second Law of Motion

• Acceleration is a change in velocity, meaning a change in speed, direction, or both.
• An external force acts on a system from outside the system, as opposed to internal forces, which 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 the system’s mass.
• In equation form, Newton’s second law of motion is $F_{\text{net}}=ma$ or $\text{Σ}\text{F}=m\text{a}\text{.}$ This is sometimes written as $a=\frac{F_{\text{net}}}{m}$ or $a=\frac{\text{Σ}F}{m}$ .
• The weight of an object of mass m is the force of gravity that acts on it. From Newton’s second law, weight is given by $\text{W}=m\text{g}\text{.}$
• If the only force acting on an object is its weight, then the object is in freefall.

4.4 Newton's Third Law of Motion

• Newton’s third law of motion states that when 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 it exerts.
• When an object rests on a surface, the surface applies a force on the object that opposes the weight of the object. This force acts perpendicular to the surface and is called the normal force.
• The pulling force that acts along a stretched flexible connector, such as a rope or cable, is called tension. When a rope supports the weight of an object at rest, the tension in the rope is equal to the weight of the object.
• Thrust is a force that pushes an object forward in response to the backward ejection of mass by the object. Rockets and airplanes are pushed forward by thrust.